Action in Ecosystems Biothermodynamics for Sustainability

Action in Ecosystems: Biothermodynamics for Sustainability

RESEARCH STUDIES IN BOTANY AND RELATED APPLIED FIELDS Series Editor: Dr P. S. Nutman FRS 14. Carbon Dioxide and Plant Responses D R Murray 15. Action in Ecosystems: Biothermodynamics for Sustainability I R Kennedy

Action in Ecosystems: Biothermodynamics for Sustainability By

Ivan Robert Kennedy University of Sydney, Australia

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Library of Congress Cataloging-in-Publication Data Kennedy, I. R. (Ivan Robert) 1938 – Action in ecosystems : biothermodynamics for sustainability / by Ivan Robert Kennedy. p. cm. – (Research studies in botany and related fields ; 15) Includes bibliographical references (p.) ISBN 0-86380-232 1. Thermodynamics. 2. Biophysics. 3. Action theory. 4. Unified field theories. I. Title. II. Series QP517.T48 K46 2000 571.4—dc21

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.

ISBN 0 86380 232 X Printed in Great Britain by SRP Ltd., Exeter

00-042513

Foreword by Rodney Roughley Formerly Principal Scientific Officer, Rothamsted Experimental Station, UK Formerly Principal Research Scientist, NSW Dept. of Agriculture, Australia Hon. Research Associate of The University of Sydney, Australia Most browsers in a bookshop who pick up a book with a title similar to that of the present book are likely to be either trained in science or be interested scientific laypeople. The approach they would find in this book, which discusses physics, chemistry and biology as one, is almost certain to differ from their formal training, particularly if that were some time ago. Perhaps in early primary learning, a link is made between the energy of the sun, the requirements of plants and the dependence of animals on plants. As we “progress” further we learn science in compartments, the knowledge in one belongs to its compartment and is used exclusively in it. After all, we are taught by chemists, physicists and mathematicians; these collective nouns in themselves imply specialisation. What a restriction this places on our thinking! Where are the naturalists and biologists of a previous generation? Is there really too much to know that we need to specialise so soon? I do not believe so. This wider view is obviously supported by Professor Kennedy, who leads us through from the particulars of the behaviour of particles, to concepts of energy, laws of thermodynamics and entropy, a term, which can mean so much, but perhaps to so few. His goal in this instance is to present a forgotten view of the properties of matter to aid the understanding of the interdependency of life forms, their sustainability and interaction with their immediate and wider environment. How is this done? By proposing a unifying view of the interplay between molecules equally appropriate to the material as to the living world. With action, quantum theory may be applied to biology and the natural environment. In doing so he removes the artificial divisions in science we have made which restrict our thinking. His approach stems from a rereading of literature beyond the limits of the electronic libraries on which we have come to depend and seeing anew, individual proposals from which he has resurrected the concept of action. It is a salutary message to current scientists that much of the writings of Planck and Einstein have been forgotten and that from those forgotten writings Action Resonance Theory can be developed! Professor Kennedy has taken basic concepts from scientific papers forgotten by a new generation and demonstrated their applicability to physical phenomena of which we are all aware e.g. solar effects on weather, greenhouse heating, modelling environmental impact of dams using the unifying concept of Action Resonance Theory. Don’t at this stage be put off! After all, action is only a property of matter and is related to our normal concept of action i.e. that of doing something or responding to changes in circumstances.

When reading crime fiction, jumping ahead a few chapters or even to the last page defeats the challenge posed by the author. Not so with this book. Might I suggest to the applied biologist that he first reads Chapter 7 dealing with environment x gene interactions so as to deal with familiar themes and see how Action Resonance Theory may be used for a new understanding of them? Returning then to the earlier chapters where the physics of action is developed is to appreciate better where the author is leading us. If only we could have done this with pure science courses as undergraduates, much of the complaining by would-be biologists may have been answered! Each reader will have his own insight renewed by different images. My image of solutions is forever enhanced following an exposition of Einstein’s description of Brownian movement in terms of action resonance. This leads to a more dynamic view of the living cell processes. Gone is the two dimension static view of metabolic pathway charts to be replaced by a picture of molecules on the move in three dimensions directed by “forceful impulses in action space”. In depicting these and other images and the role of action in them the enthusiasm of the author becomes infectious. Where does the application of action lead us? A clue is given in a detailed discussion of the necessary steps in constructing an Action Resonance Model for Global Warming. These need to be borne in mind if we accept the author’s challenge to apply Action Resonance Theory to practical problems. The author perhaps concerned that he may restrict our imagination provides no other help. Whether or not we take up that challenge, our view of the interplay between a molecule and its neighbours will be forever heightened. For those who majored in physics a new appreciation of their role in biological studies. For many of us who became biologists there is a regret that the world of physics ended early in undergraduate years. This is the last book to be edited in this Series by Dr P.S. Nutman F.R.S., my former supervisor, Departmental Head, mentor and friend. Fifteen books have been published in the Series. The subjects have ranged widely from plant structure, plant disease, nutrition and environmental issues to applied agriculture. These reflect somewhat Phillip’s scientific interests among which are plant physiology, symbiotic nitrogen fixation, genetics of the plant-microbe interactions and more latterly the history of these fields. The present book, through its unifying concept of action, its challenge to rethink our understanding of the interplay of forces, objects and living things in the future, is particularly appropriate to the theme Botany and Related Applied Fields and is a fitting publication to mark this auspicious time, as scientists and interested scientific laypeople go on to explore new ideas.

Preface

This book was written as a synthesis of objective knowledge. From a realistic viewpoint based on observation of experimental biological and environmental data rather than physical or mathematical abstraction, it tries to unify the various threads of 35 years of the author’s professional experience; it seeks simple, common-sense principles for dealing with action in ecosystems that can simultaneously describe, explain and predict their complex behavior. For an environmental scientist convinced that the real world is the best place to test theories and to discover objective knowledge, writing this book was a spontaneous development. It is hoped that Action in Ecosystems can show why no natural object should be examined in isolation. Only by understanding that any material object, in some measure, is affected by everything else will the true simplicity of nature be seen. The valuable lesson emerging from this paradox of holism versus reductionism, allowing us to find solutions, is that nature generally works by the simplest possible mechanism. The book seeks to challenge. How profound a challenge can only be judged by careful reading, with a mind open to new points of view of old subjects. To some the challenge could seem so extreme that Action in Ecosystems suggests a change as radical as that described by Thomas Kuhn (1970) in The Structure of Scientific Revolutions. But this need not be so. Instead, a facilitated evolution in thinking is proposed by the author, based on the observation that all natural change takes place by trial and error. The book specifically proposes that natural processes are always quantum processes, using impulses from energy causing rearrangements between one stable configuration or action state and another. On this basis the logic of the quantum leap, popularly considered to denote a major change, is misconceived. Only the application of a vast number of exceedingly small quantum leaps, though large ones for electrons, can achieve significant change at the human scale. A catastrophe is merely the rapid summation of many such quantum steps. The book’s most novel viewpoint is the action resonance theory. However, this novelty is deceptive, a result of its synthesis. The book could be said to contain almost nothing new. Every concept dealt with here was proposed earlier by others. However, it does propose a dynamic framework for their reconciliation. From before the time of Aristotle, through the period of renewed learning in the European Middle Ages and the new discoveries of the Renaissance (Copernicus, Kepler, Galileo, Descartes and Newton) to the modern era (Lavoisier, Fourier, Darwin, Clausius, Mendel, Pasteur, Gibbs, Boltzmann, Planck, Einstein, Schrödinger, Watson and Crick, Monod, Popper) this book freely acknowledges its sources. My Asian colleagues – friends with whom I have worked in the past 10 years (Nie Yanfu of Jinan, Nguyen Thanh Hien of Hanoi, Le Van

To and Tran Van An of Saigon) – may wish to point out that, after all, the learning of the West has things in common with the traditional ideas of energy and matter, time and eternity, developed in the East. Thus, action theory may allow the West to appreciate, as a scientific analogy, the yin and yang of Taoism, the universal causality and karma of Buddhism and the sometimes creative, sometimes destructive cosmic dance of Shiva in Hindu cosmology. It is sobering to reflect that there may, after all, be nothing new under the sun! What is new is considering such a range of scientific phenomena in one book. The actual selection of topics is strongly contingent on the life experience and interests of the author. Whatever merit it may prove to have will owe everything to those whose ideas, theories and suggested solutions to problems live forever in the world 3 identified by Karl Popper (1976) – the world of recorded human knowledge. Indeed, without the many books that gather dust on my shelves, speaking their author’s message every now and then, this book could never have been written. I am also grateful to my colleague and friend, Le Van To, who reminded me recently that this book, at least in the ideas of its initial development, expresses a dream or a vision for the future. Some verse selected from Wordsworth is reproduced below. This aptly sums up the integrating wholeness of ecosystems that this book seeks. My niece, the irrepressible Elena Pasquini of Perth, chided me with a copy of the final two verses just as I was to give a paper at one of the Australian Biochemistry Society Conferences of the 1980s, at my alma mater, the University of Western Australia, dissecting out another aspect of plant biochemical function. Books and science are fine, but there are also occasions when nature as a whole may well be the best teacher, said Elena!

The Tables Turned by William Wordsworth1 (1778) Up! up! my Friend, and quit your books; Or surely you’ll grow double: Up! up! my Friend, and clear your looks; Why all this toil and trouble? The sun, above the mountain’s head, A freshening lustre mellow Through all the long green fields has spread, His first sweet evening yellow. Books! ‘tis a dull and endless strife: Come, hear the woodland linnet, How sweet his music! on my life, There’s more of wisdom in it.

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Original Text: William Wordsworth and S.T. Coleridge, Lyrical Ballads (London: J. and A. Arch, 1798). Representative Poetry On-line: Editor, I. Lancashire; Publisher, Web Development Group, Inf. Tech. Services, University of Toronto Library, 1997.

And hark! how blithe the throstle sings! He, too, is no mean preacher: Come forth into the light of things, Let Nature be your Teacher. She has a world of ready wealth, Our minds and hearts to bless— Spontaneous wisdom breathed by health, Truth breathed by cheerfulness. One impulse from a vernal wood May teach you more of man, Of moral evil and of good, Than all the sages can. Sweet is the lore which Nature brings; Our meddling intellect Mis-shapes the beauteous forms of things:– We murder to dissect Enough of Science and of Art; Close up those barren leaves; Come forth, and bring with you a heart That watches and receives. But do stay indoors and continue to read this book! least as a mirror to nature.

You could find it enlightening, at

Acknowledgements

The impetus for writing this book I owe completely to those around me. I thank especially my students and close colleagues who, collectively, have worked with me for hundreds of years in the areas of agricultural, biochemical and environmental science, in nitrogen fixation, the nitrogen cycle, the acidification of ecosystems and the environmental fate of pesticides. These include more than a score of post-graduate students who often asked questions that still need answers. My current students, Angus Crossan (who suggested the microcosm-macrocosm theme for the cover artwork, prepared by my daughter-in-law, Roslyn Kennedy) and Rosalind Deaker, my present research associates and former students Nanju (Alice) Lee (returned from abroad in spite of better offers offshore) and Shuo Wang, research associates Paco Sánchez-Bayo, Nazrul Islam, and Daiguan Yu, Sunietha Katupitiya and Sri Sriskandarajah now moved on, and my other supportive colleagues, Robert Caldwell (devil’s advocate), Rodney Roughley, Nazir Ahmad, Colin Bailey and Rafe Champion (especially for the prolonged loan of a set of Karl Popper’s books) have provided inspiration by the excellence of their work, or helped by merely listening to my dreams. Harold Geering, my intellectual correspondent from close by, has helped to focus my thinking, providing in his beautiful handwritten commentary a useful check on some (but not all) of my excesses. Phillip Nutman FRS, the series editor, has suggested numerous means of improving the text and has allowed free rein to my imagination. For his early role at CSIRO in establishing research in symbiotic nitrogen fixation in Australia, all Australians should be grateful. Fraser Bergersen FRS, of Canberra’s ANU and one of Nutman’s first appointees to his group at CSIRO Plant Industry, suggested improvements to a draft of the first chapters, stressing a need for clarity. Colleagues and friends at the University of Sydney, who encouraged, or assisted through general discussion, the process of writing this book include James McCaughan (mentor in orthodox physics and gyroscopic motion), Barrie Fraser (applied mathematician, staunch Newtonian), Tony Larkum (plant physiologist), a younger Mark Sceats (laser spectroscopist and molecular dynamicist) 20 years ago, and Philip Kuchel (biochemist, magnetic spectroscopist), who recently provided valuable criticism of the first two chapters of Action in Ecosystems. I also acknowledge years of interaction with widely respected colleagues and critics. The late Professor Geoffrey Leeper of Melbourne University, tolerated my raw ideas, visions and dreams nearly 20 years ago, advising due prudence, a period of focus on problems of the here-and-now and the need for proper maturation of developing ideas. He also extolled to me the virtues of Karl Popper’s The Open Society and Its Enemies

with its emphasis on personal freedom (with responsibility) and the value of open access to information, and of The Poverty of Historicism with its anti-Marxist view of the development of human society and the power of individuals to affect the course of events and to make a difference. He even proposed that I meet his correspondent, Karl Popper, an introduction that I was unfortunately not then ready to take up. Leeper’s protégé and agricultural economist, the late Bruce Davidson, honorary president of our local “flatearth society”, constantly challenged conventional thinking and showed how often it could profitably be turned upon its head. The support, cross-fertilisation of ideas and friendship of other members of this open-minded lunchtime group (including the late Owen Carter, Ken McWhirter, Bob Batterham, John Bowyer, Lindsay Campbell, Fred McDonald, Ross Drynan, Fred Stoddard, David Godden, Harley Rose, Gordon Macaulay and many others) over many years was most encouraging. Brian Deverall also read the early chapters and provided some welcome advice on strategy for advancing the theory. Much further back, I must acknowledge Lex Parker, my ever-stimulating supervisor of almost forty years ago at the University of Western Australia. Lex encouraged the study of as much chemistry (tutorials with N.S. Bayliss), biochemistry (lectures from Ivan Oliver) and mathematics as possible, with more faith in me than I then merited. Four years ago, the veil of his personal gloom of Alzheimer’s disease had descended to place him well beyond the reach of mere memories. Yet, he was still rather mysteriously stimulated by the presence of a former student to perform a simple experiment in relativity, revealing the asymmetry of the reflection of a moving light source, while my wife and I met with him and Dorothy in their home in Hillway, Nedlands. From the same era, Reg Moir’s typical injunction when completing a session of lectures that “It ain’t necessarily so”, paraphrasing one of his own American mentors I believe, has also left its mark. Ton Quispel of Leiden helped inspire a respect for wholeness in biology in a young post-doctoral visitor from the antipodes, who was seeing snow for the first time in the Netherlands. Recently in Europe, Jack and Mary Pridham of Royal Holloway, the University of London, Phillip and Mary Nutman of Exeter and formerly of Rothamsted Experiment Station, Vernon and Glynne Butt of Oxford, Ton and Jo Quispel of the University of Leiden, Hans de Kruijf of the University of Utrecht, my past student Stanley Dennis and his wife Edith in Basle, Herbert Zuber of the ETH in Zurich, and Jurgen and Heidi Weder of the Technical University of Munich have provided either intellectual discussion, shelter and even free hospital casualty care following a violent collision of my head with a squash-court stone wall near Windsor, while the manuscript was being written. One brief but highly fruitful meeting in a hotel salon in the very centre of old Utrecht with Jodi de Greef, attached to the University of Groningen, led to some key principles for the intellectual design of this book, particularly his recommendation to commence with a set of basic statements. Invigorating discussions on the role of resonance in plant biochemistry, while touring the English countryside in the summer of 1998 after a tasty pub lunch, and on another sultry August day while re-tracing for hours the traditional steps of Matthew Arnold’s scholar gypsy on the slopes overlooking Oxford, with Vernon Butt, Fellow of Pembroke College, led to the naming of the theory proposed in this book. This is not to lay any of its errors at the feet of these helpful colleagues and many others I have no doubt overlooked. Indeed, Vernon in writing was critical of the liberty with which I borrowed words from better known areas to use in the action theory. In

response to his comment, I decided to include a glossary/endnotes section in the book to better define and justify their use, although this task is only partly done. In all cases, however, the willingness of these colleagues to discuss ideas simply gave me the confidence to go on. The warm receptiveness of recent colleagues in Asian countries, Tran Van An of Saigon, Vietnam and Jose Peralta of the Philippines, has also encouraged me at critical stages. I must also acknowledge the very strong support given by Guy Robinson, Publishing Editor of Research Studies Press Limited. Although he rightly leaves responsibility for the intellectual content of the book to the author and his advisors, his suggestions for improvements to the text and his refreshing attitude to a manuscript somewhat out of the ordinary has been of critical value to the author. The ever-inspirational role of my five sons (David, Matthew, Daniel, Michael and Thomas) is beyond doubt. Together, over the years at 344 Pittwater Road, we learnt the rewards of challenging work. Also their beautiful wives, our grandchildren and all the members of our very extended family too great to count – Torrs, Kennedys, Van Dammes, parents, grandparents and siblings too – most of whom lived in or near Perth, Western Australia, all helped to complete the supportive human context needed for the development of any theory. My school teachers, particularly those at Clontarf, provided invaluable intellectual and practical disciplines, a respect for geometry and the value of hard work, and a reliable map for life. Most importantly, this book is dedicated to Thea, my wife, without whose loving care, constant support and spirit of common-sense, this book would have been impossible.

Permissions

Permission in writing to reproduce material in this book has been given for the following cases. Frontispiece to Chapter 2 (p. 7): Cambridge University Press, Cambridge Texts in the History of Philosophy, René Descartes The World and Other Writings 1637, edited by Stephen Gaukroger, Figure 2, p. 36, 1998. Figure 3.2 (p. 53): W.H. Freeman San Francisco, Basic Physical Chemistry for the Life Sciences, 3rd edition, V.R. Williams, W.L. Mattice and H.B. Williams, Figure 2.10, 1978. First frontispiece to Chapter 5 (p. 99) and Figure 5.2 (p. 104): High Altitude Observatory images of the sun, National Center for Atmospheric Research, University Corporation for Atmospheric Research, National Science Foundation, USA. Second frontispiece to Chapter 5 (p. 100): from the collection of the Royal Greenwich Observatory; sunspot observations in Scheiner’s Rosa Ursine sive Sol 1630, reproduced in Pelican Books, The Face of the Sun, H.W. Newton, plate 2, 1958. Figure 5.5 (p. 122): John Wiley & Sons, Inc., New York, Environmental Modeling: Fate and Transport of Pollutants in Water, Air and Soil, J.L. Schnoor, Figure 11.3, 1996. Figure 7.5 (p. 171): American Society for Microbiology, X. Perret, C. Staehelin, Broughton, W.J., Molecular basis of symbiotic promiscuity, Molecular Microbial Reviews, 64,180-201, 2000. Figure 7.6 (p. 173): Dr Fraser Bergersen, Australian National University, reproduced from Kennedy and Cocking (1997). Frontispiece to Chapter 8 (p. 187): The Vitruvian Canon of Human Proportions, reproduced with permission from the Accademia of Venice. Frontispiece to Chapter 1 (p. 1): Original Japanese artwork is also acknowledged. The source has been lost but readers are asked to inform the author if they recognise this work, so that proper acknowledgement can be made.

Units

Physical quantity International system (SI)

CGS system

Factor (SI/CGS)

Length Mass Time Force Energy

centimetre cm gram g second s dyne g cm s-2 erg g cm2 s-2

100 1000 1 100,000 10,000,000

metre m kilogram kg second s newton kg m s-2 joule kg m2 s-2

CGS (centimetre-gram-second) units have been used throughout this book. This reflects the author’s usage in thinking, and for consistency with most of the reference material used. The choice of CGS units is quite deliberate, to emphasise the loss of information involved in the SI system, based on use of the names of famous scientists. The benefit of uniformity given by the SI system of units may not outweigh the disadvantages of this loss of information. The action resonance theory described in this book emphasises the value of dimensional analysis and suggests that the most useful system of units still needs to be designed.

TABLE OF CONTENTS

Chapter 1: 1.1. 1.2. 1.3.

INTRODUCING ACTION ……………………………….. Action at a distance ……………………………………… Sustaining ecosystems …………………………………….. Action in ecosystems ………………………………………

1 3 4 5

Chapter 2: 2.1. 2.2. 2.3. 2.4. 2.5.

DEFINING ACTION ……………………………………. The quantum of action ………………………………….. The action resonance theory ….…………………………. Brownian movement as action resonance ………………. Action versus energy and work …………………………… Aesthetics and resonant action ……………………………

7 9 14 29 36 37

Chapter 3: 3.1. 3.2. 3.3. 3.4. 3.5

ACTION AND ENTROPY………………………………… Reversible and irreversible processes…………………….. Heat and work ……………………………………………. Entropy……………………………………………………. Action and entropy………………………………………. Action, entropy and disorder …………………………….

41 43 47 48 54 62

Chapter 4: 4.1. 4.2. 4.3. 4.4. 4.5. 4.6.

ACTION THERMODYNAMICS………………………….. Spontaneity in natural processes…………………………. Enthalpy and action resonance…………………………… Spontaneous processes and work potential………………. Free energy and action potential………………………….. Action field gradients in spontaneous reactions………….. Classical versus action thermodynamics……………… .

65 67 70 77 84 94 96

Chapter 5: 5.1. 5.2. 5.3. 5.4. 5.5.

ACTION FROM SOLAR ENERGY .……………………… Solar action ………………..……………………………… Solar action and storms on earth ………………………….. Action resonance in the atmosphere ……………………… Action modelling of global warming ……………………… Climatology and agricultural production.... ……………….

99 101 108 116 128 123

Chapter 6: 6.1. 6.2. 6.3. 6.4.

PHOTOSYNTHETIC ACTION - rH AND rP ………….. Storms in green plant cells ……………………………….. Oxidation-reduction potentials and the rH value ………….. Biochemical phosphate transfer potential (rP) ……………. Action parameters and the life force ………………………

135 137 142 148 151

Chapter 7: 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. 7.7. 7.8.

THE GENOTYPE-ENVIRONMENT INTERACTION …….. Action processes define microbes, plants and animals …… Life processes – carbon, nitrogen and mineral nutrition…… Symbiotic interactions …………………………… … Chance and necessity – selfish genes forced to be altruistic.. Order from chaos …………………………………………. Productivity in natural and agricultural ecosystems ……… A cautionary note ………………………………….. …… The origin of life …………………………………………

153 157 164 166 174 178 182 184 185

Chapter 8: 8.1. 8.2.

THE ACTION RESONANCE THEORY …………………. The action revision ………………………………………. A metaphysical research program ……………………….

187 189 203

ENDNOTES AND GLOSSARY ………………………………………….

213

BIBLIOGRAPHY …………………………………………………………

235

INDEX …………………………………………………………………….

243

1

INTRODUCING ACTION

Artwork by an unknown Japanese artist, from a greetings card; aquatic, avian images inspirational for the author of this book.

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“Everything is in flux, and nothing is at rest.” “All things are in motion always, even though … this escapes our senses.” Aristotle (3rd Century BC, Athens, Greece)

“Our main concern in philosophy and in science should be the search for truth. Justification is not the aim; and brilliance and cleverness as such are boring. We should seek to see or discover the most urgent problems, and we should try to solve them by proposing true theories …; or at any rate by proposing theories which come a little nearer to the truth than those of our predecessors. … a theory is true if and only if it corresponds to the facts.” Karl R. Popper (1972) Objective Knowledge: An Evolutionary Approach, p. 44, Oxford University Press, Oxford, UK

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Chapter 1

INTRODUCING ACTION Action at a distance Sustaining ecosystems Action in ecosystems

1.1.

Action at a distance

Since a falling apple around 1665 worked its magic in the imaginative mind of a youthful farmer at Woolsthorpe in Lincolnshire, the meaning of the word action and of the equal and opposite reaction, has been investigated in science and technology. More than 300 years ago this irreversible process had consequences that led to the development of a theory of gravitation still used by space agencies even today. It should be noted, however, that Isaac Newton’s intellectual concept of action was the equivalent of force1 - which he defined as the rate of change of linear momentum2 (or net impulse per second) which could be equated to mass x acceleration. Action as defined in this book is certainly related to force and it is well illustrated by the impulse and the outcomes that were excited by a falling apple. But in the terminology of the 20th century, action has physical dimensions clearly distinct from force. In contrast to force, variations in action3 involve the product of impulse and a radial parameter related to the spatial separation of matter. Just how action is proposed to be generated and its linkages to force and energy will be explained in the next chapter. This book, one in a series of monographs in the applied plant sciences, seeks to promote a novel approach. It will do so by focussing on the relevance to ecosystems of the physical property of action, considered as a complement to energy4. The physical dimensions of action given in the footnote show that, like energy, action expresses a quantitative measure of relative motion by a defined amount of matter. But in their nature, energy and action are as distinct as chalk and cheese. It will be shown in this book that energy is to action as cause is to effect. Perhaps surprisingly, it will also emerge that energy transmitted between molecules is continuously required to sustain action, providing the basis for a realistic definition of the term sustainability. In proposing the attractive force of gravity between the sun and the planets, Newton was intrigued and rather dismayed5 by the associated idea of action at a distance. This implied that there could be an apparently instantaneous effect of one body on the motion of another, although the two bodies were separated by a vast distance. Newton sought an understanding of the cause of this mutual attractive To express the physical dimensions of various properties in this book, symbols for both rectilinear (MLT-1) and radial (mrω) motion will be used; M, m = mass; L, r = length or radial extension; T-1, ω = the inverse of time or frequency (see Endnotes). 1 Force has physical dimensions of MLT-2 or mrω2 or mvω. 2 The physical dimensions of momentum are MLT-1, mrω or mv. 3 Action has the physical dimensions of ML2T-1, mr2ω or mrv. 4 Energy has the physical dimensions of ML2T-2, mr2ω2 or mv2. 5 “That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance …. is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.” Isaac Newton (1693) In a letter to Richard Bentley, quoted by Karl Popper (1965) Conjectures and Refutations, p. 106-7.

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interaction, but eventually decided against making any specific proposals in his major work, Principia Mathematica. This is shown by his assertion that “I feign no hypotheses”, in making a statement possibly critical of others such as Descartes, who had engaged in speculation about the specific mechanism of such action. Newton concentrated, instead, on successfully providing a mathematical description of the motion of bodies influenced by gravity and how an inverse r2 law of attraction for massive bodies could predict elliptical orbits. In the half-century after the publication of Newton’s Principia in 1687, the long debate in Europe regarding the principal conserved property in natural systems was eventually resolved in favor of the concept of energy rather than of momentum6. This set the stage for developing the discipline of thermodynamics in the 18th and 19th centuries. Since then, in the development of western science, energy has become the key reference property to which most physical and chemical processes are related. And there should be no doubting of the importance of energy. But action, the integral of energy x time, has special significance because it is more directly related to perceivable physical and chemical effects. By focussing on some examples in the environmental and plant sciences, this treatise will advance the case that too much attention may have been devoted to energy and insufficient to its complement, action. Action is an exact but complex property describing the physical state of a system. It may be considered as varying only in extremely small increments from one instant to the next and the total action should be viewed as a dynamic, additive property of all the molecules of a system, indicative of their energy distribution or quantum state. In this context, the popular use of the term “quantum leap” should be reconsidered since this would be the smallest step possible for a stable rearrangement of the system’s action. The neglect of the property of action may even now be limiting our capacity to understand how ecosystems function, how they evolved and whether they can be sustained at a time when human demands for food and shelter are increasing dramatically. It will be argued in this book that the development of action theory may now be needed to properly understand physical, chemical and biological phenomena, necessary to safeguard and sustain the Earth’s ecosystems. A challenge deliberately set in the book is to show how the property of action that is derived by considering interactions between sets of molecules can lead to conclusions that have validity for whole ecosystems.

1.2.

Sustaining ecosystems

The different kinds of ecosystems show many obvious contrasts. Rain forests, productive ecosystems rich in energy flow and action, are characterized by vivid spectacle, broad diversity of species, rapid turnover of biomass and relative constancy and balance of species content. In contrast, a desert ecosystem usually provides sparing productivity overall, but with highly fluctuating organic or biomass content7. 6

The brilliant analysis of Mme. Emilie du Châtelet, close colleague of Voltaire, Newton’s strong proponent in France, favouring energy (mv2) and Leibnitz’s view rather than the momentum (mv) preferred by Newton as the measure of motion, deserves more recognition (Bodanis, 2000). 7 The inland basin of Lake Eyre, Australia’s mythical “inland sea”, is characteristically a torrid zone of arid, saline and desolate landscapes. In the year 2000, for only the fourth time in the 20th century, Lake Eyre is filled with fresh water amidst striking scenes replete with abundant plant, animal and bird life.

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Agricultural ecosystems also display a variable content, dependent on season, geographical location and the cropping regime. They are generally mono-cultures sustained by high inputs of nutrients and the capacity to absorb energy, aimed at maximizing the production of particular species or their fruits. Marine coral reefs amaze with their colorful diversity of species. An arctic landscape provides a sharp reminder of the influence of temperature on biological productivity, yet also of the adaptive power of life. Adequately defining these landscapes and the important factors controlling their long-term sustainability is a complex and unsolved problem. As a first step, it would seem prudent to define better the requirements for sustaining an ecosystem. A simple production function8 for biomass in ecosystems could be: Ecosystem biomass = f(genetic base, water, ambient T, available nutrients, energy input, coupling agents, pathology, pest control, etc.) Depending on the scope and intensity of the analysis, each of these factors may be replaced by a subset of defining factors that may be needed for a fuller description. While energy input is a key component and has been the key operational basis for some descriptions of ecosystems, the consideration of energy alone has severe limitations and cannot provide an adequate description. The inherent sustainability of any of these ecosystems of variable productivity is not necessarily different, provided the inputs and outputs associated with each can be maintained. As a theme that will be developed later in this book, of more importance than the gross productivity may be the durability of the coupling agents or engines responsible for converting the inputs of each ecosystem to its outputs in the face of severe environmental fluctuations, and their capacity to adapt to these fluctuations. While this approach stresses the importance of mechanism in sustaining ecosystems, it also implies that these mechanisms can respond to environment in a non-additive fashion and that non-linear synergistic or holistic outcomes may be the rule in coherent communities rather than the exception. The importance of the genotype x environment interaction cannot be overstated. Understanding this interaction is essential to know the overall productivity and the capacity of each ecosystem to withstand impacts on its functional biological systems and to repair itself. The sustainable biomass in an ecosystem cannot be understood simply as an additive result of various factors. This conclusion explains the failure up till now of the Malthusian hypothesis regarding the linkage between agricultural resources and human population. On the contrary, the complex interaction between these factors using increasingly efficient coupling agents defines a highly flexible degree of productivity in response to advances in technology. The key role of these coupling agents in ecosystems of linking the utilization of energy inputs to the generation of the action is of paramount importance. 1.3. Action in ecosystems A thesis to be examined is that action will provide the most rational basis for assessing the capacity to produce biomass and sustain ecosystems. While only a 8

A production function is a mathematical equality between the quantity of product in a process and a function of the factors affecting the process.

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limited range of phenomena are to be examined in this short book, action is proposed to be a universal property for application to studies of the flora and fauna of natural systems. The basis for this universality is considered to lie in the relationship of action to thermodynamics, which will be discussed in the early chapters. Using an historical approach to scientific advances in energetics, the logical basis for using action as a thermodynamic property is presented. A major benefit to be derived from action theory will be the enhanced relevance to biology of the landmark developments of physical sciences in the twentieth century, such as the quantum theory and extending even to the theories of relativity. Thus, the significance to biology of the work of outstanding physicists such as Planck and Einstein can extend well beyond the theory of energy quanta and the nature of Brownian movement by colloidal particles. Further, it will be shown that action theory helps to explain the thermodynamic nature of both irreversible and reversible processes, leading to important conclusions regarding the role of non-equilibrium in biology. Just as an ecosystem can be examined for factors affecting its productivity as indicated above, so its action can be expressed as a set of functions: Action in Ecosystems = Σf(mass, space, time, energy, water, nutrients, temperature, coupling agents) Thus, the physical reality and the dynamic complexity of the contrasting ecosystems described above may be characterized by a unique action profile of each ecosystem. But does this statement of the role of action really simplify the study of ecosystems? Readers of this book who are prepared to allow adequate freedom to their imagination should expect to achieve new and more integrated ways of thinking about natural processes while seeking to understand the role of action. But the reader should also be assured that the development of action in ecosystems will be made on a familiar background of biological processes, observations and concepts. By examining a range of case studies related to key non-equilibrium processes in living systems, the possible significance of action and its power to integrate the diverse properties of ecosystems may be revealed. The action theory for ecosystems is advanced in the spirit of conjecture and refutation9, as part of the process of advancing human knowledge (Popper, 1976). It is called a theory because of its universal nature, but the action theory is a hypothesis like any other, subject to being tested and rejected if it fails these tests. It is the author’s earnest hope that every reader of this book, on its completion, and having completed his or her own critical tests, will at least have achieved an enhanced viewpoint of the dynamic unity of natural systems - complex and diverse, yet of the most remarkably basic simplicity and integrity.

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Perhaps the scientific philosopher who has done most in the 20th century to advance the case for realism tempered by common-sense, Karl Popper (1976), stated that “Scientific theories, if they are not falsified, forever remain hypotheses or conjectures. Progress consists in moving towards theories which tell us more and more - theories of ever greater content. But the more a theory says the more it excludes or forbids, and the greater are the opportunities for falsifying it. So a theory with greater content is one which can be more severely tested”.

7

DEFINING ACTION

Descartes’ cosmology shows the sun at the centre of its cosmic cell, surrounded by its planets arranged on the Copernican model, crossed by a comet on a hyperbolic path. His vortex theory relied on pushes from corpuscles in which inertial motion of bodies in a straight line was modified by the disposition of matter. Reproduced with permission, Cambridge Texts in the History of Philosophy, René Descartes The World, 1637, Edited by Stephen Gaukroger, Cambridge University Press, United Kingdom 1998.

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“The order of views thus becomes the unique space, the fundamental space of nature. At first we appear to have things the wrong way around. For we are accustomed to regard the order of the space of objects as fundamental, and to picture the order of the space of views as derived from the order of the objects in which they are physically situated. To us this seems the positive way of thinking. Nevertheless, the inversion, which, in this simplified world, makes the order of views or total perceptual contents appear as autonomous, and as the network of the very order of the bodies, is necessary. In the light of rigorous analysis it in fact provides the only possible application of space geometry to the content of such an experience.” Jean Nicod, (1924) “Geometry in the Sensible World” p. 146 in Geometry and Induction, University of California Press, Berkeley and Los Angeles, 1970.

“We can thus consider the following as rather certainly proved. If a ray of light causes a molecule hit by it to absorb or emit through an elementary process an amount of energy hν in the form of radiation, the momentum hν/c is always transferred to the molecule, and in such a way that the momentum is directed along the direction of propagation of the ray if the energy is absorbed and directed in the opposite direction, if the energy is emitted.” Albert Einstein, (1917) “On the quantum theory of radiation” p. 182 Physikalische Zeitschrift 18, 167-183

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Chapter 2

DEFINING ACTION The quantum of action The action resonance theory Brownian movement as action resonance Aesthetics and resonant action

2.1. The quantum of action Action is not a new concept. The idea can be traced back to the ancient Greeks, reemerging strongly in 18th century Europe when proposed by Maupertuis as the principle of least action1. In Germany the idea of action had earlier been considered by Leibnitz and by Euler. The brilliant French and Irish mathematicians, Lagrange and Hamilton, gave a key variational role to action in their descriptions of the mechanics of conservative systems. The Scot, P.G. Tait (1863, 1883), also had great confidence in an important role eventually being found for action in physics. He considered this role at some length in his co-authored Treatise on Natural Philosophy with Lord Kelvin (Thomson and Tait, 1867) and in an article in the 10th edition of Encyclopedia Britannica published in Edinburgh. In these days before quantum theory, progress in understanding was usually hampered by a static, cumulative view of action as the integral of momentum with respect to distance or of kinetic energy with respect to time. One hundred years ago, near the beginning of the 20th century, a need to define the fundamental quantum of action2 for the partitioning of energy as heat radiation was realized by Germany’s Max Planck; his brilliant theoretical reasoning rescued classical physics from the crisis of the ‘ultraviolet catastrophe’3 that, contrary to experimental data provided by Kirkhoff, predicted an eventual infinite energy requirement as the frequency of oscillation of matter increased with increasing temperature. Planck’s mathematical theory recognised that there was some fundamental requirement that the thermodynamic property of entropy never be less than zero4. His basic concept of the quantum of action was then readily integrated

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Pierre Maupertuis (1698-1759), eminent French astronomer and mathematician, proposed that nature conformed to a rule of economy in which action defined as œmv ds is a minimum. Unfortunately, as this book concludes, the concept as advanced was flawed or misunderstood and seems to have been completely rejected by scientific fashion in the nineteenth century as too teleologic. 2 The quantum of action, h, was defined by Planck with physical dimensions of erg.sec (ML2T-1, mr2ω). 3 A famous problem which involved a question about the distribution of energy at extremely short wave-length; for more detail, see endnote on black body radiation. 4 “The hypothesis of quanta as well as the heat theorem of Nernst may be reduced to the simple proposition that the thermodynamic probability of a physical state is a definite integral number, or, what amounts to the same thing, that the entropy of a state has a definite, positive value, which, as a minimum, becomes zero, while in contrast therewith the entropy may, according to classical thermodynamics, decrease without limit to minus infinity…I would consider this proposition as the very quintessence of the hypothesis of quanta” (Planck, 1913, vii-viii).

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by Albert Einstein with his theories regarding the specific energy5 and momentum6 of the quantum of electromagnetic radiation ņ in explaining its power to eject the material particles known as electrons from the surface of metals. Years later, G.N. Lewis named quanta as photons. Subsequently, the same action constant as that defined by Planck (h) was needed for the theory of quantum mechanics developed by Bohr, Heisenberg and others. Schrödinger’s wave function for calculating the energy distribution of electronic orbits in atoms also incorporated the quantum of action as a key mathematical factor. Statistical mechanics too, a development in thermodynamics initiated by Gibbs, Maxwell and Boltzmann towards the end of the 19th century, later used Planck’s quantum of action to estimate the partition functions determining the distribution of energy in molecular systems. All these theories, then, clearly imply a fundamental link with energy in which action is a dynamic concept rather than static. Action, as employed in this book, is a physical property with dimensions identical to those of Planck’s quantum of action - often expressed as the product energy or work multiplied by time. This definition is in accord with the popular use of the word action in everyday life. Indeed, as humans we can hardly imagine a meaningful existence without it. It is proposed here that the physical property of action can play a strong unifying role in science, allowing general application of the quantum theory to biology and the environment. Strangely, although action has implicitly been given a basic physical role in science throughout the 20th century, it is rarely mentioned in physical and chemical treatises, and has never been seriously considered in a biological context. Such long neglect of an important and powerful concept that this book shows can connect the fields of quantum physics and chemical thermodynamics to biology is hard to understand. Changes in the action state of a particle or molecule can be considered as the product of impulse7 and a radial coordinate or range scaling parameter8 that couples the relative motion of any two particles. Action has the same physical dimensions as angular momentum9 (see Figures 2.1a and 2.1b). But this correspondence must be handled with care, since angular momentum is usually considered as a vector of three-dimensional coordinate systems indicating the quantity of rotational motion or spin of an isolated particle or body. For expressing the total action of a set of randomly distributed molecules in dynamic equilibrium with its surroundings, this measure of angular momentum would not be satisfactory since the total of the vectors for all molecules would be close to zero, thus ignoring the action. Any estimate of the total action of the system requires a positive measure of all the relative motions of the particles and therefore cannot be determined from reference systems with both positive and negative coordinates.

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E=hν defines the energy (E) of a photon, where h is Planck’s quantum of action and ν is the frequency of radiation of the photon. 6 p= hν/c, where p is also equal to mc, the momentum of the photon, and c is the speed of light. 7 The physical dimensions of momentum and impulse are MLT-1, mrω. 8 Linear or radial extension, L or r. 9 The physical dimensions of both action, a scalar quantity, and angular momentum, a vector with a direction, are ML2T-1 ≡ mr2ω.

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Fortunately, this requirement can be met, but only if a natural reference system for the observation of molecular motion is chosen. This must be one that considers the relative motion of all the molecules in the system as positive and of equivalent value, with no unique reference frame or origin. At first, this requirement may appear alien to our mathematical thought. Despite Einstein’s conclusive efforts and the fairly general acceptance in physics of his theory of special relativity, we still usually prefer to consider the intellectual concepts of space and time as absolutes, as though a set of objects or a real system is being viewed by God using an celestial clock of invariant speed to measure change. We ourselves mimic God, in imagining we can observe the whole Universe or even a local system of molecules at the same time. Proper consideration will show that such instantaneous perfect knowledge of complex systems by humans is impossible and the only absolute we can measure relates to the simultaneity of observation of signals arriving at a particular place at a particular time. To be otherwise, a method for instantaneous communication across all space would be required. For us, given the simultaneity of local observation of signals, all else is extrapolation.

Fig. 2.1a: Uniform atoms, such as argon molecules, in a three-dimensional action field. Instantaneous sensing of the actual position of all molecules in the field is impossible. Information regarding position cannot be transmitted faster than the speed of light. Therefore, the “order of views” of molecules must be relative to their position in the recent past, depending on their separation. Their actual current position can only be predicted.

Fig. 2.1b: Action as relative motion, calculable using objects apparently stationary at the distant horizon as reference points; motion as angular velocity (ω = dθ/dt) is shown as successive snapshots but is to be regarded as continuous. Alhough a scalar quantity, action can never have negative values. It is an exact multiple of Planck’s quantum of action, h/2π, as a result of the quantisation of impulses of radiant energy and their capacity to sustain motion.

Therefore, physical phenomena involving the interaction of molecules through space can only occur for any particular molecule or at any other point as a melange of impressions involving sensible impulses originally launched from every different molecule at various different times in the past. These discrepancies in time between actual events, which provide the origin of signals and their sensible observation elsewhere, may only be corrected subsequently from a knowledge of the distances

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between molecules and the speed of transmission of signals in the intervening medium and their associated impulses. The speeds vary for each method of signalling and according to the medium of transmission and the method of detection of impulses (e.g. the speed of light or other electromagnetic emissions, the speed of sound, the speed of a courier plus the delay in reading the dispatch, etc.). Consequently, there may well be a need to make such corrections by intelligent or sensible beings, in order to anticipate the future (e.g. to avoid a predator or to predict an eclipse). It is even possible that most of our problems regarding the relativity of signals and reference frames, addressed so elegantly by Einstein in his theory of special relativity, stem from our reluctance to face this reality. The need to do this was explained by the young Frenchman, Jean Nicod10, in the opening years of the 20th century (see Nicod, 1923). The clear implication of Nicod’s thought on physical geometry (possibly influenced by Liebnitz’s theory of a universe of interacting monads) is that we must abandon reference frames specifying a simultaneous space of objects if we are ever to achieve a realistic universal model congruent with observation. Instead, the succession of instantaneous views of space from every observation point where a signal may be received or emitted must be considered as the more realistic reference frame specifying the position of objects in relation to the observable universe. When the metaphysical viewpoint expressed in the quotation from Nicod’s treatise Geometry in the Sensible World given at the beginning of this chapter is taken with Einstein’s theory regarding the transfer of momentum between molecules as a result of recoil from absorption and emission of quanta, we already have the main features of the action resonance theory. Then, using the rational assumption that matter everywhere in the universe should exhibit the same physical response to signals sensed as impulses – otherwise our science is futile – we can make accurate general predictions of position that relate to the future or the past. Despite Nicod’s negative opinion (in the final paragraph of his treatise) of the attempt by physicist-mathematician Henri Poincaré to relate geometry and action, we will show that action theory can successfully display geometrical succession as a dynamic effect of energetically driven exchanges in the three-dimensional action of the universe’s matter. Development of this approach may provide a flexible and universal frame of reference that avoids the disadvantages inherent in absolute or inertial reference frames. A common feature for the measurement of action and angular momentum of individual bodies is their inertia11, whether in the spin of electrons, rotating molecules, the rolling fly-wheels of industrial machinery or galaxies. Inertia, as well as mass, is a property of all matter, but differs from mass since it depends on the spatial distribution of the matter contained in a body. This inertial mass12 is of key 10

Jean Nicod (1893-1924) was a protegé, when at Cambridge University in the United Kingdom, of Bertrand Russell. Nicod performed only briefly on Europe’s philosophical stage but with a clarity of intellect rarely seen in the 20th century. Unfortunately, his achievements have been scarcely mentioned after his early death at 31. His uniquely challenging and dynamic approach to geometry still seems completely fresh and has periodically teased the mind of the author of this book. Indeed, his objective insights into the relativity of sensation and motion have provided a key guide to the logical development of action resonance theory. 11 The physical dimensions of inertia are mr2; thus action is the radial rate of change (ω) of inertia, mr2ω (see Figure 2.1b). 12 The poor general appreciation of the role of inertia and inertial forces was well illustrated recently in the case of the making of a film of an episode set in the 1920s based on the life of the famous Australian aviator, Sir Charles Kingsford-Smith. The film-makers were unable to reproduce the heroic feat of one of his companions, Mr Taylor, of draining oil from a disabled engine on one wing of their

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importance in measuring the angular momentum of a body or a set of bodies. An intriguing property of rotating bodies, much observed but poorly explained, is the absolute conservation of angular momentum. A heavy fly-wheel takes much hard effort to set it in rotational motion, but once in motion it is equally hard to stop. We take this observation for granted, but how is it so? By the end of this book the reader may have grasped some understanding of how, through relativity, dynamic physical geometry as envisaged by Nicod and action theory, angular momentum is conserved. The reader will already recognize this tendency for conservation of angular momentum in the variable rate of spin of the pirouetting Olympic ice skater as she extends and retracts her arms. In this case, the impulses required to generate her action or angular momentum arose initially from the biochemical processes of muscular contraction and the reaction force of skates on ice. We clearly see that the rate of rotation of the skater is slowed down during the extension of her arms but, in the absence of new impulses exchanged with the ice surface, the total action tends to remain the same because the friction is slight. We can even calculate the conserved angular momentum and inertia involved, explaining change in her speed of rotation from our estimates of changes in her inertia as she gracefully redistributes her mass. Observe that, unlike energy, the idea of action can be more directly perceived by the human mind since it involves geometrical measures impacting on our senses and that can be pictured or imagined. Energy is used as an abstract quantity, harder for humans to imagine, particularly in its less obvious form as potential energy. However, this book will seek to show that there is a simple and mutually necessary instantaneous relationship between action and energy. Indeed, the full meaning of potential energy as a physically real property will be more easily understood when it is related to action. If achieving sustainability in the action of natural systems while conserving energy is our objective, knowing this may be essential. Qualitatively, it is possible to recognize in living systems a hierarchy of action processes, proceeding from the scale of interacting molecules in cells (about 10,000 billion billion molecules, 1022, per cubic centimetre) to the concerted actions of whole organisms and communities of organisms. This hierarchy extends across all the scales of microcosm and macrocosm. Furthermore, action and energy can extend across these scales; the generation of action at one scale associated with a new input or internal release of energy can spontaneously generate action at other scales and degrees of freedom. This finding provides an important ordering principle that we will claim is relevant to chaos and catastrophe theory. But for now, the reader is asked to consider the scale only of molecular systems, which at any moment might be

aircraft in flight to be transferred to the ailing engine on the other wing, enabling the aviators to safely return to base in Sydney from an aborted trans-Tasman mail flight. The film director had placed the replica aeroplane in a hangar, using large electric fans to simulate the air velocity of its forward motion over the ocean. Try as they would, the actors were quite unable to successfully transfer any of the engine oil under these windy conditions, which simply blew away. However, the aviation expert advising the film director had overlooked the role of the motion of the aircraft in flight and the significant stabilising effect of its resultant inertia – similar to that of a bicycle remaining upright as long as it remains in motion. As a result, an awful suspicion that the story might have been concocted by the aircrew as a publicity stunt, bothering Ian Mackersey, Kingsford-Smith’s biographer advising the film-makers of A Thousand Skies, gained some credence. However, a proper knowledge of inertial action physics could have allayed these fears; these heroes fully deserve their honoured status and Taylor the award of the George Cross. For the sake of authenticity, the scene in the film should be reenacted in actual flight, incidentally providing a test of action resonance theory.

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regarded as a dynamic complex of pirouetting and dancing objects, to determine if the action theory developed in this book can be shown to have any practical merit. 2.2. The action resonance theory Here, to illustrate the theory at one scale, a physical model of the action field for a system of molecules at ambient temperature will be presented. This hypothesis proposes the existence in all molecular systems above the absolute zero of temperature of a spontaneous interaction involving resonant exchange forces. These forces are, in part specific to each chemical species, even when these molecules behave according to the ideal gas laws13. This proposal, which forms one of the bases of action resonance theory, may seem unusual but a case will be made that it is implicit in quantum theory and other treatments of dispersive forces between molecules. However, it is most important to realize that the action theory considers all the molecules of a particular species in a system to be an interacting set or ensemble and that the total action is constituted from all the motion in the molecular field at a given temperature. The reader must banish any thoughts of isolated molecules or even small numbers of molecules as being representative, since action theory predicts that, without companions, these are likely to behave in an anomalous fashion. The classical kinetic theory of Maxwell proposes that the individual molecules of an ideal gas do not interact. The molecules are treated as particles with independent linear trajectories, with point centres of mass. However, they are still considered as able to collide with other molecules and the walls of the vessel. Note that molecules approaching the walls are anomalous since they have a 100% probability of collision and reversal of their direction of motion in the near future. Molecules in the interior have a lower probability of collision in the same period, except in dense systems such as liquids or solids. For non-ideal gases, interaction between molecules is considered to indicate binding energy, inferring an attractive force between any two molecules; overcoming this would require an input of energy or chemical work equal to the binding energy in order to overcome the attraction. Thus, the term “binding energy” actually infers a deficit of the total energy the system would need to allow the molecules, atoms or sub-atomic particles to behave independently of one another. The basic proposition of the action resonance theory is that the emission and absorption of quanta generates impulsive exchange forces between molecules that are primarily dispersive or repulsive; this effect results from the conservation of momentum and molecular recoil (Einstein, 1917). This distinction between attraction and repulsion as fundamental should provide critical logical and experimental tests of the action resonance theory. The inability of anyone up till now to provide a mechanism for directly attractive forces between particles, pulling them together, other than as a mathematical formalism or operational 13

The ideal gas law states that, for each chemical species in a system, the product of pressure (P) and volume (V) is a constant at a particular temperature (T); i.e. PV = nRT, where R is the molar gas constant and n the number of moles of gas. Action theory can provide an explicit explanation of this equality, based on the principle of conservation of linear momentum or impulse, energy density and the resultant torques exerted on molecules.

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method, may ultimately decide between current theories proposing attractive force and action resonance theory. Action resonance theory implies a singular basis for the generation of all forces between particles or molecules, with “attraction” always the net result of a complex three-dimensional set or matrix of dispersive pushes from impulsive energy. In action theory the conservation of linear momentum as the basis for exchange forces is considered to be the fundamental principle from which all other regularities or laws regarding force can be derived. A set of basic explanatory statements or theorems will now be given to illustrate the logical effects of this universal principle. 2.2.1. Basic explanatory statements of the action theory Consider a vessel filled with a gas mixture such as air – predominantly of N2, O2, Ar, CO2 and H2O molecules – at a given temperature T. Each of these five chemical species has available a three-dimensional space dictated by the total volume of the vessel and the total number of molecules. The following postulates or basic statements, drawing on concepts well accepted elsewhere, are proposed: • At each instant, each molecular species exists as a field of matter and energy corresponding to its quantum or action state, characteristic of the temperature of the system. If a succession of snapshots of sufficiently short duration of 10-20 seconds could be taken (a technically impossible task, since no film is so responsive or chemically so fast), this would reveal the current action state displaying the corresponding threedimensional morphology and the inertial velocities of the molecules involved. In such a brief interval an electron in the ground state of a hydrogen atom14 will only travel only several times its own width (2.19 picometres). Light will travel only 300 picometres or 137 times further, 3% of the width of the hydrogen atom. As a result, the dynamic geometry or action state of the system of particles will appear more or less stationary and there would only be the very slightest smearing out of the positions of primary particles. • Fluctuations in action state of molecules within a system at equilibrium with its surroundings result from the exchange of energy quanta between molecules at the speed of light between one part of the system with another. A new set of snapshots, taken moments later following the first fluctuation in the action field, would reveal a complex system with slightly different local dynamics. It is proposed that there are normally extremely frequent exchanges of such energy quanta and ground state energy, emitted and absorbed or reflected by molecules in adjacent regions of the action field. In systems at equilibrium with their surroundings, these momentum exchanges are considered to be resonant, since the quanta in the system are conserved and are continuously in transit, either between or within molecules, with no net change in the overall action state. Not only should the molecules and the momentum of a given species be considered as an interacting set but the resonant quanta in continuous transit at the speed of light, the means of their interaction, should be included as an integral and complementary 14

A description of the Bohr hydrogen atom, with an action revision, is given in the Endnotes/glossary.

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extension to the molecular set. The momenta of these molecules and their radial separation correspond to the momentum (ps) and spatial (qs) coordinates referred to in Hamiltonian dynamics as phase space (see Prigogine, 1980, p. 21). It should be obvious that the product of these coordinates of linear momentum and radial separation has the physical dimensions of action. • In action theory, the conservation of linear momentum is the most critical feature in the exchange of impulses as quanta or ground state energy between the mobile surfaces of material particles, giving the efficient cause of all forces. This is the fundamental principle of the action resonance theory, from which all other outcomes or laws regarding forces may be derived. Resonance implies no more than the capacity of energy quanta or ground state energy to regularly exchange impulses15 between the mobile surfaces of material particles such as molecules, according to the principle of conservation of linear momentum. All material atomic surfaces (e.g. electrons, nucleons)16 provide extremely dense reactive surfaces on which energy quanta can resonate or be reflected, either internally from surfaces within molecules or externally between molecules. Relative to the speed with which detectable impulses are delivered (the speed of light) and the highly discontinuous nature of the dense internal particles of molecules, most space is available for transfer of momentum on quanta. Because of their strong penetrating power in matter, the degree of interaction possible via energy is proportional to the total matter or mass of the primary particles rather than the apparent external surface area of the molecules. Furthermore, all such impulses delivered by quanta between matter, because of the principle of conservation of momentum, will cause an equivalent and opposite change in velocity by recoil of the material particle concerned. This conservation principle occupies a key position in action theory - being the unique basis for the generation of forces in ecosystems. • All material particles mutually screen or eclipse other particles from impulses by forming an umbral shadow for energy transmission opposite to their direct line of radiative action; such screening17 varies in potential with the inverse square of the distance of radial separation of particles. 15

The concept that quanta deliver characteristic impulses affecting the momentum of molecules was established by Einstein (1905, 1917). 16 In considering the probability that a particular quantum of energy will interact with a molecule which it encounters, we must acknowledge the fact discovered by Lord Rutherford that most of the hard matter in an atom or molecule is highly concentrated in dense particles such as the nucleons (protons or neutrons) or electrons. For example, the quantum model of the hydrogen atom developed in the early 20th century is one in which the total volume of the central proton together with that of the electron is less than one-trillionth (that is, 1 part in 1012) of the total volume of the atom. The rest mass of the proton is 1836 times greater than that of the resting electron (1.6x10-24g versus 9.1x10-28g). The mean density of the proton (for a radius = 1.2x10-13cm) can be calculated as around 1014 g cm-3 while that of the electron may be about 1013, but the electron is much more mobile. Even so, most quanta can obviously traverse a molecule without encountering an electron or a nucleon although they are bound to do so eventually, depending on the overall density of the matter. 17 In action theory, screening from the impulses of energy leads to local coupling between pairs of mutually interactive masses (m1, m2), causing acceleration (rω2) of each towards the other generating their kinetic energy. This is balanced by an opposed force involving direct dispersive interaction between the two masses as well as other matter distributed on the internal aspect of their relative

17

At temperatures typical of ecosystems, variations in energy content and the rate of impulses from quanta are only rarely sufficient to dissociate the material particles (electrons and nucleons) from each other. This is because the time integral of the random forces from the impulses of energy directed on each particle from the exterior, less screened, hemisphere of a molecule is normally matched to the time integral of the random forces on the same particle from the umbral, more shielded, interior hemisphere. The effect of screening is to scatter energy, leading to reflection or diffraction depending on whether there is a reversal in direction or a deviation only. Any binding process between separated particles results in the emission of quanta from the system’s energy field, characteristic of their extent of mutual interaction, the strength of binding depending on the equilibrium of dispersive forces reached (see Figure 2.2). It is also important to note that the rate of exchange or frequency of impulses from energy resonating between any pair of molecules must vary in inverse proportion to the radial separation, increasing as the molecules approach each other and decreasing as they recede. The quantum is regarded as extracted during the transition from the total radiant energy of the entire action field and not selected instantaneously from any single direction as suggested by Figure 2.2. The action model of the hydrogen atom given in the Endnotes allows calculation of the quanta emitted or absorbed for electronic transitions between action states. If drawn to scale for a proton (H) of diameter 1.0 cm, the electron on average would be about 100 metres distant in the ground action state n=1 (equivalent to 5.29 x 10-9 cm). For the excited action state n=2, the electron would be 400 metres distant, 2,500 times as far as shown in the diagram. So the two screening cones would be much more elongated, their sides intercepting the nucleus tangentially with only a slight deviation from parallel lines. Because of statistical averaging of its motion, either from observations with time intervals characteristic of molecular collisions (about 10-13 sec), or by considering the median position now of a large number of hydrogen atoms in the system, the electron is not localised. It will appear fuzzy or smeared out to fill the van der Waal’s volume of the atom. As a result, molecules do not readily penetrate one another’s van der Waal’s volume unless the velocity of the molecule should approach that of the electron. trajectories. Since the magnitude of this screening effect must be inversely proportional to the square of the separation we have rω2 = C/r2; thus, the characteristic celerity (Ca) for the couple is defined here as Ca = a3ϖ2 = r3ω2, constant for circular motion (see Endnotes, Kepler’s observations). The magnitude of the celerity is dependent on the mode of interaction and the total quantity of mutually interacting matter. For mutual interactions proportional to the total mass we have (m1+m2)G = Ca = r3ω2 for circular orbital couples, where G is the gravitational constant. Then F = m1m2G/r2 = m1m2rω2/(m1+m2) = m2rω2 where m1>>m2 or F = m2rω2/2 = m2r2ω2 = m1r1ω2 where m1 = m2 and r = r1 + r2. Where this centripetal force is in equilibrium or balance with an outwardly directed centrifugal force, also caused by an acceleration proportional to the exchange of impulses, a stable orbit is maintained in which r is the constant radial separation for circular orbit or is the mean radius for elliptical orbits. Because the true measure of inertia in an impulsive interaction of an orbital couple at equilibrium is the constancy of action or angular momentum, we can write r2ω = @ = nh/2π, arbitrarily setting m2 = 1.0. Then, for a dominant couple where nh/2π = @ remains constant in the epoch of observation, C = n2h2/4π2r = r3ω2 = rv2; v2 = C/r = n2h2/4π2r2 and v = nh/2πr. For all other nondominant couples, the specific action and potential energy must constantly vary, corresponding to changing action states and radiant energy exchange. Similar solutions can be obtained for more restricted modes of interaction between particles such as the electromagnetic, dependent on the propensity for mutual resonance between systems of particles such as protons and electrons.

18

r1

Fig. 2.2: Virtual action resonance model of the emission of a quantum of energy from a hydrogen atom (not drawn to scale) for electronic transition from quantum state n=2 (action = h/π) to quantum state n=1 (action = h/2π). During the transition the instantaneous screening potential for the electron (e) by the nucleus (H), proportional to 1/r2 where r is the radial separation e-H, is increased by the difference in volume of the oscillating umbral or eclipsed cones ABC – ABC. The change in conic geometry with the transition suggests that more field energy is needed to sustain the electron in state n=2 than in state n=1, equivalent to the quantum of radiant energy emitted (hȞ). This is just equal to the increase in kinetic energy in the transition; thus the decrease in potential energy is twice the size of the quantum emitted (see Endnotes), also equal to twice the decrease in total energy which can be equated to real energy.

•

As systems of molecules become more concentrated, less energy or quanta per molecule will be required to provide sufficient impulses and pressure to sustain the system at a given temperature.

Whenever one particle or set of particles approaches another during compression, the local action field will diffuse radiant energy as quanta to the external field while equilibrating. This is a result from greater screening18 by matter, shorter resonance 18

In action theory, screening is predicted to have great significance, not only in terms of establishing bonding forces proportional to mCa/r2, as suggested in the previous footnote discussing celerity and the zero point energy at the absolute zero of temperature, but also determining the change in heat capacity of molecules as the temperature is raised. For linear gas molecules, a very simple action method exists to estimate relative heat capacity, depending on the number of atoms and their alignments in space. Using the customary three-dimensional coordinate system, each isolated atom presents six axial points of view for the generation of action, as an outcome of the forces or torques operating with a rate of impulses from quanta over a given range or distance for a finite time. For a monatomic molecule such as helium or argon, the heat capacity at constant volume has been observed to be Cv = 3k/2 (where k is Boltzmann’s constant per molecule), corresponding to just six points of view in three dimensions. To the extent that one atom completely screens another nearby, each bond will diminish the number of external points of view of each atom by just one; thus diatomic molecules such as hydrogen, nitrogen or oxygen present only 10 aspects for interaction with the impulses from external quanta on the molecule rather than 12 and the heat capacity would only need to be 5k/2 rather than 3k. Carbon dioxide presents 14 aspects, or four less aspects than three completely separated atoms, indicating Cv = 7k/2. In polyatomic molecules, the extent of screening and hence the reduction in energy absorbed by the system and needed to sustain the molecule depends on all spatial orientations of atoms, their radial separation within the molecules and the temperature. Because of the rapid increase in this paracrystalline complexity with molecular size, the calculation of heat capacity rapidly becomes more complex, but action theory can provide a basis for the stability of different quantum states, by

19

times leading to more frequent impulses for quanta and more frequent molecular collisions. Conversely, more energy as quanta will be required to sustain molecules separately whenever the volume of the system is increased while doing work on its surroundings. In action theory, these reversible, variable, screening effects have the most obvious outcome of producing the so-called attractive van der Waal’s forces between molecules. Such attraction is an illusion created by spatial variation in the intensity of dispersive forces, as a result of screening effects by molecules. The extra screening on compression of matter distorts the energy field, reducing the ratio of the space external to molecules to their internal volume in which energy can oscillate, reducing the need for energy per molecule at any temperature, T. In action resonance theory, all bonding between electrons and nucleons, atoms and molecules producing coherence between particles has this basis and the bonding process itself must involve the emission or release of quanta. Screening possesses a cyclic, dynamic, quality as a result of periodic realignments of the particles involved, affecting the strength of bonding. Elsewhere in this book, the idea that the kinetic energy of particles is a result of the extent of screening and the balancing of forces carried as impulses of resonant energy is developed. The more complex the molecules, the greater is the opportunity to set up harmonic screening from transient alignments of atoms and electrons. Thus, resonance plus screening allows the interacting system of molecules to economise on the density of quanta needed to maintain physical structures. Screening can also explain non-ideality in concentrated solutions, where the thermodynamic properties of real molecules diverge from those for ideal systems where they are considered to act independently of each other. • Molecular collisions enhance the intensity of the action field, by causing increased exchange of quanta and of momentum as the two molecules approach in the collision; molecular momentum exchanged in collisions is always counterpoised by exchanges of momentum carried on energy. Collisions or close encounters between molecules involve lowering the action/quantum states with respect to each other and other like molecules in the hemisphere being approached, but higher action states with respect to other like molecules in the receding hemisphere of the system. The closer the approach, the greater the magnitude of the quanta emitted. By resonant exchange of quanta at the speed of light between the two approaching molecules and the field at large during collisions or close encounters, the repulsive force generated can be progressively amplified because of the shortened distance and transmission time, sufficiently to decelerate and then reverse the direction of momentum of the particles19. maximising the alignments and degree of screening possible for a given energy content, thus minimising the overall action at any temperature. 19 We can test whether this proposal for generation of internal repulsive force by action resonance is feasible by doing a simple calculation, seeking to reverse the direction of motion of a molecule with linear momentum of 10-18 g.cm.sec-1. From Einstein’s equation for momentum (p=hν/c), an energy quantum with frequency 108 sec-1 would have a linear momentum of ca. 6.6x10-27x108/3x1010 = 2.2x1029 g.cm/sec. Therefore, action resonance equivalent to absorption and emission equivalent to ca. 1010 exchanges (or reflections) of this momentum would be required during the collision process. In a collision of duration 1 µsec between two molecules separated on average by ca. 10-7 cm, such a momentum exchange could be provided by quanta able to traverse the intervening cavity 3x1011 times in 1µsec at the speed of light or once in 3x10-17 sec. For exchanges involving quanta of lower frequency, or quanta exchanged from greater distance, correspondingly more rays of quanta would be

20

Incidentally, such a responsive interaction provides a logical basis for the equality of action and reaction, proposed by Newton. • Exchanges of quanta constantly transfer momentum within the molecular system, in direct proportion to their frequency and the temperature of the molecules; the consequent balanced accelerations when the system is at equilibrium are uniquely dispersive. The frequency of quanta dictates the frequency of concerted impulses felt by particles and determines the rate of change of velocity or acceleration of molecules and thus their temperature. The impulses of quanta act to repel the molecules, by conserving linear momentum, whether quanta are emitted, absorbed or reflected. Such exchanges of quanta are a consequence of the changes in the spatial relations of molecules, their nuclei and their electron shells, providing an efficient cause for the principle of conservation of linear momentum of molecules and larger bodies. Action may be generated (or reduced) in all of the degrees of freedom of motion in molecules, such as translational, rotational, vibrational or electronic, dictated by the strength and position of the impulse delivered to the molecule and the current inertial state of motion. These transfers of momentum act as a repulsive force between the absorbing and emitting molecules, or between groups within complex molecules, that can be illustrated in a manner similar to the Feynman diagrams for exchange forces between electrons and other subatomic particles. In effect, this dispersive force is an essential element of the integrity of the set of molecules at any instant, sustaining its changing morphology and preventing coalescence of the set. Without such thermodynamic exchange forces, it is proposed that their threedimensional structure would collapse.

A set of subsidiary statements, related to irreversible changes in the action state and rearranged chemical states of molecular systems characteristic of non-equilibrium systems follows: • In non-equilibrium systems, changes in the rate of exchange of quanta provide the asymmetric forces by which physical and chemical rearrangements of the threedimensional structure or topology of the molecular set can occur.

required to reverse the motion. For a precise calculation, the generation of such exchange forces must consider all momentum exchanges between the complete sets of the molecules involved in the collision. It can be concluded that such a time-variable exchange force is quite feasible, as a result of the mutual amplification of impulses by resonance. The concluding sentence in Einstein’s (1917) paper, after he had derived an equation indicating the average momentum transferred by radiation to a moving molecule, asserted, “one can, therefore, consider a theory to be justified only when it is shown that according to it the momenta transferred by the radiation to the matter lead to such motion as is required by the theory of heat.” That is, the force delivered by the absorption and emission of quanta is responsible for the momentum (and its associated kinetic energy) of the molecules.

21

Non-equilibrium is characterised by dissonance in quantum states, where quanta are not matched to molecular temperature or there is a gradient in energy density and molecular temperature. By contrast, at equilibrium, the action resonance can be defined as harmonic where the frequency of the radiation matches that of a vibrating or recurrent motion in a molecule. Such recurrent motion could correspond to electronic, vibrational or rotational modes, leading to the absorption and re-emission of quanta correlated with new rearrangements of the action or quantum state of the molecule. Action resonance theory explains that quanta do not mysteriously disappear at molecular absorption, as they may seem to in current quantum theory. Instead, they continue to exist as virtual quanta constantly in motion absorbed in the ground state energy field to reappear when a collision occurs, leading to a rearrangement in action state. They may also be converted to different frequencies (e.g. fluorescence) as part of a cascade of developing action states of lower energy as the energy of the non-equilibrium state is redistributed through the system. Quanta, together with ground state or zero point energy, remain constantly in motion, the quanta transmitting signals as momentum at the speed of light within molecular systems, except at the precise instant of reflective or diffractive changes of their direction of motion. • The total impulse from ground state energy at a given temperature is proportional to the mass of a molecule or its constituent particles. Most of the energy of a system exists in the ground state background, only partly accessible as quanta linked to variations in action state corresponding to changes in the physical or chemical state of molecules. Such quanta can only be detected when a state of non-equilibrium exists using agents undergoing action transitions requiring quanta of the same frequency. A black photocell is a good example of such an absorbing detector for light. Only in nuclear reactions or processes involving the complete annihilation of material particles like electrons is more than a small fraction of this ground state energy detectable. Impulses from the ground state energy are continuously transmitted between molecules but these involve so little energy and momentum that no net change in action state from individual impulses can be detected except for motion generated when an asymmetric field is maintained indefinitely. This continuous background of random impulses could be considered to include the well-known quantum noise of systems containing polarisable molecules. Because most of the volume occupied by molecules is space, energy usually traverses this volume rectilinearly without interaction, passing through to interact with more distant molecules. Moreover, the small proportion of the total molecular volume filled by electrons and nucleons (protons and neutrons) ensures that the mass and interactive surface of these particles for energy are equivalent. So the total impulse received by a molecule from all directions is proportional to its mass and not to the molecule’s superficial area defined as the external surface swept out on a much longer time scale by its electronic shells. It is reasonable that the momentum of the particle (i.e. its mass x velocity) is proportional to the total momentum of the quanta intercepted in a given time – this is a magnitude which also depends on the intensity or space density of the three-dimensional shower of quanta and ground state energy.

22

The temperature of a particular substance depends on the frequency of energy quanta and the capacity to accelerate the velocity and action of molecules, a vectorial or directional property. Pressure, on the other hand, depends on the total number of impulses from quanta on the internal particulate surfaces of molecules per unit time and the density of such surfaces, which amplifies the impulse rate and the energy or heat capacity. Not considering the question of energy transfer between molecules, more quanta of lower frequency corresponding to a lower temperature in a molecular system can exert the same pressure as fewer quanta of higher frequency corresponding to a higher temperature. Equality of pressure merely demands that the total rate of impulse per unit area of surface be equal. • Heating increases the radiant energy density, increasing the action state of each set of molecules present as a result of increased resonant energy exchange as quanta, generating increased torque and increased velocity20 of the molecules. A greater space density of resonant quanta coincident with heating will result in more frequent impulses, momentum transfer within the set of molecules and of the action generated. The energy quanta are readily dispersed between the atoms within molecules and between molecules. All the modes of freedom of motion in molecules ņ translational, rotational, etc. ņ will be excited to higher action states provided the momentum of the quanta is adequate to generate the force required for these transitions. It is proposed that a faster molecule or sub-molecular particle can compensate for smaller interactive surface area or mass by intercepting more impulses from ground state energy in a given time, even assuming that the speed of the particles is insignificant compared to the speed of quanta or light21. The relative velocities of molecules and atoms will indicate the rate at which they traverse action states and thus the required emission intensity and space density of quanta in the action field needed to sustain the molecular set. Conversely, the more rapid the various motions of molecules, the more energy quanta can (and must) be maintained in transit. As an aid to the imagination, consider the direct relation between the speed and surface of motion of the hands of a juggler and the number of objects kept in the air. This number plainly increases in proportion to the speed and frequency of periodic recurrence of the juggler’s hand motions. As a consequence of more excitation of higher energy motion or action in molecules (vibrational and electronic), the peak of the energy spectrum of these quanta and the size of the impulses generated increases as the temperature is increased. At higher temperatures, with more quanta delivering greater momentum to molecules, a greater proportion of the quanta or total energy can be considered as acting inside polyatomic molecules, providing higher internal electronic and vibrational action states within molecules. By contrast, at lowered temperatures in a gas, most of the action becomes external and rotational or translational.

• Hotter, faster molecules will traverse action states and emit quanta more frequently as a result of new arrangements and collide more often. Consequently, 20 21

Velocity has physical dimensions LT-1, being rω or v for an individual molecule. c much greater than v.

23

the average resonant force or torques generated in these collisions must depend on the product of momentum and velocity of the individual molecules. Faster molecules will collide more frequently, proportional to their velocity; force is proportional to the rate of momentum exchange, so the absolute momentum counts. As a logical corollary of the assumptions of the action resonance theory there must be a tendency for the product of momentum and velocity for all molecules to become equal. This provides the traditional force associated with the concept of temperature, measured as the rate of exchange of molecular momentum in collisions. Furthermore, this force will be opposed by the pressure considered as a resonant force exerted by quanta per unit area on internal molecular surfaces or simply as the concentration or space density of radiant energy as resonant quanta22. This force will be exerted as a torque averaged over the mean values generated for numerous couples of molecules. Where the absorptions or emissions of quanta cause changes in action states, the action gained or lost will be equal to the energy of the quantum or work multiplied by the time taken for the transition. Because each set or species of molecule interacts and equilibrates with other sets of molecules through collisions, this tendency for equality of the product of momentum x velocity, or temperature, will become universal for all molecules in a system that has reached temperature equilibrium. This equilibration is possible because of the ultimate transfer of all momentum via quanta all travelling at the same velocity although not necessarily providing impulses at the same frequency. Despite this equilibration, there will be statistical variation in the velocities of molecules according to a normal distribution, as shown by Maxwell and Boltzmann. All the sets of different molecules in the system will also experience the same torque or turning moment from impulses of energy as resonant quanta when at equilibrium. • The action state of the set of molecules at a given temperature varies with the pressure or concentration of the set of molecules. The concentration of molecules determines the mean value for their separation and the path length and transit time of quanta between molecules. Increasing the pressure by isothermal compression maintaining temperature constant reduces the action per molecule, because the radial separation or extension (r) becomes less. In any case, for fundamental reasons associated with the periodicity of motions, probability, collision frequency and the path length of quanta between emission and 22

That is mv x v = mv2 = mr2ω2 = 3kT will tend to become a constant for all molecules. This follows from a simple action dimensional analysis assuming that the mean radiant impulses per molecule equals the linear momentum per molecule; there must be sufficient force generated to reverse its momentum at a wall. Also, the relative frequency of impulses on molecules from quanta (hνi/c) and of molecules on molecules (mv) is proportional to (c±v)/v, their relative speed. Then, for c>>>v, the assumption of equality of impulses from quanta, and molecular momentum means c/v x Σhνi/c = mrω/2 = mv/2 (r is the mean separation between molecules; so r/2 is the radius of action; see footnote 17 introducing the property of celerity); thus Σhνi/v = mv/2 and so Σhνi = mv2/2. Pressure is regarded as the space density of radiant energy or of quanta present in the space occupied by each molecule, i.e. P =Σhνi/r3. Then Pr3 = Σhνi, = mv2/2. Equating 2Nr3/3 = V where N is the number of molecules, we have the perfect gas law, PV = = NkT = RT for N of one mole.

24

absorption or successive reflections, the magnitude of the total repulsive impulses per unit volume from the exchange of quanta varies with the pressure. • The momentum and forces exerted by quanta in ecosystems are characteristic of the ambient temperature. Quanta emitted in the earth’s ecosystems are usually of low energy and frequency (corresponding to quanta normally associated with excitations of vibrational, rotational or translational states), but producing an extraordinarily large number of impulses. These random, resonant, exchanges of quanta23 between molecules provide sufficient impulses to act as a moment continuously altering the action state of each separate molecule with respect to all others. The effect of such random and incessant impulses would be to ensure that the paths of the molecules are non-linear, moving on tortuous trajectories as though space is curved. Where a system is heated above the temperature of its surroundings, radiant energy will be emitted from the periphery of the system as molecules cool, generating quanta of frequency proportional to the temperature. • Each molecule in the system able to fluctuate has a continuous propensity to interact specifically by exchange of resonant quanta with all other molecules of its particular set, generating its chemical potential. This is the logical outcome of the total energy as quanta in the action field spontaneously and continuously redistributing so as to generate the same temperature or torque for every molecular set - but with a unique spectrum of 23

For the future development of action theory, it will be helpful to define more precisely the nature of quanta and energy. From experimental observation of the effects of energy and the general theory presented here, it seems obvious that there must exist a fundamental unit of impulse, which we call the acton. A quantum of energy acting to cause a molecular transition in a system will require a cooperative train of actons of definite frequency and wavelength to be added to those already interacting within the set of molecules. A single acton can deliver reflective impulses at a rate dependent on its speed and the radial separation of interacting primary material particles, such as electrons, protons or neutrons. An action analysis of the hydrogen atom given in the Endnotes/Glossary concludes that the impulse delivered by an acton or set of actons with an effective mass of 7.37 x 10-48 g and an interaction frequency of once per second would be 2.2 x 10-37 g.cm sec-1 (for radial separation of 3 x 1010 cm). A perfectly aligned interaction between an electron and a proton separated by only 5.3 x 10-9 cm (the radius of the hydrogen atom) could then deliver a total internal impulse from this acton mass of 2.49 x 10-19 g.cm sec-1, assuming the transmission rate of impulses is limited to the speed of light. This results from 5.66 x 1018 impulses per sec, from half this number of reflections. Then the emission of a quantum from an excited atom involves a sudden fluctuation in the geometrical orbital of an electron, altering its radial separation from other particles, reducing the separation from the nucleus; this process spontaneously causes the emission of a finite set or train of actons or units of impulse, depending on the change in quantum number. This set, derived from the total energy field, comprises the quantum of energy. These quanta or trains of actons will either be spontaneously absorbed (and exchanged by reflection) elsewhere in the system of molecules, or they will be transmitted through its boundary. In general, in a system at equilibrium, a quantum will either be re-absorbed producing a fluctuation within the system or exchanged with one of the same magnitude from outside the system. Incidentally, such a definition of the quantum clarifies the problem of defining the duration of a photon (a finite sequence of actons). The quantum will be released simultaneously with the collapse of the electron’s orbital, dictated by the classical speed of motion of the electron. The duration of the photon is then equal to the interval taken for the orbital to collapse since the length of the train of actons emitted is determined by this process.

25

quantal frequencies associated with transitions in each different set of molecules. This outcome enables a specific dispersive interaction between each species of molecules, which we shall make future reference to as providing the chemical potential for each set. This positive dispersive interaction between molecules and frequency-specific quanta occurs while the molecules progress on a more or less curvilinear trajectory across the vessel, randomly colliding with resonant quanta and other molecules or the boundary of the system. Thus, the real trajectory of a molecule should be considered as a rapid succession of new action states, reflecting changes in relative radial separation and relative speed with reference to each other gas molecule in the field. Since no molecule is bound to any other in the ideal gas, there is no suggestion that any one molecule is periodically orbiting another. However, in non-ideal gases and liquids, molecules such as water do associate to a degree depending on the temperature. They do this while minimising their action by screening each other from the impulses of the action field and can be regarded as being in curvilinear orbit24 around each other and other molecules in the association, as long as the association is maintained. These basic statements of the action resonance theory lead to certain logical results regarding the physical and chemical interactions of molecular systems. These logical predictions will be examined for consistency with actual phenomena in the remainder of this book, to help test the validity of the action resonance theory. 2.2.2. Calculating action Action is the outcome of the application of force to sets of molecules, a property proportional to the speed of motion by molecules and atoms within a bounded system. Having generated action, the energy from the quanta employed to generate the impulses is paradoxically now essential to sustain it. Thus, the nature of action demands that it must be continuously be regenerated by exchanges of impulses between molecules. More explicitly, the action or energy-time trajectories of atoms depend on the speed of translation of the molecules but also on their rate of rotation and their amplitude of vibration. The greater the speed or frequency of all these motions, the greater and more complex the action surface traversed by all the particles, including electrons, contained within molecules. In general, because of the net effect of impulses from quanta, the individual particles or atoms within molecules will spiral coherently through space, on variable axes with respect to the trajectory of the centre of mass of the molecule. Using mathematics to model all these motions in a system of molecules may seem a formidable task. However, for straightforward reasons based on the principle of conservation of momentum and randomisation of the trajectories of quanta, it is reasonable to conclude that the molecular trajectories are forced to adhere to a minimalisation principle - that of least action ensuring that motion is non-linear and space-time is curved. This favored or most probable distribution of the trajectories of 24

In action resonance theory, smooth orbits corresponding to the shape of conic sections (elliptical, parabolic and hyperbolic – see Endnotes) are considered to be a property of bodies with large inertial mass, whereas the relations between energy and matter in the Brownian motion of microscopic particles, molecules and sub-atomic particles result in trajectories much more uncertain or erratic, because of more frequent collisions and the greater effect of individual quanta on the momentum of particles with low inertia (see Endnotes: Gravitation, Kepler’s observations).

26

motion of the molecules is also consistent with the least possible rate of impulses of quanta on molecules or the lowest average pressure on the molecule. Put simply, the most probable distribution of action states is also concluded to be the most ‘probeable’ spatial distribution of molecules, where the mean free path or probing length for resonant quanta travelling at the speed of light is, on average, the greatest length possible. As a result, the rate of impulses and intermolecular force is minimal. This surprising result is actually derived from the simplest of causes. Any variation in the initial geometrical density of a specific set of molecules, or an injection of new quanta as heat, will automatically generate a local increase in the rate of molecular collisions with a greater rate of exchange and dispersion of quanta. This generates a greater dispersive force in the locality, which automatically accelerates the nearby molecules of the resonant set away from the immediate locality, thus reducing the concentration in this region. Such quantum by quantum randomization of the molecular distribution as a result of action resonance will continue until a minimum level of action is achieved for the actual energy content of the system, when the action resonance is also minimal. The disorder of the initial state of local stress providing a dispersive force is replaced by a more orderly arrangement where the stress is minimal. Characterized by dynamism, achieving the most favored equilibrium arrangement must establish a least-squares geometric distribution of the inertia of both like and unlike molecules in space, within the appropriate statistical limits for such a random process. Although we tend to associate random processes with the notion of blind chance, there is actually nothing more certain than the outcome of such a random process involving many impulsive exchanges between a large number of molecules and a much greater number of quanta. This random process is effected by the agency of the speed-of-light exchange of the impulses from a vast number of quanta, by which each molecule continually forcefully signals its presence and can also sense others, progressively moving towards the least action equilibrium dictated by the current field conditions, one step after another. Fortunately, exact modelling even of the motion of a sub-set of molecules is not necessary for the present discussion. This is because in a system containing very large numbers of molecules, all possible states of motion (speeds, geometric orientations) will be present at once according to a statistical distribution and we are more interested in the average values in such stochastic processes. Then for large numbers of molecules, it is possible to calculate a statistical time-averaged radial separation of each molecule from all neighboring molecules in the set. An angular velocity25 can then be established for each neighboring couple of molecules of a particular chemical species; in principle, a statistically averaged, one-dimensional translational action26 can then be calculated for each set of molecules of a particular chemical species. Action can be considered as being continuously generated and sustained in a set of molecules as the product of impulse (from quanta) and the radial separation or range of separate molecules. Since the physical dimensions of action involve an inertia term that only allows the square of the separation to vary27, the plausibility of the principle of least action where the sum of the squares of the radial separations between molecules is minimal becomes more obvious. It seems, then, that trajectories of Angular velocity = dθ/dt=ω. One-dimensional action,@ = mr2ω = mrv. Change in action = Σhνi/c(impulse) x r = ∆mr2ω. 27 Inertia, I = mr2; Σmr2 is minimized when all r is the same, with an even distribution of molecules. . 25 26

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molecules are automatically plotted locally using the minimalising principle of least squares to produce maximum separation of molecules and least physical stress from impulses. Temperature28 now appears not only as the linear or rotational kinetic energy of molecules but also as the continuously sustained average product of the rate of impulses from quanta or force and the radial separation of molecules, better known as torque. This viewpoint is justified because, although the trajectories of molecules may appear independent of one another, in fact the action resonance field generates radial inertia in all molecular couples and internal work from the random impulses of quanta is necessary to separate one molecule from another. An equality of kinetic energy and torque is the result. All of these relations between force and momentum, action and kinetic energy, torque and temperature are consistent with classical physical theory based on simplified two-dimensional coordinate systems. Neither approach need be considered as being in conflict with the other. However, recognition that reality in action space is always a four-dimensional manifold (including relative change or time) and that the motions or velocities of real molecules are never truly independent or ever linear, except from one impulse from actons to the next, is obligatory in action resonance theory29. Furthermore, one must consider field energy as impulsive quanta delivered from an infinite potential range of directions as inherent in the system. The kinetic energy of matter involves the outcome of an intimate complementary relationship where the momentum of energy is forcefully opposed in the spatial matrix to the momentum of matter, taking into account the effect of screening on impulse rates. For conservative systems, the kinetic energy of particles or bodies is generated partly by the screening potential of other molecules or bodies, reflecting an escaping tendency of matter from the impulses of energy. In this equal and opposite relationship between matter and energy, hitherto not regarded as mutually dependent, the huge difference at normal temperatures in the relative velocities of radiant energy (of invariant velocity) and of the particles of matter (c/v) allows continuous detailed balancing between the relative impulses that each substance can deliver. In principle, the assumptions of the action resonance theory provide the logical basis for the absolute calculation of particular action states and the geometric determination of the magnitude of the quanta necessary to achieve transitions between different action states. The relative changes in action state with changes in the temperature and volume of a set of molecules can readily be determined. Examples of such calculations will be given later in other publications, when the thermodynamic 28

Σhνi/c = impulse; Σhνi/cδt(force) x r = mrω2 x r (torque) = mr2ω2 (2 x kinetic energy). Thus the physically real model of action resonance infers that inertial force does not arise solely from an innate tendency of bodies in motion to continue in a straight line, as in Newton’s definition of inertia. Motion in a straight line is only maintained between one impulse and the next and the body will experience either smooth or erratic motion as the outcome of a dynamic staccato of impulses from quanta from all directions, to which the body must be completely responsive offering no inertial resistance whatsoever. This analysis almost invariably dictates a non-linear or curved trajectory for all real objects. Indeed, without carefully directed impulses to maintain a rectangular inertial guide, straight line motion must always be considered an unattainable abstraction, even if a stationary reference point to define it could be specified. In an action field at equilibrium with no net redistribution of energy content occurring, the actual inertial principle must now be the conservation of action or scalar angular momentum as a result of the overall effect of all the impulses being continuously received from the field. The conservation of linear motion and thus of linear momentum cannot be valid except for brief time scales of less than 10-22 seconds, or as a mathematical abstraction using stationary but fictitious coordinate systems as means of reference. 29

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consequences of these assumptions have been developed. It will be shown that these consequences are consistent with classical and modern viewpoints, although new content will emerge from the theory. Dimensional analysis of action as the product of mass, linear extension or radial separation and velocity of a monatomic gas shows that heating a system of molecules at constant volume will increase the action in direct proportion to the increase in speed or velocity30 of the molecules. This follows since neither the mean radial separation nor the mass of the molecule can change on heating at constant volume, at least in the case of non-relativistic velocity. Thus, the only variable31 with change in temperature is the frequency of oscillation. From the kinetic theory the temperature is proportional to the square of the velocity of the molecules. During heating, infra-red radiation (heat) as photons can be considered as providing the source of the primary impulses required to increase the action/quantum state of the set of molecules, producing their greater mean velocity. Thus, doubling the one-dimensional action of a monatomic gas such as argon will require raising the temperature by a factor of four. Increasing the volume of the same system at constant temperature will also increase the action32. This results from the direct proportionality of action on the mean radial separation of molecules in the set. In three-dimensional terms, the volume is directly proportional to the action. Thus, changes in both temperature and in volume (or concentration), key properties governing the thermodynamic properties of a molecular system, can be generalized as changes in action. It will be seen in Chapter 3 that this allows a logarithmic correlation to be made between entropy and action. This important relationship provides the basis for the claim made in this book that the property of action enables the linking of quantum theory and thermodynamics. Obviously, changes in the action of a system are related to differences in energy, since the internal energy content (as resonant quanta) is a measure of the rate of change in the system’s internal action. Because action varies directly with the frequency of oscillation of matter and energy varies with the square of the frequency, this definition infers that the marginal requirement for energy will diminish as the action increases to large quantum numbers. This is well illustrated in the quantum theory for atoms like hydrogen, discussed in the Endnotes/Glossary. Alternatively, action can be considered as the product of energy with time. It is important to recognize that the change in action during a molecular process is not directly proportional to the change in energy or the work done on a system. The quantity of action generated depends on the linear parameters of the system being acted on as well as the size and rate of impulses. In this book it is asserted and will be illustrated from case studies that action is as relevant to the function of ecosystems as energy. Understanding the significance of action for biological systems is derived initially from current concepts of biophysics and biochemistry. However, as a result of the operation of natural selection in evolution, we anticipate that biological systems will have developed a highly 30

Action (mr2ω) at constant volume (r = constant) can only vary with ω unless there is chemical change; according to kinetic theory, kinetic energy = 3kT/2 = mv2/2=mr2ω2/2 ; thus T= mr2ω2/3k and three-dimensional translational action, @3 is proportional to ω3 and therefore increases proportional to T1.5. 31 I = mr2 is constant with changes in T at constant V; thus @ varies with ω and kinetic energy or T vary with ω2. 32 rω or v (on average) is constant at constant T; therefore changes in @ = mr2ω will be proportional to r=V0.33 and @3 will be proportional to V.

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discriminating “appreciation” of the nature of the forces acting at the microscopic level, and of how to best exploit their physical impulses to do biological work. 2.3. Brownian movement as action resonance In 1827, Robert Brown (botanical assistant to Sir Joseph Banks, the president of the Royal Society and colleague of the Pacific explorer James Cook) first described the erratic but incessant movement of microscopic pollen particles suspended in water. He soon proved that the motion of the pollen grains he examined was independent of whether the particles were living or dead, dispelling any notion that this remarkable, continuous, movement could be ascribed to any vital force. The idea that the movement was a result of natural, molecular agitation, a function of temperature, was slow to emerge. According to Perrin (1909), Carbonelle around 1877-1880 was the first to suggest a thermodynamical origin to the Brownian movement, pointing out that particles of very small area might exhibit irregular motion from molecular collisions “because the law of large numbers no longer leads to uniformity.” Gouy (1888) went further, suggesting that no other cause than spontaneous molecular agitation could be imagined. He showed that the cause of motion could not be attributed to vibration of the preparation, convection from heating or the source of illumination, since the motion was undiminished while the light intensity was reduced a thousand-fold. Some opposed the idea of Brownian movement as possibly contrary to Carnot’s principle and the second law of thermodynamics stating that thermal work cannot take place in the absence of a temperature gradient. It was surprising to many to discover a form of motion, presumably subject to friction, that was nevertheless perpetual and required no added energy. However, from the experimental evidence, it is obvious that every fluid is formed of elastic molecules that are in a constant state of motion. There is no need for the input of additional energy, as long as the fluid is maintained in surroundings at the same temperature and any frictional loss of energy in collisions is perfectly reversible within the system. Today, we take the existence of molecules as distinct material entities for granted. However, the study of the Brownian movement early in the twentieth century proved to be a persuasive tool in the confirmation of molecular reality at a time when the alternative idea of matter as a continuum of energy was also strongly entertained. Included in his landmark publications of 1905-1906, Albert Einstein recognized the thermodynamic significance of Brownian movement and provided a theory and mathematical treatment for both Brownian translation and rotation that lent itself to experimental testing (and possible refutation in the sense advocated by Karl Popper). Einstein (1905) stated, in his clear prose “In this paper it will be shown that according to the molecular-kinetic theory of heat, bodies of microscopically-visible size suspended in a liquid will perform movements of such magnitude that they can be easily observed in a microscope, on account of the molecular motions of heat. It is possible that the movements to be discussed here are identical with the so-called Brownian molecular motion.” He proposed that microscopic particles, even though they were much larger than gas molecules, would produce an equivalent osmotic pressure on a membrane impermeable to the particles as a gas at the same concentration if the particles are confined by the membrane to one region of the solvent. Further, he stated that an

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equilibrium between this osmotic force exerted on such a membrane by collisions of the particles and a separate thermodynamic diffusion force exerted on single particles would be established33. According to Einstein, the condition of dynamic equilibrium existing in a confined volume results from “a superposition of two processes proceeding in opposite directions”. These were a movement of the suspended material under the influence of the thermodynamic force, acting on each single suspended particle. Secondly, there was a process of diffusion, which is to be looked upon as the result of the irregular movement of the particles produced by the thermal molecular movement. Equating these processes then enables us to calculate the diffusion coefficient. Einstein realised that the instantaneous velocities of Brownian particles from individual collisions, which should, in theory, have kinetic energy equal to that of colliding gas molecules at the same temperature, could not be measured directly. Nevertheless, the mean net displacement of a particle at various time intervals could be estimated and checked by experiment34. In 1906, Einstein extended his analysis of Brownian particles to determine how light in weight a particle must be to remain suspended in a fluid in spite of gravitation35. The distribution of Brownian particles in the gravitational field was exponential, similar to the exponential barometric distribution of gas molecules in the atmosphere proposed by Laplace. He also dealt with the Brownian rotation of spherical particles36, introducing the idea of a moment (providing a torque) that acted on the particles inducing rotation. In the action resonance theory, such a moment would correspond to the resonant absorption or emission of quanta carrying momentum, causing rotational repulsion of the spherical particle. Following this mathematical analysis, Einstein observed that “the angular motion produced by the molecular motion decreases therefore with increasing r much more rapidly than the progressive motion.” This indicates that rotational action compared to translational 33

In his mathematical treatment of Brownian movement, Einstein introduced the idea of the intermolecular thermodynamic diffusion force, K; then -Kυ + RT/N.∂ υ/∂x = 0, or, Kυ - ∂p/∂x = 0, where υ was a reduced volume (the inverse of the volume per particle) and ∂p/∂x an osmotic pressure gradient in direction x. Then, if the particles suspended in a liquid of viscosity η have spherical form of radius r, the thermodynamic force K imparts to the single particles a velocity v = K/6πηr and there will pass a unit area per unit time vK/6πηr particles. If, further, D signifies the coefficient of diffusion of the suspended substance, and µ the mass of a particle, as the result of diffusion there will pass across unit area in a unit of time, -D∂(µv)/∂x grams or -D∂v/∂x particles. Since there must be dynamic equilibrium, we must have vK/6πηr - D∂v/∂x = 0, (RT/N.∂v/∂x.(1 /6πηr) = D∂v/∂x). We can calculate the coefficient of diffusion (D) from the two conditions found for the dynamic equilibrium. We obtain (by elimination in the above), D = RT/N(1/6πηr). All of these terms can be recast in terms of the action resonance theory using dimensional analysis. Thus, D has dimensions of r2ω, corresponding to radial separation times velocity. The larger the radial separation for a given velocity (r, rω ), the greater D. This seems logical, in view of the flatter trajectory at greater r. For molecules of different mass at the same temperature, r2ω and D varies inversely with m0.5, because mr2ω2 is constant at T. Viscosity has dimensions of mrω/r2 (momentum transferred per unit area). 34 Einstein derived an expression for the distribution with time for diffusion outwards from a point source of n particle (x, t) = n/√(4πDt) x e-x(exp)2/4Dt ; and the root mean square displacement in time t is √x2 = √2Dt. An alternative interpretation of the distribution equation is that it provides an estimate of the probability of finding a particular particle at displaced to x at time t. 35 From this dW = C e-m gδh/kT. 36 Einstein proposed a moment D acting on a sphere of radius r, mounted so as to be capable of rotation in a liquid of viscosity η, would rotate the particle with angular velocity ψ = D/8πηr3, and then (α2) = tRT/N4πr3 where α is the angular displacement at time t.

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action becomes much more noticeable as the size of particles is decreased. Einstein concluded his paper with the wish that some experimental scientist would soon provide data to test his theories regarding Brownian movement. This challenge was soon taken up. To test Einstein’s relationships for both translational and rotational Brownian movement, the French scientist Perrin (1909) obtained data from microscopic observations of size-graded natural latex particles from Vietnam, suspended in water. The data were entirely consistent with Einstein’s theory, for Brownian translation and rotation and for the distribution under gravity; this enabled him to produce excellent estimates for that time of Avogadro’s number, the number of molecules in one mole of a chemical substance. So impressed were scientists of the day with his confirmation of molecular reality that Perrin was soon awarded a Nobel Prize, well before Einstein himself was awarded one in 1923 for his 1906 work, not on Brownian movement but on the photoelectric effect. 2.3.1. Brownian movement as a thermodynamic force In terms of the action resonance theory, the thermodynamic force invoked by Einstein in his derivation of the diffusion coefficient would play the same role as the force exerted in the action field, caused by quantum exchange interactions. In a system at thermal equilibrium without gradients in chemical potential, these quantum action exchanges must involve reversible transitions and at ambient temperatures in ecosystems, these would be restricted to changes in action state involving translational, rotational or vibrational motions of the particles. It is implicit in action theory that all relative changes in position of individual pairs of particles must involve quantum transitions, as the relative trajectories of particles change as a result of random exchange processes. As stated above, at ambient temperature, such quanta would necessarily be small in magnitude, both in energy and momentum and in the strength of the impulses. However, as a result of resonant reflection, the intensity of impulses from the action field each molecule or Brownian particle is subjected to would be correspondingly large. Resonant exchanges of the same quanta provide amplification of the force exerted. As indicated above, collisions between the particles including those with solvent molecules are held to be especially active in stimulating emission of quanta from the local field, each emission or absorption providing a recoil. These exchanges correspond to frictional processes. However, they are clearly reversible, since the Brownian processes can continue indefinitely. A system of Brownian particles in a heat bath has no energy flow across its boundaries and no net work can be done by the system. Nevertheless, the action resonance theory does require that one region of the system is able to do reversible work on another region and vice versa. So the disappearance of a particular action state at one locality (i.e. the emission of a quantum) is matched by the appearance of another action state by the absorption of a quantum elsewhere in the system, involving alternative states in like particles only. It is interesting that such a real force derived from fluctuations in the action field of the same type proposed by Einstein to induce Brownian movement as highlighted in the quotation at the beginning of this Chapter has been considered unnecessary. Indeed, the thermodynamic diffusion force proposed by Einstein was later referred to as “a fictitious force” in the notes on Einstein’s papers prepared by Fürth, quoted in the Dover translation made by A.D. Cowper (1956), and alternative statistical derivations of the diffusion coefficient has been preferred. The molecular-kinetic theory for gases and liquids has considered the heat energy of the system to be totally

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contained in the kinetic energy of the molecules or particles. Collisions of molecules have been considered simply as elastic processes conserving momentum and energy without needing quantum theory to explain them. Here, it is proposed that sustaining the kinetic energy and pressure of a system of particles requires the exchange forces produced by fluctuations in the action field as an essential complementary feature. Inequalities in these forces also provides the essential mechanism for all changes in their action or quantum states. For example, if the temperature of the system is increased from an external source of thermal radiation to a new equilibrium value, the kinetic energy, the action and the entropy of the system of particles will necessarily increase simultaneously, depending on the heat capacity of the particles. That physicists have traditionally dismissed the need to consider such quantum exchange forces is no more emphatically put than by Schrödinger in his book What is Life?. For the non-equilibrium irreversible phenomenon of diffusion of potassium permanganate down a concentration gradient in water, he made the following comment. “The remarkable thing about this simple and apparently not interesting process is that it is in no way due, as one might think, to any tendency or force driving the permanganate molecules away from the crowded region to the less crowded one, like the population of a country spreading to a region where there is more elbow room. Nothing of the sort happens with our permanganate molecules. Every one of them behaves quite independently of all the others, which it very seldom meets.” Schrödinger then provided a purely statistical argument for the greater rate of diffusion of the permanganate molecules from the higher towards the zone of lower concentration. Ironically, the book What is Life? was written to emphasize the role of the quantum theory in living systems. The author went to great lengths to indicate a role for quantum processes in evolution and proposed a key role for quantum fluctuations in the mechanism of mutation of genes. He went so far as to proclaim that the order from order principle in biology was the result of a “new physical principle”, but then pointed out that this was “nothing else but the quantum theory over again”, implying that it might be applied much more widely. We completely agree with this statement of Schrödinger. However, just why he thought the quantum theory should not be applied to Brownian processes and that a kinetic and statistical theory without the benefit of his quantum ideas should be used instead to explain diffusion is a mystery. Perhaps the too harsh application of Ockham’s razor prevented Schrödinger from making this small but “quantum leap” of the intellect. 2.3.2. Action fluctuations, exchange forces and statistics Let there be no misunderstanding of exactly what is being proposed in the action resonance theory. Contrary to what Schrödinger said, an internal, temporarily irreversible force causing the net direction of motion of the permanganate molecules towards zones of lower concentration is definitely being proposed in the action resonance theory. Apparently, as discussed earlier, Einstein proposed an analogous force in considering Brownian movement and his analysis of crystal structure and heat capacity also has overtones of a dispersive force field associated with quantum states. The force results from the recoil of reversible quantum fluctuations in the action states of the molecules. Obviously in a diffusion gradient, the action resonance force would be diminished in the direction of lower concentration, because of the lower intensity of the action field there. Furthermore, it is asserted that without such quantum

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exchange forces derived from the action field, the molecules would not need or be able to move or change direction at all. Statistical mechanics is held, admiringly by some, to allow derivation of all the main results of thermodynamics without the need to refer to the physical nature of molecules at all. The metaphysical significance of this remarkable result has seemingly escaped most scientists during most of the 20th century. Such success must mean that this theory applied to “statistical” particles includes assumptions about statistics that rely on the real physical properties of particles. One must remember that all experimental tests of statistical theory rely on physical methods that involve forces between molecules, from the use of colored marbles to that of computers. Indeed, the use of mathematics without a testable physical model has no ultimate power to provide evidence about nature because all of its conclusions must be determined by the initial assumptions and should be considered as tentative. One could therefore be excused for being suspicious of physical theories that rely on mathematics alone or even that allow conclusions to be drawn that do not accord with common-sense and experience. The apparent reversibility of time inherent in Newtonian mechanics is one such conclusion37. Others have accepted that atoms exist and then have sought statistical thermodynamical conclusions based on microscopic models by trying to obtain solutions of the Newtonian equations of motions for a system of particles with an enormous number of degrees of freedom (Buchdahl, 1975). Although this analysis has made some progress, at least in mathematical terms, it can hardly be held as having succeeded in providing a dynamical model consistent with the conclusions of classical thermodynamics, let alone non-equilibrium thermodynamics. We suggest that the time invariance of Newtonian mechanics provides at least one insuperable barrier to ultimate success in these attempts, as well as the lack of dependence of the magnitude of forces, both internal and external, on time. We will show in detail elsewhere that the forces of action resonance fluctuate locally at the molecular level with time, since they are most strongly elicited in collisions. Furthermore, the theory can only allow a positive direction for time, from the past to the future, consistent with the fact of irreversibility of sub-microscopic processes. However, statistical mechanics might still succeed were it to correct these deficiencies, by allowing the existence of quanta carrying momentum, opposed to that of the molecules. In this connection, it may prove significant for future theoretical developments that the product of the dynamical variables of phase space employed in this analysis is usually given the physical dimensions of action (p x q, momentum x position coordinate). The contours in phase space represented by a set of rectangular hyperbolae would indicate different states of action, each contour line separated in magnitude by the fundamental unit of Planck’s quantum of action, generated by the addition of the speed-of-light impulses of one quantum. 37

The so-called time-invariance of Newtonian mechanics suggests that any irreversible process such as the diffusion of permanganate down a concentration gradient can be reversed in time, just as a movie film of diffusion run backwards would show the color concentrating in one region, rather than smearing out as is always observed by humans. In this context it is of interest that from an analysis of the quantum exchange forces of action resonance in a complex molecular field it is easy to show that such reversibility is not allowed (I. Kennedy, unpublished), unless one violates the principles of momentum conservation and of least action. One concludes, therefore, that our common-sense impression that time can only flow towards the future is correct and that the set of mathematical assumptions involved in Newtonian mechanics was incomplete. Thus, the direction of time’s arrow from the past to the future has a simple physical basis in action resonance.

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True, the quantum theory of the 20th century was initially based on a physical model and the results of experiments obtained from studying the spectra of heated atoms such as hydrogen. The simultaneous use of mathematics in quantum mechanics, agreeing with experiment, is thus soundly based. Obviously, quantum theory should be applied wherever possible, since its results are based on the observable physical properties of particles, even when these properties seem surprising. But the mathematical development of quantum mechanics has also become more formal (Popper, 1982), less and less dependent on a realistic physical model, even with strong warnings about the danger of accepting electronic orbitals as corresponding to real orbits of particles. The inability of quantum mechanics to deal with much more than simple molecules has also severely curtailed its potential application to ecosystems. Is it being too bold to suggest that, despite its undoubted success in correctly predicting the spectra of many elements, quantum mechanics is now being held back by some incomplete initial assumptions? If so, action resonance theory, a new kind of statistical mechanics cum quantum theory that stresses the unique role of dispersive exchange forces between molecules, even when behaving ideally, may prove superior for ecosystems. To do so, it must subsume the best outcomes of both these earlier theories in its own predictions. Only the further development of the new theory, still at an elementary stage, can provide a fair trial, although its basic statements can be examined now and compared with experience. To stress the difference in philosophy between action resonance mechanics and classical statistical mechanics, a strong metaphysical assertion is made at the outset that statistics and probability theory only have validity for explaining the real world because action resonance forces are always present in real systems, guiding the physical trajectories of molecules even at systems at equilibrium. Only in the case of a symmetrical set of atoms, such as the noble gases like helium, neon and argon, will the force fields of action resonance appear random. Asymmetry38 in the structure of most other molecules has the propensity to generate asymmetric fields, since field shapes and directional intensity will reflect the shapes, screening effects and dynamic response on collisions of the molecules themselves. In this case we may conclude that the asymmetric structure of molecules is a source of information leading to non-random effects, even affecting the preferred direction of motion of molecules. That action resonance forces are ubiquitous and involve impulsive exchange forces mediated intermittently by energy quanta and by ground state energy between such molecules (until now, may we suggest, acting as a hidden 38

Part of the early genius of the 19th century French chemist, Louis Pasteur, who later established microbiology, was his recognition that tartaric acid, a product of wine-making, had stereoisomeric asymmetric forms. These asymmetric molecules both have exactly the same chemical composition but different optical activity allowing their solutions to rotate the plane of polarised light in different directions. Pasteur showed they also formed crystals with unique symmetry. He postulated that certain molecules, as a consequence of the geometrical arrangement of their constituent atoms in space, were optically active and that such molecules could not be superposable on their mirror images (i.e. they must be dissymmetric). Pasteur postulated further that the molecules of an optically active substance must be superposable on the mirror images of the molecules of the enantiomorph of that substance. So the enantiomorphs, dextrorotatory tartaric acid (as an analogy, equivalent to a right-hand glove) and laevorotatory tartaric acid (analogous to a left-hand glove) are mirror images of each other, but neither can produce a mirror image of itself. Since Pasteur’s time, an important role for asymmetry has been shown in biology, since organic molecules in living cells such as amino acids, organic acids and nucleic acids such as DNA are asymmetric and optically active. In future publications, these phenomena will be extended using action theory, allowing their information content for biology to be explained.

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variable in quantum mechanics) is made as the prime foundation statement of this new-born discipline. 2.3.3. How can work be done if all sets of molecules equilibrate at kT? The reader may still feel that a Brownian system, even if endowed with internal forces derived from the action field as impulses of quanta, is of limited interest. After all, these forces are reversible when expressed in a system at equilibrium. No work seems possible since all sets of molecules in the system have the same average kinetic energy. Furthermore, the total internal forces even at the boundary of the system are in equilibrium with similar forces directed onto the boundary by sets of molecules in the surrounding external system. This follows from the equality of the product of pressure and volume39, derived from the conclusion of the kinetic theory that the kinetic energies of all kinds of molecules are equal, specified by temperature. This equilibrium at the boundary is independent of the particular kind of molecules. From action resonance theory, one can infer that the product of momentum and velocity of molecules will, on average, be a constant. The condition for equilibrium of a system comprising a number of different sets of molecules such as those in air is that all molecules in the system, within a statistical range and always conserving momentum in individual molecular collisions, will have the same capacity to do work. If one set of molecules has a lower capacity to do work - that is, it was recently mixed into the system at a lower temperature – it will gain momentum and velocity, as a result of collisions and action resonance, or the principle of equal action and reaction. The hotter sets of molecules will cool slightly as a result of losing some of their individual momentum. During the equilibration process, one set of molecules through its action resonance field will have done work on the other set so that the action resonance fields are now equilibrated. This occurs when the energy of the action field (and thus the momentum of the associated quanta) per molecule is the same. But when all the sets of molecules have now on average the same temperature this equilibrium seems to rule out the possibility of particular sets of molecules doing further work, either internal or external such as expansion work. This is true of the individual molecules of a closed system, such as the scientist’s experimental flask, where none of the molecules can cross the boundary and all return to the body of the system. But in the real world, processes take place in open systems, where molecules may cross boundaries into regions where their action state and associated field energy are often different. A molecular reflection at an impermeable boundary does not involve a change in action, since action is independent of direction. Only when there are changes in the action state and field energy of the system, such as when one molecule of a set passes through a boundary, or during a general expansion, or when molecules rearrange into different molecules, can a work process take place. This is because such transitions in action state across such gradients will either release or absorb a quantum of field energy sufficient to allow work to be done. The basis for this lies in the final statement of the action resonance theory given above in this chapter, which proposed that a specific force field related to the chemical potential of a molecular set exists. This critical factor, which makes life possible, will be examined in more detail in Chapters 4 and 6.

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PV = nRT ; for one molecule, PV/nN = kT = mv2/3 or mr2ω2/3.

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2.4. Action versus energy and work Living systems, through the expression of their genotypes, explore and exploit the environment in order to grow and reproduce. As a result of an indefinite series of adaptations to their environment, they gradually optimize their ability to exploit physical and chemical sources of work potential. These adaptations, acting through the random processes of mutation in genes, simultaneously match changes in the environment and select the fittest combinations for amplification in the replicating genetic code. These successes are achieved by the complex, re-iterative, process of biomolecular evolution, acting through natural selection of variants. What is the essential nature of these biological solutions? In fact, life demands the synthesis of coupling agents that can trap and exploit sources of work or action potential and direct flows of molecules into new products with the needed properties. The primary source of action on Earth is sunlight - a continuous stream of quanta carrying momentum, able to provide significant impulses in the photosynthetic apparatus. Ecosystems as living systems are obviously dynamic, although this is true of all systems, animate and inanimate. Their activity is expressed under the normal thermodynamic restraints of all real systems. Various principles of physics and chemistry constrain the outcome of the genotype x environment interaction and the productivity of ecosystems. Clausius’ statement of the first and second laws of thermodynamics - “the energy of the world is constant”; “the entropy of the world increases to a maximum” – it would seem, must be obeyed40. However, a better understanding of the nature of these laws is needed, particularly for an everyday world with many non-equilibrium processes. While no new life force is needed to explain the ecological richness of rain forests or the complexity of human civilization, a general concept that can integrate the total outcome of the forces functioning in complex ecosystems would be valuable. It is proposed here that the action resonance theory can provide this integration. In physics and chemistry, the greatest reliance has been placed on energy as a primary quantity of significance. The first law of thermodynamics41 regarding the conservation of energy as heat or work has been of undeniable guiding value in science. This law of conservation of energy, was first clearly stated by Helmholtz in 1847, following clarifying statements by Carnot and Mayer. There are no direct proofs of the law but since it accords with most human experience it is generally accepted; indeed, the law is supported by the inability of many experimental tests to disprove it. Despite its importance, as a means of explaining the functional properties of life the role of energy may have been overestimated. Rarely is its use more than weakly informative of mechanism in biology. The most valuable phenomena in biology, of the highest significance in ecosystems are often only very weakly related to their energy content. Instead, we shall make the case that the decisive factors in ecosystems are often more directly related to the judicious and efficient use of energy to smoothly generate action than to the magnitude of energy itself. The concept of 40

Some may prefer more humorous expressions of these laws such as “you can’t win”, “you can’t even break even”, and for the third law indicating that only a perfect crystal at absolute zero K, has no disorder or entropy, “abandon all hope of achieving order”. 41 st 1 Law: ∆E = q – w; E = energy, q = heat, -w = work.

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action resonance, where energy is continuously recycled by resonant threedimensional exchange of quanta, thus sustaining a system by “static” internal forces, compared to the directed forces involved in the one-off absorption or emission of radiation, introduces a new way of thinking about energy. Furthermore, the hypothesis is advanced that these action exchange forces are a primary source of order in living systems, generated non-randomly as a result of the asymmetric nature of biological molecules involved. It will be up to the reader, by relating action to their own interests, to decide the validity of this new way. 2.5.

Aesthetics and resonant action

In contrast to energy, action is more readily perceived by our human senses, primarily by sight or sound but reinforced by the effects of inertial and other forces associated with changes in states of action of human movement. Thus understood, action is obviously not restricted merely to the motion within molecular systems, but can appear at all other physical scales. It can be recognised in the relative motions of larger complexes made up of molecular systems, living cells and communities of organisms. Or of macroscopic assemblies of molecules in fluids (e.g. vorticity in water or in global air masses or in circulating gases on Jupiter) and of microcomplexes of particles at the subatomic level (e.g. the Bohr model for interaction of protons and electrons in the hydrogen atom). Any alteration in the relative mobility of complexes in a system, both internally and externally, merits inclusion in action theory. Whenever directed impulses result in a change of the state of motion and energy of bodies at any scale, changes in the action state of a system are involved. Consequently, the action model should extend smoothly across the boundaries of scale, allowing its concepts to be applied universally. An aesthetic quality derives from action. This quality may dismay scientists who prefer a strictly operational approach to scientific problems. As mentioned, some scientists have considered it a virtue that the main conclusions of classical and statistical thermodynamics, for example, can be made mathematically without any reference to the internal properties of systems of molecules. However, the biothermodynamics of action to be developed in this book will reject as an adequate guiding principle this operational, or instrumentalist approach - as Karl Popper (Popper, 1982, p. 102) has critically described it. Instead, Popper clearly prefers theories that are not only instruments, but which can also attempt to describe and explain physical reality, citing his friends and colleagues Albert Einstein and Erwin Schrödinger as strongly favoring this approach. The benefits of this realistic approach are many. For example, it will be suggested that deviations from ideal gas theory may become readily explicable when using an action field theory. Action theory not only attempts to describe physical systems as a means of prediction, but can also explain them. Further, the behaviour of molecular systems at high density and their thermodynamic properties may be better understood when the mutual screening effects of molecules on the resonant momentum exchanges of the action field are considered. In addition, a more highly physical interpretation of entropy to be explained in Chapter 3, made possible by its close links to action, could provide a strong stimulus to innovation in subsequent developments of action thermodynamics.

38

Understanding the impact of certain aspects of human activity that are considered aesthetic, such as the appreciation of art and the act of listening to and appreciating music, may also require action resonance – as outcomes of the transmission of intermolecular forces by quanta. The action resonance theory extends the kinetic theory, by recognizing that resonant quanta of energy are an integral cause of action in all molecular systems. The very success of the quantum theory justifies the general inclusion of energy quanta as a coherent aspect of molecular systems, comprising the zero point energy plus the integral of the heat needed to achieve the temperature of the system. The resonant impulses from these quanta on the nearby material surfaces of molecules (electrons and nuclei) provide a variable dispersive thermodynamic force, generated particularly strongly during collisions, able to sustain the action and kinetic energy of a system of molecules. The fundamental principle of conservation of linear momentum provides the basis for these intermittent intra- and inter-molecular forces, that act to sustain the internal and external integrity of individual molecules and the dynamic morphology of sets of molecules. Molecules are now seen as put in motion or halted by impulsive exchanges of quanta and as also deriving their current inertia from such dynamic exchange forces. Inertia in action theory is the cumulative effect of impulses, not as an inherent property of matter, but continuously generated by energy. Quanta spontaneously adapt themselves by screening to molecular environments, providing a distribution of specific frequencies for each molecular set, tending to generate the same temperature (or torque) for all sets of molecules in the system. All these proposals may seem novel, but Einstein clearly explained their basis almost a century ago, in part of his work that has been strangely ignored. By contrast, the classical kinetic theory of Maxwell implied that ideal gas molecules should not interact. Because this is demonstrably untrue, even for the noble gases such as helium, neon and argon, the van der Waals’ attractive forces were introduced to describe the behaviour of real molecules, except at very short separations when dispersive or repulsive forces between the electron shells were found to predominate. Any radiant heat energy added to a system was regarded as completely absorbed by the increased kinetic energy of molecules. The forces between molecules were considered to be dependent on static electromagnetic properties of their particles, continuously exerted and attractive in nature. While momentum was regarded as conserved in collisions between molecules considered as hard spheres, no microscopic mechanism was given to explain the change in motion. Action resonance theory provides the efficient cause for these changes in motion and electromagnetic forces and the polarized distribution of protons and electrons are considered as the net result of the dispersive exchange forces exerted by quanta, under the influence of screening, rather than the cause of attraction. In the action theory, radiant energy is continuously required to sustain the kinetic energy at the equilibrium temperature. Attraction itself is always considered to be an illusion, resulting from the net effect of screening of molecules from direct impulsive interactions with the energy of the rest of the system, thus reducing the total quantity of resonant radiant energy needed to sustain the system at a given temperature. In a system at equilibrium, molecules naturally follow trajectories that minimise the rate of impulsive interactions, providing constant least action and the least energy content of the system. Furthermore, during transitions from one action state to another, or during nonequilibrium processes, the system will spontaneously seek a least action route to the extent that this is available. Such a result occurs because forces are dependent on the

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distribution of matter and those between molecules determine that their states of motion are in constant opposition to each other. This new general theory, though very comprehensive and naturally complex in nature, actually requires far fewer arbitrary assumptions, providing a simple mechanism for the generation of forces, the relative motion of molecules and their inertia. Since changes in potential energy can now be set equal to the sum of radiant energy and kinetic energy, it also provides a logical basis for the first law of thermodynamics of the conservation of energy42. In the next two chapters, we shall show how the action resonance theory just as readily explains the second law ņ showing the availability of energy to do work.

42

For conservative equilibrium systems, action theory predicts that: U = mc2 – mv2, where U is the absolute potential energy. Then -∆U = ∆mv2 = ∆mv2/2 + Σhνi. Thus, the change in potential energy (∆U = -∆mv2) is equal to the change in kinetic energy (∆mv2/2) plus the change (emission or absorption) in radiant energy (Σhνi), regarding emission from the system as a negative change in its potential energy. The radiant energy has formerly been called the total energy.

7KLVSDJHLQWHQWLRQDOO\OHIW blank

41

ACTION AND ENTROPY

Impulse lines, radially emanating from stress centres, etched into cooling agar on a microscope slide, indicates the magnitude of the forces exerted during cooling, desiccation and contraction of systems containing macromolecules. These lines, magnified here about 200 times, are reminiscent of the paths of elementary particles from particle disintegration in cloud chambers. From a photograph taken by the author in 1980.

42

“Twice two equals four: ‘tis true, But too empty, and too trite. What I look for is a clue To some matters not so light.” Translated by Karl Popper, and quoted in Conjectures and Refutations, p. 230, from W. Busch Schein und Stein (1909) p. 28 of Insel edition, 1952.

“…I have turned my thoughts away from causes of motion to consider solely the motions that they produce; I have entirely excluded forces inherent in bodies in motion, obscure and metaphysical entities which can only cast shadows on a science that is itself clear.” Jean D’Alembert promoting the Newtonian and instrumentalist approach in France during the 18th century, quoted in S.W. Angrist and L.G. Hepler, Order and Chaos, Laws of Energy and Entropy, Penguin Books, p. 50, 1967, Middlesex, England. Action resonance exchange forces are inherent in bodies in motion and their influence depends on the shadows cast by screening by matter, as proposed in Chapter 2. Excluding them may have been an ironically unwise move on the part of D’Alembert.

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Chapter 3

ACTION AND ENTROPY Reversible and irreversible processes Heat and work Entropy Action and entropy Action, entropy and disorder

3.1.

Reversible and irreversible processes

Classical thermodynamics was developed during the past century and a half, promoted by a galaxy of scientists - Carnot, Mayer, Clausius, Helmholtz, Joule, Maxwell, Gibbs, Boltzmann, Planck, Poincaré, Bose, Einstein, Lewis and Eyring - to name just a selection of the most outstanding. Thermodynamics is held by many scientists to contain intellectual achievements of the highest quality and even beauty, rarely equalled elsewhere in science. For the disciplines of physics, chemistry and engineering science, these achievements can be considered as crucial and form the logical basis for many practical applications such as the internal combustion engine, heat pumps for refrigeration and rocket engines for the exploration of outer space. Here in inner space, thermodynamics can surely aid the study of biology. Indeed, amongst the discipline’s pioneers of the 19th century, Mayer and Helmholtz were both physiologists who applied their biological observations to the enunciation of the principles of thermodynamics. Therefore it would be expected at the end of the 20th century that thermodynamics would be of some significance to most biologists and ecologists in their daily work. On the contrary, thermodynamics is rarely appealed to now by any biologists and practically never by molecular biologists. Indeed, the latter manipulate genes and the sequences of amino acids in proteins, usually quite ignorant1 that there could be thermodynamic constraints to their ambitious proposals. Sometimes, this apparent lack of utility of classical thermodynamics for biology or the study of ecosystems is excused as indicating the need to develop a new kind of thermodynamics. Such a thermodynamics, it is claimed, would be more applicable to real-world processes which are said to be characterised by irreversibility. ‘Irreversible’ processes are said to be all around us in everyday life, such as falling apples, the downhill flow of the water in a mountain stream or the rise of heated air and gases in a chimney above the hearth of a fireplace. Brilliant scientists of the past half century, notably Ilya Prigogine (1962; 1980) and A. Katchalsky (Katchalsky and Curran, 1967), have attempted to develop such a new thermodynamics of irreversibility. This intellectual discipline proposes that real-world processes are about change and the processes of becoming rather than of continued being, the latter case more apt for systems at equilibrium. Although their intellectual achievements have been formidable, the 1

“Where ignorance is bliss, ‘tis folly to be wise”? scarce resources at their disposal most efficiently.

- Not if scientists and human societies are to use the

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proponents of this new thermodynamics have only partially succeeded, as judged by their moderate influence thus far on modern biology. Perhaps this relative lack of success may be attributed to the failure till now to provide a suitable physical model clearly demonstrating the role of irreversibility for biological or environmental processes. It will seem ironic if action thermodynamics, a natural outcome of the action resonance theory of quanta outlined in section 2.2., should prove to be the new development in thermodynamics actually needed. For action thermodynamics has much more in common with the classical theories and the more conservative approach favored by Morowitz (1968), who emphasized the key role of the steady state coupled to energy flow in biology. As we will show in this and succeeding chapters, action thermodynamics is more readily related to classical concepts of entropy, free energy and chemical potential, enthalpy and even to equilibrium - at least of a metastable kind that is maintained while particular environmental forces remain current - than with proposals for a unique role of irreversible thermodynamics. As our discussion unfolds, any absolute distinction between irreversible and reversible processes will seem less valid than has been thought. The concept of reversibility has probably been overused in thermodynamics, since it often infers a state of equilibrium where any active process or change must have ceased, allowing laboratory measurements to be more easily made. But classical thermodynamics also recognises the importance of the initial conditions of non-equilibrium that favor spontaneous processes. One could question, then, the absolute need for or ultimate validity of irreversible thermodynamics. Very likely, we will suggest, it is the lack of separate or ultimate validity that explains why the new discipline of irreversible thermodynamics has not emerged in the past 25 years, as many had hoped. This lack of distinctiveness of irreversibility from reversibility emerges even from considering systems of molecules initially at chemical equilibrium, since the position of equilibrium may always be disturbed by introducing an environmental stress, such as heating or cooling (adding or removing quanta). In both cases there is a spontaneous readjustment, according to Le Chatelier’s principle. This principle states that a system at equilibrium, when stressed, finds a new position of equilibrium if possible by adjusting so as to reduce the stress. Such a readjustment invariably causes a flow of molecules, perhaps resembling an irreversible process, but actually cooling a heated system or warming a cooled system. Perhaps the best known example of an irreversible process is the unimpeded flow of a gas into a vacuum. But even here the direction of an irreversible flow of air from one container into another initially holding a vacuum may be reversed by an extreme change in environmental conditions. This could be achieved by cooling the air in the first flask to a very low temperature in a bath of liquid helium. Thus, reversible states at chemical equilibrium may be destabilised and even irreversible gas flows may be reversed – simply by introducing changes in environmental conditions. If these observations about the lack of a distinctive thermodynamic nature for irreversible processes are true, it will be difficult to conclude that irreversibility itself should be assigned any special significance. An irreversible process by definition involves no work, so that its true role in ecosystems may lie in the opportunity it presents to evolve counter processes or coupling agents that oppose the irreversible process so that work can be done. In this case, the extent of irreversibility is reduced. We may

45

recognise such evolution in flows sustained for a long period, such as the rapid flow of water by gravity in a young river to the sea. Halting or reversing such a process might require a very long period and very major readjustments of the landscape. However, erosion caused by the flow gradually generates meandering flow with greater back-forces, reducing the rate of the flow and erosion and the apparent degree of irreversibility. The generation of hydroelectric power in the stream can further reduce the erosive power, the result in Australia when most of the flow of the Snowy River was diverted via a tunnel to the dams of the Murray-Murrumbidgee system in the 1950s. This has provided a much gentler flow of the Snowy’s water through irrigated rice-fields, vineyards, orchards, billabongs and river to the sea a thousand miles away from its original ocean outlet. However, nature will always act to offset the most optimistic plans of humankind, as implied by Le Chatelier’s principle. Given the inevitable raising of the water table in the Murray basin and the increased evapotranspiration, the Murray River is now precariously balanced between adequate flow and excessive salination. The author suggests that there is no true distinction between reversible and irreversible processes and no essential difference in the underlying physical processes at the level of the forces of interaction between molecules. The rate of a process would then simply be the change in action with time, generated by the prevailing environmental conditions, which will favor a flow in one direction and not the other. Indeed, as Einstein considered, irreversibility may be merely the result of improbable initial conditions of the system. However, this conclusion does not diminish the importance of non-equilibrium or irreversible states in ecosystems since these are the ones that generate changes of action. Probably of more interest than irreversibility are the steady state flows that arise from non-equilibrium, as a result of the operation of transient thermodynamic forces in a system. Flows of energy through a system even generate non-equilibrium in cyclic processes that can continuously carry out work. For example, the evaporation of sea water by the heat energy of sunlight, its active circulation as vapour in the atmosphere and its subsequent precipitation from clouds over land is one such process. Only the fall of rain in this cycle under gravity constitutes a true irreversible flow. Even here, work processes of rock or soil erosion may result from the impact energy of rain drops and streams, caused by gravitational acceleration, as the water and sediments are carried towards the sea. Already nature is opposing one non-equilibrium process with another, in performing this work of erosion and transport. As mentioned above, it is also possible in such an irreversible system to interpolate local equilibrium, such as by building a dam. The equilibrium established between the action of the water pressure and the reaction of the dam’s concrete or earth wall is metastable, however, viable only as long as the dam’s gates are closed or the integrity of the wall’s structure is sustained. The subsequent release of water may then generate electrical power by utilising some of the gravitational potential energy provided by sunlight to provide motive power for turbines. The water eventually flows into the river below with reduced kinetic energy, causing less erosion and warming at the river bed. Even by the turn of the 19th century, Joule’s dream of simply measuring the mechanical equivalent of work and heat at a waterfall had such remarkable sequels as the development by the British of the hydroelectric plant upstream of the Swat River Canal in

46

what is now Pakistan, using water pressure directed through a tunnel in the foothills of the Himilayas2. This book will not be able to provide a complete description of classical thermodynamics. The reader is referred to any of a large number of excellent texts for this level of detail (see Appendix, Reference Texts). Here, a novel approach to the classical laws will be taken, with the aim of highlighting the generation and exchange of action in natural systems including ecosystems and, in this chapter, to draw attention to a new-found relationship between action and entropy (Kennedy, 1983, 1984a, 1984b). Action resonance thermodynamics allows us to employ rational thought and commonsense to solve problems rather than by appealing to natural “Laws”. Nonetheless, without some review of the main findings of classical thermodynamics, it will be impossible to begin our discussion. But the reader will be spared a highly mathematical treatment of thermodynamics in this book. Those with more interest in the mathematics of action thermodynamics should study the footnotes and the endnotes, where a little more mathematical rigor is included. More complete mathematical development3 of action thermodynamics is expected to be the subject matter of new publications by the author and colleagues in the near future. The first law of thermodynamics was discussed in Chapter 1. This is the familiar law of conservation of energy, first clearly stated by the physiologist Helmholtz in 1847, following earlier statements by Mayer and Joule. There are no direct proofs of this law but it is generally accepted since it agrees with most human experience. Indeed, the law is supported by the inability of many experimental tests to disprove it. However, it is worth remarking that for most processes it is necessary to appeal to the concept of potential energy as well as kinetic energy to preserve the law. Such potential energy often appears so formal that one could be excused for questioning its physical reality. In other cases, new kinds of energy have been invented in order to save the appearance of this law. More accurate may be the observation that energy is constant for any particular set of conditions or state and that the same energy content will be apparent whenever that state is revisited. It may be instructive to note that Henri Poincaré (1892) made the observation that everyone believes firmly in the first law of conservation of energy because the mathematicians think it is an experimental fact and the experimentalists think it is a proven theorem of mathematics. Furthermore, the most significant energy-yielding process in the universe near the earth, the generation of solar energy, only adheres to this law if Einstein’s principle of the equivalence of energy to mass multiplied by the square of the speed of light is appealed to:

2

Our admiration for such engineering feats and the benefits they bring, culminating in the construction of the mighty Tarbela Dam on the Indus River generating half Pakistan’s electrical power, was exemplified to the author by the momentary exclamation of a Pakistani colleague when we viewed the much smaller but no less remarkable Swat hydro-station built by the British, that “They deserved to rule!”. However, the wisdom of such constructions is at least partly called into question by nature itself, when the problem presented by rapid silting of the Tarbela Dam from the easily eroded rocks of the youthful Himilayas is considered. 3 Those readers of a mathematical bent are invited to participate in this challenging development and to interact with the author of this book and his colleagues (email: [email protected]; [email protected]).

47

E = mc2 This mass-energy equivalence of the theory of special relativity is not usually thought to be relevant to everyday processes, but this viewpoint may turn out to be mistaken. An alternative equation linking energy and rotational motion given in the footnote below suggests a simple linkage between the energy and the action of physical objects in motion - where energy is considered4 to indicate the rate of change in action. The full implications of this alternative relationship between energy, mass or inertia and action still need to be explored and explained. The action resonance theory discussed in Chapter 2 provided a new viewpoint on energy. Novelty is derived from the proposal that quantum exchange forces between molecules, expressed as a rate of exchange of momentum caused by the frequency of the associated impulses, depend on the radial dimensions of the resonant spaces or cavities in which quanta are exchanged. Thus, the very distribution or extension of matter itself modifies the nature of energy, by its effect on the rate of interaction between material particles. Furthermore, the action resonance theory recognises that energy exchange and flow in molecular systems is both continuous and an essential process that sustains the successive quantum states of the molecular structures from one instant to the next. In action theory, potential energy takes on a highly realistic, less formal, aspect that many will find more amenable, and that by verification of its actual presence, should allow testing of the theory. 3.2.

Heat and work

The first law of thermodynamics, governing the relationship between the total energy content of a system and the relative quantities of heat and work, may yet yield new richness with respect to its intellectual content. Heat as energy is currently often regarded as simply reflecting the motion or kinetic energy of molecules. But as proposed in section 2.2., a complementary aspect of heat as molecular motion is the occurrence of resonant quanta providing a thermodynamic exchange force in the system. It is considered that these resonant quanta must provide momentum sufficient to exactly balance the rate of momentum exchange exerted by the molecules in collisions. Resonance allows energy as quanta to be recycled, amplifying the interactive forces between molecules when the distance between them shortens. If the reader agrees that these proposals are valid, or at least will allow them a trial, perhaps we should wonder at such intellectual novelty in 2000, even in the case of such familiar concepts as heat and energy. Daily experience suggests5 that work may be freely converted to heat. The equivalence of work and heat evolved in the boring of brass cannon, was shown by the American Count Rumford (Benjamin Thompson) in the eighteenth century when he was 4

The relationship between energy and action is more obvious in the following alternative expression, E = ΣIiωi 2 ; In this equation, the action (@ = Iω) is the moment of inertia (I = mr2) times frequency (ω). Thus, E = Σ@ω. 5 Even 20th century song writers have been happy to note this equivalence. Consider the songwriter’s theme of the animated dance scene “Steam heat” in the score of a Hollywood musical (of long-forgotten title) with lyrics including “Work is heat and heat is work!”.

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in the employ of Karl Theodor of Bavaria in Munich. In the mid-19th century the Englishman, Joule, in whose honor the unit of energy is now named, was also intimately concerned with the study of the conversion of work to heat. He set about establishing its exact mechanical equivalent when fascinated on his honeymoon in the Alps by speculating about what happened to the gravitational energy of water when it plunged in a waterfall. Rumford’s observations on the apparently inexhaustible source of heat involved in the boring of the cannon led him to reject the caloric or fluid theory of heat. However, the caloric theory of heat persisted, with supporters of such intellect as Lavoisier and Carnot in France and as prestigious as the Englishman Sir Humphry Davy. Furthermore, despite the firm rejection of the concept of heat as the fluid caloric during the 19th century, we might even have to admit that when heat is considered as resonant quanta, then its rejection as a fluid may appear to have been premature. For energy of the magnitude of the order of RT as the heat content of a mole of an ideal gas with only the translational degree of freedom of motion at 3030 K would be represented by quanta of a mass of only 2.8 x 10-11 g. This is just 28 picograms, much too light to be measured with any known mechanical balance. How could the scientists of the 19th century have anticipated that heat might have involved a dynamic fluid of such lightness and travelling at such speed as quanta? This would have needed the revolutionary proposals of intellects as towering as those of Planck and Einstein. Yet John Dalton in 1808 was able to propose caloric not as continuous but as “an elastic fluid of great subtility, the particles of which repel one another, but are attracted to all other bodies”. Perhaps Dalton might then have gone further, to consider that the particles of caloric exchanged momentum between his molecules at a rate reflecting their great speed of transmission at the speed of light, similar to the quanta that Einstein proposed to explain the photoelectric effect in 1906. Admittedly, this would have been a major step but possible if heat and light had been related even from the everyday evidence of striking a flintstone, given that the Dane, Ole Roemer, had successfully estimated the speed of light in 1676. Might Dalton then have concluded that caloric could generate motion in molecules, if amplified by resonance as proposed in Chapter 2, thus formulating an action resonance theory almost 200 years earlier? Perhaps it is possible that the too strict application of Ockham’s razor deprived scientists of the 19th century of this more complete view of heat when they restricted it to the motion and kinetic energy of the molecules - an outcome that we might say was unfortunately favored by the operational approach. In any case, we can only continue almost 200 years later with the task that Dalton sought to start, now that we have the huge benefit of two centuries of extra analysis and observation. 3.3.

Entropy

The concept of entropy was proposed by Rudolf Clausius in Berlin in the mid-nineteenth century to aid understanding of the extent to which heat could be used to perform mechanical work, and the direction that spontaneous processes will take. Since that time, the term has been employed to mean various things, not only in the physical sciences but

49

also in the social sciences. He first called the quantity he wanted to define Verwandlungsinhalt - transformation-content, before coining the word entropy6 from the Greek words en (in) and trope (a turning, change) to indicate that part of the energy content of a thermodynamic system unavailable for performance of external work. Importantly, for any spontaneous process involving a change of state, the total entropy change was proposed to be positive. This is the most explicit expression of the second law of thermodynamics, the famous law of increasing entropy. 3.3.1. Clausius’ view of entropy as a measure of heat content Pioneers in thermodynamics such as Carnot and Clayperon observed that while work could be converted to heat, there were limits to the efficiency of the reverse process of converting heat to work. It is clear that not all the heat in a molecular system used as working fluid can be converted to external work, for that would require its temperature to fall below that of its surroundings. In the action resonance theory, the need for some heat to be retained by the molecular system is even more obvious, since it is considered as essential to maintain the dynamic structure of the molecular system. Clausius, building on the work of Carnot and Clayperon regarding the maximum possible conversion of heat to work, formulated the second law of thermodynamics in terms of the entropy increase observed for spontaneous processes. He recognised that the entropy was a property of the physical condition of a system and that it could therefore be termed a function of state. This means that entropy will always have the same value in a system of particles under defined conditions (temperature, volume, pressure, composition), whichever path is taken to reach that particular state. Although entropy is usually indicated as having dimensions of energy per unit temperature (ergs or Joules per degree K), it is logically a ratio or a dimensionless number, since the temperature is an intensity factor that can be considered as having the physical dimensions of energy or torque (see Chapter 2). Thus, the entropy is merely a capacity factor for energy in a molecular system at a defined temperature. Temperature is more traditionally defined by the kinetic energy of a system of perfect gas molecules7. The heating of water from absolute zero provides a suitable case study to consider change in entropy. Clausius proposed that the entropy change with heating could be determined by the integral of the heat reversibly absorbed by the system as temperature is increased. At zero degrees Kelvin, where the ice can be considered as one molecule because of bonding between hydrogen and oxygen, the atoms of water are motionless and the entropy is zero. As heat is added as radiant energy (e.g. by using a microwave oven) the resonating quanta accelerate the molecules and their action and entropy increase as the temperature increases. This is considered as a reversible process since the process at any instant can be reversed by immersing the water body in a bath at a marginally lower temperature. This reversible process is one where the entire package of energy as quanta added is used to do internal work in the system. For reversibility to exist, it is essential that the same package of quanta must be available to be emitted from the system into the 6

A common attitude to this concept is reflected in the remark of Canada’s humorous essayist of the 1930s, Stephen Leacock, that ‘All physicists sooner or later say “Let us call it entropy,” just as a man says, when you get to know him, “Call me Charlie”’. 7 KE (mr2ω2/2) = 3/2kT so, T = 2/3 KE/k; Boltzmann’s constant, k, is also dimensionless.

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surroundings. Any loss of quanta (such as by friction) from the system that cannot be recovered will mean that the process cannot be reversed. Experimentally, the change in entropy in a chemical system can be measured by defining a reversible process of heat transfer at a given temperature8 and integrating the exact differential (see footnote). The gradual heating of water beginning with ice as a continuous crystal at absolute zero (0oK) to its state at 273.15oK where it melts, then to its boiling point at 373.15oK where it vaporises and then as superheated steam is a good illustration of such a reversible process showing increasing entropy as heat energy is added to the system. The entropy of ice at 0oK is zero, where the mobility of the hydrogen and oxygen atoms making up the water crystal is also zero (see Figure 3.1). At the temperature range of living cells (ca. 273 – 373oK), the atoms of water are now highly mobile, having an increased entropy reflecting the heat added to bring the system to its temperature. Each increment of heat energy leads to a more mobile state of the atoms in the water molecules, corresponding to increased kinetic energy as the temperature of ice or water is increased and to the changes of state during melting and boiling.

Fig. 3.1: Three-dimensional structure of water in ice, showing hydrogen bonds as dashed lines connected to oxygen atoms. Near absolute zero Kelvin, there is minimum vibration and action of the hexagonal crystal, apart from some slight disorder resulting from oscillation of hydrogen atoms between oxygen centres ( O-H---O O---H-O). As radiant heat is added, all atoms begin to vibrate as a result of the impulses of action exchange forces around the centres shown. Eventually, at the melting point clusters of water dissociate, rolling across the surface of other clusters and exchanging water molecules. At the boiling point, another reversible transition state exists, in which water molecules are vaporised separately.

It is of interest that distinguishing work from heat is at least partly a matter of definition and judgement. The heating of the molecules of a fluid may be regarded as 8

dS = dQrev/T; so S = ∫0TdQ/T - Clausius.

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work if that was the intention for the process. Obviously, the heating of water as steam at constant volume may be considered as work if the increased pressure in the steam at higher temperature is then used to drive a piston and provide driving power to the wheels of a locomotive. On the other hand, the distribution of thermal energy into kinetic energy of molecules in the absence of a cylinder and piston, as occurs in friction, is usually regarded as a loss of the capacity to do work. Yet in both systems, the change in entropy will be exactly the same if the temperature and the heat or package of quanta absorbed by the system is the same. Furthermore, the heat absorbed by the system may then be used to carry out a work process. For example, extra heat added to the atmosphere will only temporarily raise the temperature and kinetic energy of the air molecules since the heated air will rise against gravity, becoming less dense and cooler as gravitational work is performed. This work process may be considered as the work of expansion against the pressure of the atmosphere, but since the pressure of the atmosphere depends on the force of gravity it is convenient to consider this as work against gravity, with the heat energy now conserved as gravitational potential energy. 3.3.2. Boltzmann’s statistical view of entropy Ludwig Boltzmann, a century ago, recast entropy as a statistical measure of the randomness of a system, so that the more possibilities there were for different arrangements or complexions of a system of particles and the greater its randomness, the greater was its entropy. A system could be expected, then, to assume the most probable arrangement of its parts. The associated concept that increasing entropy denoted increasing disorder or uncertainty in a system of molecules was also advanced. The question of whether greater entropy necessarily means greater disorder forms a central theme in this book. The approach Boltzmann used to estimate the entropy of a collection of molecules of a given total energy was to focus on the number of possible arrangements or states (i.e. molecular speeds, directions of orientation, energy levels) of the system. The number of different ways or states to arrange a given system is called its degeneracy. It was then possible to relate the entropy of the system to its degeneracy9, expressed in a simple equation proposed by Boltzmann, shown in the footnote. The form of the equation was actually established by a process of trial and error since theoretical consideration of the nature of entropy demanded that any suitable mathematical definition must have certain characteristics. These characteristics were, firstly, that no system should have greater entropy than when each state was equally likely, indicating the least constraints on distribution of the energy across states. Secondly, knowing from probability theory that the joint probability of two independent events is the product of their individual probabilities, then only a logarithmic function10 of the probabilities seemed able to provide the correct value. The logarithmic form was necessary to allow the mathematical definition to include both the multiplicative property of the individual probabilities and the fact that entropy is extensive, so that the entropy of a whole system equals the sum of the entropies of the parts. 9

S ≡ k ln Ω, for distributions where each state is equally likely – Boltzmann. ln (a.b) = ln a + ln b.

10

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The constant k is Boltzmann’s constant, of numerical value dependent on the choice of units. Boltzmann’s constant k must also be a dimensionless number. The equation relating entropy and the logarithm of the degeneracy is central to the discipline of statistical mechanics, developed by Ludwig Boltzmann in German-speaking Europe, J. Clerk Maxwell in England and Willard Gibbs in the United States in the late nineteenth century. Gibbs proposed a more general mathematical definition11, based on Boltzmann’s approach. It is possible to relate these statistical definitions of entropy to quantum theory, since the probability of different states can be considered for quantum states, defining the distribution of energy. It is interesting that it is sometimes claimed that the main results of this statistical approach to systems of particles can be developed without specific reference to energy, thermodynamics or the properties of molecular systems. However, Boltzmann’s purpose had been to explain the second law of thermodynamics on the basis of the atomic theory of matter by combining the laws of Newtonian mechanics with the theory of probability. In his work, he attempted to establish that the basis of the second law is statistical and that a system will approach a state of equilibrium because this is the most probable state. Despite its rather mysterious nature, the concept of entropy has been extremely fruitful intellectually, generating several alternative interpretations and finding application not only in chemistry and physics but also in the social sciences. Possibly, this intellectual richness is partly because it has been conceptually so taxing to human understanding. The concept of entropy as statistical has even found applications in information theory, based on the proposal that the more information one has about a system the more it is constrained and the less its entropy. A subjectivist theory of entropy proposed by Leo Szilard was strongly criticised by Karl Popper (1976) when he examined the theoretical case where knowledge of the position of a single molecule in a cylinder was considered to amount to negative entropy that could be exploited to do work using a suitably placed piston or coupling agent - resulting in a decrease in negative entropy and loss of knowledge. This case has resonances with that of Maxwell’s demon (see Figure 3.2), a minute being able to selectively exploit the greater energy of the faster moving molecules of Boltzmann’s distribution of velocities. Popper rejected this subjectivist view of entropy on the grounds that no valid argument can be presented for this intrusion of external human knowledge into physics. The more objective view of Popper based on realism is the attitude preferred by the author of this book. We now have two different definitions of the entropy of molecular systems to reconcile. The Clausius definition of entropy directly involves the total thermal energy content of the molecular system as a function of its temperature or the kinetic energy of the molecules and the Boltzmann definition is concerned with the probabilities of different states and the degree of randomness possible in the system. In the first case, the greater the energy content of the system for a given temperature, the greater its entropy. In the second case, the greater the number of ways of distributing a given energy content, the greater the probability and the greater the entropy. It seems obvious that, if both 11

The more general statistical definition given by Gibbs is S ≡ -kΣipilnpi, where pi is the probability of a particular state for which Σipi =1, but where different states may have different probability. For equal probability of each state, pi = 1/Ω and Σipi = 1; then S ≡ -kΣipilnpi ≡ -kΣi1/Ω ln1/Ω = k1nΩ.

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approaches are to yield the same numerical result, this agreement can be no coincidence and there must be some more basic, underlying, cause for this agreement.

Fig. 3.2: The demon was proposed by Maxwell to defeat the Second Law of Thermodynamics by separating fast molecules from slower ones. But the action resonance theory would not allow the demon his way because the kinetic energy of molecules depends on screening potentials of the action field and impulses from the rays of energy it contains as well. Therefore, he would have to transfer the action field to maintain the kinetic energy, which is impossible (diagram modified from Williams et al. 1973, with permission from W.H. Freeman and Company, San Francisco).

3.3.3. A new viewpoint regarding entropy In fact, the new view of entropy proposed in this book provides the underlying cause of agreement. This is that entropy can be mathematically related to the action of the system. Since the energy content will define the action in the system and the action is related to its quantum number, the two viewpoints may be reconciled. This physical view of action and entropy automatically rejects any viewpoint that subjective knowledge or information of the state of the system can influence its thermodynamics as proposed by Szilard, allowing work to be done. Because of the absolute need for the action field to match the kinetic energy of molecules with complementary quanta carrying energy-momentum, where the former is contingent on the latter’s resonant impulses, the capacity of Maxwell’s demon to operate by separating molecules of faster velocity can also be excluded. Perpetual motion within a Brownian system at equilibrium is possible but not if energy is extracted from the system to do external work. However, it will be shown later in this book that living cells do trap the energy quanta associated with the action and kinetic energy of particular molecules in highly specific reactions catalysed by the biological macromolecules known as enzymes. But this will in no way allow work to be done that cannot be paid for by energy consumption, contravening the laws of thermodynamics.

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Even so, human knowledge and information about molecular systems certainly can play a crucial role in our capacity to benefit from many sources of negative entropy or action potential by allowing us to provide coupling agents capable of exploiting them (e.g. windmills or hydroelectric power stations). Indeed, a case will be made in this book that all living systems must have sensory mechanisms that provide information or knowledge of the surrounding environment, essential to the effectiveness of their decision-making and survival as thermodynamic entities. But this information field in ecosystems can only be the action field referred to in Chapter 2 and the effectiveness of communication through impulses can only increase with increasing quantum exchanges, action and entropy. But this seems to be the very opposite conclusion to that proposed by Szilard, that equated maximum information with a minimum of entropy! Nevertheless, it is true that a system of molecules far from equilibrium with its surroundings has the maximum capability to generate information, but only when the necessary quanta to generate subsequent action are being made available. The lantern on the hill, when alight, provides one such example of actual information flow. It is insufficient that a system may contain a large amount of negative entropy (contained in kerosene plus air) to state that it can supply information. This negative entropy or free energy is only a potential to generate information until an efficient coupling mechanism for transmission of the information is supplied. From his rural experiences of half a century ago, the author can describe exactly the coupling agents necessary. To send an effective signal at night to the surrounding countryside, one needs a well-trimmed wick, an ignited flame well shielded by a glass chimney from the wind to allow steady convection and preferably, for brightness, an incandescent mantle. The mantle amplifies the light made available from the resonant action of the electrons in the flame where gas molecules, heated by the reaction of chemical oxidation, cool. Modern youth will, no doubt, find some sophisticated means of communication more in tune with the technology available to science fiction than a lantern, but will it be as welcoming as the lamp on the hill? 3.4.

Action and entropy

One of the most significant proposals to be made in this book is that entropy can be mathematically related to action. The action resonance theory described in section 2.2. provides the physical mechanism for this relationship. It does so by proposing that the resonant exchange of energy quanta provides the intermittent dispersion force that generates and sustains the kinetic energy and the action of the molecules. Entropy, then, is a capacity factor for the quantity of energy quanta needed to sustain the action of the system, under given conditions of temperature, physical state (e.g. solid, liquid or gas), pressure, volume and composition. Clausius’ definition of entropy (‘turning into’ or changing) seems particularly apt and prophetic, since it is a measure of the energymomentum of the quanta providing the force capable of generating and sustaining the action of a system of molecules at a given absolute temperature. As indicated in Chapter 2, the momentum of quanta can be considered to provide a moment, generating torque,

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even in gaseous molecular systems where the motion of molecules may appear to be independent. Whenever the entropy of a molecular system increases, such as when it is heated, its action will increase. Whenever the entropy of a molecular system decreases, its action will decrease. Thus, when we cool a system of molecules we reduce both its entropy and its action. However, to cool one system of molecules we must do work on or warm another. This will increase the entropy and action of the second system. In fully considering the nature of the relationship between entropy and action we can expect to enrich our knowledge of both. However, the author freely admits that, when writing this book more than 10 years after the link was first proposed (Kennedy, 1983, 1984b), only limited aspects of the relationship between entropy and action have been explored and the reader is invited to help extend this examination. 3.4.1. Action resonance reconciles the Clausius and Boltzmann definitions of entropy The mathematical relationship established12 between entropy and action within any degree of freedom of motion of the system is logarithmic, like Boltzmann’s relationship between entropy and probability. Boltzmann’s constant is required in this equation in order to satisfy the current choices of the units of entropy. Alternatively, one may state that the action of a degree of freedom of motion in a molecular system is an exponential function of entropy. Like many of the phenomena examined in this book, the actionentropy link was proposed in a biological context, related to the neurological disorder Myasthenia Gravis (Kennedy, 1983). In this paper, the auto-immune disorder in individuals with this disease is shown to cause antibody-binding processes linking acetylcholine receptor molecules producing aggregates with increased action and entropy, but reducing the overall action and entropy of acetylcholine receptor molecules. This leads to a chaotic state in which membrane structure at the nerve-muscle junction cannot be sustained and disintegrates, presumably because of the greater inertia and momentum of the aggregates. This conjecture regarding entropy and action involves a linking of quantum field theory and a knowledge of the quantum number of a molecule in a field of molecules that defines its action. Since the total action of a system at temperatures above absolute zero is a large multiple of h/2π, Planck’s quantum of action, the threedimensional action ratio for each molecular set yields a number indicative of its quantum state. The Boltzmann distribution implies that the total energy of a set of molecules at ambient temperature will be distributed so that most of the molecules occupy the lowest energy states with a smaller proportion occupying the higher states available. We can illustrate this fairly crudely by suggesting that energy states in a small set of say 18 molecules might be distributed so that eight molecules will occupy the lowest energy state corresponding to an action of one unit per molecule. The next highest state might then have four molecules of action two. The third, fourth and fifth action levels could then contain three, two and one molecules each for total action of 38 units, with the total action in each level being eight, eight, nine, eight and five units respectively. While the change in action of the different levels is integral (based on units of h/2π), in general the 12

Where action = @, k = Boltzmann’s constant and h = Planck’s quantum of action, then translational entropy, St = kΣln(2π@/h)3N , where @ = mr2ω.

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increase in energy with increasing action states falls off exponentially with the energy level, less and less extra energy being needed as the action increases by integral values. The action resonance theory suggested in Chapter 2 that this distribution is a result of the change in screening potential with separation, which is inversely proportional to the square of the radial separation of dense particles, or of their speed since this determines the frequency of interaction with other molecules. This pyramid-like arrangement of energy states would correspond to less action and energy than if six action levels contained three molecules, giving a total action of 63 units. Only if the total energy of the system of molecules was increased (i.e. more heat energy was added) could the initial distribution of molecules change towards the second arrangement. However, the latter arrangement would still be highly improbable, even if sufficient energy was supplied, since the additional energy would not just be applied to the redistribution of this set of molecules but would lead to gradual dissociation of the molecules into atoms with greater action, unless they were noble gases, or even of nucleons with greater action. Of course the possibility of chemical reaction, or of nuclear rearrangements (e.g. fusion of hydrogen to helium) that attends this could also mean that an orderly change of energy-action distributions as energy is added to a set of molecules would not be possible. This tendency of energy to partition across the boundaries of the hierarchy of material structures, leading to added action both interior and exterior to the level being examined in any study, is of great importance to the functioning of the earth’s ecosystems, as will be discussed in the later chapters of this book and plays a key role in their organisation.. At any level, however, the molecular state equilibrated with the surroundings at a given temperature conforms to a minimum energy, least action distribution. The action resonance theory proposes that the favored hierarchical arrangement is the result of dispersive forces between the molecules from the impulsive exchange of quanta, physically causing the distribution of states observed. This allows us to observe how these three concepts of entropy í the integral of the total energy per degree Kelvin (Clausius), the statistical distribution (Boltzmann) and the logarithm of the action ratio may be integrated into one. The least action solution is then the direct consequence of these momentum exchanges, yielding a hierarchy of molecular energy states; the dynamic structure will be retained as more heat energy is added, although the shape of the distribution will gradually change with a greater proportion now of higher action states. The concept of least action must be understood as an optimum configuration or conformation of the system related to a particular energy content. At equilibrium with the surroundings, the total action of a system of constant volume cannot be greater unless more energy is added. Equally, the action cannot be less than its actual value unless the total energy is reduced by cooling. Any arrangement with less action than the equilibrium value would be unstable because it would involve an arrangement of the system with some parts being subjected to more stress from impulses than others, leading to a spontaneous readjustment to reduce this effect. An arrangement of the molecules with a higher total action than the equilibrium value would also not be sustainable at the current energy content, and a spontaneous readjustment must then occur. Considering that the temperature will tend to equilibrate with that of the surroundings, the system will achieve

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the least action consistent with the minimum energy configuration of the system because any excess energy is radiated to the environment. It can readily be shown that the one-dimensional action is directly proportional to the cube root of the volume of the system of molecules and to the square root of the temperature. Conversely, the cubic action is proportional to volume (or inversely proportional to concentration), or to the square root of the temperature cubed. This follows from the proportionality of action to radial separation (holding temperature constant) and velocity (holding volume constant). All relationships involving concentration then take on the dynamic quality of action in this theory, as well as the static quantitative notion of density with which we are so familiar. Changes in concentration during reactions or diffusion then correspond to changes in action state. For di- and polyatomic molecules, the relationship between entropy, action and temperature will be governed by the numbers of degrees of freedom of motion within the molecules as indicated by the heat capacity. Thus, for change in volume the change in entropy is a logarithmic function of the three-dimensional action13. For changes in temperature, the change in entropy of a monatomic gas is also a logarithmic function of the change in translational three-dimensional action14. Whether changes in action result from a change in the volume available for each molecule of a set or as a result of an increase in the temperature of the system, the relationship between change in entropy and the change in action remains the same. These changes need to be interpreted in terms of action resonance and the capacity and need of the system to contain more quanta as temperature increases. The heat capacity of the molecular system depends partly on the square of the speed of motion of the material particles making up the molecules. The greater the radial separation of the material surfaces, the greater the heat capacity to maintain a given pressure, since pressure depends on the rate of impulse on molecular surfaces. Maintaining pressure while volume increases therefore involves an increase in temperature. The greater the speed, the more frequent the emissive collisions and the greater the capacity to interact with quanta. Both radial separation and speed or velocity may appear to affect the capacity of the system as a three-dimensional or cubic relationship as they both affect action. However, the increased action and entropy possible in a molecular system only requires the system to contain extra quanta during temperature increases by heating but not from increased volume without external work. For polyatomic molecules, the total change in action with changes in temperature will be reflected by changes in the total heat content. Changes in action with temperature must relate to all degrees of freedom of motion, including electronic, vibrational, rotational and translational. However, consideration of the action resonance model of quantum exchanges indicates that these degrees of freedom must often be directly linked and that the internal emission or absorption of a quantum can accelerate or decelerate all degrees of freedom of motion of a molecule simultaneously. Thus, equipartition of energy occurs automatically between different degrees of freedom of motion since all the motion is sustained by the same field of energy. 13 14

∆S = Rln(V2/V1) = Rln(@2/@1)3. ∆S = Rln(T2/T1)1.5 = Cvln(T2/T1) (nb. Cv=1.5R, heat capacity for a monatomic gas).

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We must also assume the existence of transition states as the temperature and volume of a molecular system changes, to some degree even in liquids and gases as well as solids. These result from the existence of crystalline configurations of greater stability, because of screening that reflect the dynamic shapes of particular molecules, even in liquids and gases. Obviously, the heat capacity, the entropy and the action of polyatomic molecules will be greater than for monatomic molecules because of the greater capacity (dense surfaces of nucleons and electrons in motion) to exchange quanta and momentum. Although the median kinetic energy of all kinds of molecules or microscopic particles at the same temperature is the same, the greater inertia of polyatomic molecules demands that more energy must be added to the system for large molecules than for small. This is reflected in their greater heat capacity and the extra energy per molecule is contained in the field as greater potential energy, coincident with the greater action of these larger molecules. Moreover, the maximum entropy and action for a system of polyatomic molecules will only be reached when enough heat as quanta has been added to completely dissociate all the atoms from each other as well as the electrons from each of the atoms (i.e. in a plasma). One can imagine that for diatomic or polyatomic molecules, the action per molecule will be greater as temperature increases as a result of increased molecular rotation, amplified for particular atoms by increases in bond length (equivalent to higher vibrational quantum states). Thus for polyatomic molecules, to the dynamic image of curvilinear translation of the centre of mass of a monatomic molecule must be added the overall spiral motions of the individual atoms of polyatomic molecular complexes. The action resonance theory explains the concept of quantum states in all degrees of freedom of motion as a spontaneous outcome of the resonant interaction of momentum-carrying quanta with each molecular set and between atoms in molecules. The specific wavelengths or frequencies of the quanta would be a natural function of differences in the frequency of recurrence of configurations, derived from several factors. These include molecular shapes, the average speed of motion of the molecules (temperature), the speed of transmission of radiation, the probe-ability of the molecular field - affecting the mean path-length of quanta between emission and absorption - and the frequency of collision processes with other molecules which acts to stimulate the emission of quanta. 3.4.2. Action resonance and the van der Waals’ attractive forces There are inevitable, rational consequences of the interaction between quanta and molecules. Since quanta travel at the speed of light (c=3x1010 cm s-1), a single exchange can occur in 10-18 seconds for a path length of 3 Angstrom units (3x10-8 cm) between molecules. If the path length between the electron shells of molecules varies, so will the possible rates of interaction. The absorption and emission (or reflection) of quanta, through strict conservation of momentum, is the source of thermodynamic force between molecules. Force is clearly intermittent and quantised in the action resonance theory, since it depends on the exchange frequency of the quanta. Time itself must be quantised in action theory, since no change in action occurs except at the instant of emission or absorption of quanta, when impulses are exerted. Indeed, without changes in action states there is no time.

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The density of quanta in action space must determine the magnitude of the force that can be exerted. As a result, compression of the molecules will increase the density of quanta, reducing the path length for interaction by quanta and amplifying the force and pressure. Compressing the system of molecules will also increase their frequency of collision proportional to the change in volume, increasing the frequency of emission of quanta since this is stimulated in collisions. Thus the overall instantaneous effect of an incremental compression of molecules and quanta, before equilibration by molecular rearrangement or heat flow takes place, will be to increase the force exerted proportional to the inverse of volume squared (i.e. proportional to 1/(volume x volume)15. Because of increasing screening and greater resonance, the denser the system of molecules and the lower the action per molecule, the less quanta are needed per molecule at a given temperature. This reduction in the density of energy appears to indicate an attractive force (i.e. more energy is needed to dissociate the molecules or less is needed to sustain them at a given temperature). This force is named after van der Waals, who introduced the corrected van der Waals’ equation16 relating pressure-volume energy to kinetic energy of the molecules. In this equation, the pressure or resonant energy density is reduced by a factor proportional to the inverse of the volume squared. Thus, considering pressure as the representation of the true energy density, the correct temperature or torque for molecules can be met by a lower pressure because of these effects. This condition can be satisfied by a lower pressure as the correction term (a/V2) becomes larger with smaller volumes of the system. Action or quantum states for molecules correspond to the space-time trajectories for the individual atoms, both enabling and requiring the action field to contain sufficient radiant energy and momentum exchange to sustain the molecular system at a particular temperature. The obvious mathematical conclusion17 from this analysis is that the sustainability of a dynamic molecular configuration at a particular temperature depends on maintaining an adequate matching of the energy-momentum tensor with the action matrix. 3.4.3. The action and entropy of water This conjectured relationship between entropy and action provides a new viewpoint regarding the nature of entropy, that should not conflict with the previous definitions. Considering the entropy and action of the molecules in ice and water, during the process of melting the exchange of energy-momentum as quanta reflected from molecular surfaces randomly produce impulses and torques or turning forces, generating rotational and translational action in clusters of water molecules. This rotational or rolling motion allows mass flow of the water as a fluid. Such water clusters are called flickering clusters, because individual water molecules and even hydrogen atoms are continually deserting one cluster and joining another, as would be expected from the operation of the action exchange forces able to break weak bonds between molecules in more forceful collisions. On subsequent heating, the action of water clusters is further increased in accordance with the increased rate of impulses from radiant energy, raising the 15

Force = change in momentum/sec; therefore, force α 1/V2 or 1/r6. (P + a/V2)(V – b) = nRT. 17 Such a mathematical solution is needed. 16

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temperature and resulting in even greater translational and rotational motion. Since the mean velocity of molecules or groups of molecules is expected to be proportional to the square root of the temperature, the action will also increase in the same proportion in a constant volume system. However, the relationship between entropy content and action is a logarithmic function of the action. At the boiling point, water molecules must be completely separated from remaining clusters by forceful breaking of hydrogen bonds from the impulses of quanta, increasing their action per unit mass, and then subjected to an increase in translational action proportional to the increase in volume in air, as discussed above. The volume increase for one mole (18 g) of liquid water to vapor at 100oC (18.75 mL liquid to 30,600 mL gas) at 1-atmosphere pressure is 1632-fold so there is a corresponding increase in action. It may be calculated18 that about 56.5% of the entropy change can be ascribed to increased action from increased volume and radial separation for each water molecule. In ice, each water molecule is tetrahedrally bonded to four of its neighbours by four hydrogen-bonds, a structure which is most stable at the absolute zero of temperature (0oK). If the remaining 43.5% of the entropy increase at vaporisation during boiling is associated with the breakage of hydrogen bonds, this analysis suggests that the residual bonding at 373.15oK is equivalent to approximately 0.88 moles of hydrogen bonds (17.7 kJ/mol) per mole of water; each hydrogen bond requires 20.08 kJ of energy per mole to be broken. Thus, less than 25% of the hydrogen bonding in ice at 0oK remains in water at 373.15oK. It is interesting to observe that in principle no heat is required for the reversible transition of a dissociated water molecule in the fluid to a dissociated water molecule in air. This is because the torque exerted on molecules, or couples of molecules, by the impulses from quanta are proportional to the radius of action. Exchange of water molecules between the air and the liquid or even ice can occur at any time at any temperature because no more energy is required to sustain each system. However, according to the action resonance theory, heat is required to do the dispersive work of injecting an extra water molecule into the huge set of water molecules in the atmosphere, against the gravitational field. Nevertheless, we can conclude that slightly more energymomentum as quanta is required to sustain vaporised water molecules in the atmosphere than in liquid water because the ‘probe-ability’ for quanta is less. Note that whenever such pressure-volume or gravitational work is done, the addition of heat does not increase the temperature. However, because the temperature of air and its degree of saturation with water may vary, suitable allowances must be made to enable exact calculations. Furthermore, depending on the temperature and the humidity of the air, either condensation (i.e. precipitation) or vaporisation (i.e. evaporation) of water will occur, governed by the relative density of quanta in the air or the condensed phase which determines the sustainability of the system under any environmental conditions. As long as a source of extra heat is available (e.g. sunshine) vaporisation from water surfaces, the foliage of vegetation and any moist materials will continue, as a result of the extra resonant force or action potential being made available. When the sun sets and the water 18

∆S = nRln(V2/V1) = nRln(@2/@1)3 = (1 mole)(8.314 J/mole-deg)ln(1632 = 61.5 J/degree; the total entropy change from the heat of vaporisation per mole (40.60 kJ/mole) has been determined to be 108.8 J/degree, so 47.3 J/degree must be ascribed to increased action on breakage of H-bonds in water prior to volatilisation.

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and atmosphere cool as a result of heat radiating to space, the reverse process of condensation and the formation of dew on moist surfaces will proceed. 3.4.4. Hot air balloons and clouds At first it seems relatively easy to understand why a hydrogen, helium or hot air balloon rises in air. Inflated to the same pressure, the internal gas is lighter and its density is less. According to Archimedes’ principle, the vessel containing a lighter gas will experience an upthrust equal to the mass of the fluid displaced. The downthrust equals its own mass and the net upthrust is the difference between the two. Therefore a mole of helium weighing 4 grams in a balloon (24.45 litres at 298oK and one atmosphere pressure) will experience an upthrust of about 24.8 grams force, or 24,304 dynes, having displaced nitrogen (78% of air) and oxygen (21% of air) of molecular weight 28 and 32. This upwards force exists despite the fact that the balloon must be inflated with helium to either equal or exceed the atmospheric pressure, so that the internal force exerted per unit area on the balloon fabric matches or exceeds the atmospheric pressure. A theoretical proposal to explain the lifting force involving action resonance can be made. Considering the ssymmetric distribution of air molecules in the gravitational field, a gradient of total molecular surface exists, increasing at lower points in the gravitational field because of the greater density of air, with a sharp demarcation in density at the earth’s surface. The hot air spontaneously expands initially within the balloon because of the increased space density of quanta produced by the combustive chemical reaction, doing pressure-volume work from the impulses of energy. However, the local molecular environment is asymmetric, with more reactive work on molecules being done by quanta on a descending path in the gravitational field than on an ascending path. The probability of encounters by quanta on molecular surfaces is greater in the direction of increasing density (down) than it is in the direction of decreasing density (up). Therefore the field of quanta will be denser on the ascending path than on the descending path and more momentum will be delivered to hot air (or helium) from below than above. The overall effect is to generate greater upward force on molecules in the balloon than downward force and a net upward thrust. This upward thrust will continue until the point at which the density of surrounding air, the density of the gas in the balloon and the temperature of both is the same. Since the lifting process will have done pressure-volume or gravitational work, cooling the heated air equivalent to the increased gravitational potential energy will be expected to occur. Another beneficial case is the increased entropy and action of sun-heated sea water as it vaporises to form clouds. A spontaneous process proceeds in which the energymomentum of quanta from sunshine furnish the heat of vaporisation and the impetus to move the clouds over elevated land. Here, the requisite quanta can no longer sustain water molecules against gravity as a result of adiabatic cooling (work against gravity) to the point where condensation (more quanta released to the atmosphere as heat) and precipitation of rain occurs. Certainly, the overall entropy (and action) of the system has increased as a result of the operation of this dissipative structure (see Prigogine, 1980) but an essential purpose for the function of ecosystems has also been achieved. Systems such as hot-air balloons and clouds in the rainfall cycle can be maintained as long as fossil fuels and sunshine are available. Fortunately, this will be an extraordinarily long time as

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can be predicted from Einstein’s equation relating mass and energy and the loss of mass in the burning of fossil fuels and in the nuclear reactions on the sun. 3.5.

Action, entropy and disorder

Entropy has been traditionally associated with disorder, or even chaos. It has been correctly recognised that spontaneous processes generally involve an increase in entropy and that the system evolves in a direction decreasing its capacity to do work. Certainly, the sense of less order can be recognised in the greater mobility of molecular systems as heat energy is added from absolute zero where the entropy, the action resonance and exchange of quanta is also zero. However, from the vantage point of action thermodynamics, to speak of more disorder now seems far too harsh a term for increased entropy, particularly when its relationship to biological action is accepted. For biological systems a significant degree of suitably constrained entropy and action is essential for life processes and even for the passage of relative time to occur. Indeed, action is an essential feature of life and the frequency of changes in action state are an essential feature of our sense of the passage of time. As discussed above, the entropy of water in the range where life occurs compared to absolute zero is substantial. Furthermore, considered as a capacity factor for the energy essential to sustain the dynamic structure of molecular systems at any temperature, it can only be concluded (as a former colleague, Geoffrey Leeper remarked) that “entropy has suffered from an unnecessarily bad press”. Without a significant degree of entropy, neither life nor biological time exists. The world of absolute zero where entropy is zero is a timeless world, and it will be natural in action resonance theory to displace time from a primary or absolute role and replace it with the relative frequency of fluctuations in action and entropy as the true measure of change. Time like space no longer has absolute status in action resonance theory and both these phenomena become metaphysical or abstract notions without true physical reality. In fact, the new relativistic meanings now available for mass as the content of reactive matter for receiving the impulses of sustaining energy, generating recoil, and distance as a spatial variable of magnitude dictated by the relative speed of signalling, leaves us with action as the only invariant and realistic property (see Endnotes – Dimensional analysis). This viewpoint of entropy as a measure of the rate of fluctuation in action states (and even of time) can only enhance its positive value in our search for meaning in the natural world. The statistical approach of Boltzmann to entropy referred to above can also be readily accommodated by action resonance thermodynamics. The availability of many different arrangements, configurations or molecular complexions infers mobility and fluctuation in order that these different options may be explored by the system. Later in this book, it will be demonstrated from various case studies that an appropriate mobility is a feature of all living systems and an optimum quantity of action or entropy of organisms is essential for their function. It seems clear that a more positive attitude to entropy (and action) should be taken because the increased entropy is caused by forces that are essential to the function and evolution of ecosystems. There is no need to defy the second law of thermodynamics of increasing entropy or to invoke some new principle not already

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implied in the second law to explain the evolution of life on earth. As will be discussed in Chapter 7, even the evolutionary development of higher organisms is a natural outcome of the quantum exchange forces of action resonance. These forces automatically generate hierarchical structures as outcomes which are themselves characterised by an optimised entropy and action compared to the starting materials on which their construction is based. The starting materials are simply cold water and mineral nutrients interacting with a genetic code, conveniently wrapped by the membranes of germ cells able to grow in a favorable environment that includes periodic sunshine. Nevertheless, the increase of action and entropy without limits would spell doom for life on earth, by disintegration. Fortunately, there are severe natural constraints on the capacity for entropy to increase on our planet, from operation of the principle of least action and the development of hierarchical dissipative structures described by Prigogine. Our later discussions on action theory will show that the second law of increasing entropy is essential for the evolutionary process and the development of biodiversity. An important virtue of action resonance thermodynamics is its ability to stand traditional thinking about entropy on its head. Understanding all this may eventually allow us to predict the optimum level of entropy and action for ecosystems and a more sustainable future.

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ACTION THERMODYNAMICS

Order and patterns from chaos - action deposition cells formed by irreversible reactions from a thermodynamically stressed solution. Drops of a stable solution of human serum albumin (20 mg/mL) in 10 mM Tris-buffered saline at ph 7.4, NaCl (9 mg/mL), sodium azide (0.2 mg/mL), polyethylene glycol (MW 6000, 0.5 mg/mL) were placed on a microscope slide, a glass coverslip added to prevent evaporation and a small drop of ethanol placed on the slide adjacent to the coverslip. From rapid diffusion by ethanol under the glass surfaces, chaotic conditions were set up by the redistribution of energy; precipitation cells of polymers and solutes were produced within a few seconds, eventually reaching a new stable equilibrium. The development of this order from chaos as a result of redistribution of energy and matter in this system is entirely consistent with the second law of thermodynamics. The development of such beautiful complexity, such as the cardioid, ring and radial deposition patterns shown, reflects the morphology of the solution’s constituent molecules and the action exchange forces exerted by energy released in the solution interacting with the precipitating molecules.

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“We will now briefly consider the important quantity called action. This, for a single particle, may be defined as either the space integral of the momentum or as double the time integral of the kinetic energy, calculated from any assumed position of the moving particle, or from an assigned epoch. For a system its value is the sum of its separate values for the various particles of the system. No one has, as yet, pointed out (in the simple form in which it is all but certain that they can be expressed) the true relations of this quantity. It was originally introduced into kinetics to suit the metaphysical necessity that something should be minimum in the path of a luminous corpuscle. But there can be little doubt that it is destined to play an important part in the final systematizing of the fundamental laws of kinetics.” P.G. Tait (1883) Mechanics. Encyclopedia Britannica, 10th Edition, 15,723.

“The value of a theory depends on both the success with which it coordinates a wide range of presently known facts and its fertility in suggesting places to look for presently unknown new phenomena.” Percy W. Bridgman in Encyclopedia of Science and Technology, Vol. 13, 548, McGrawHill, New York, 1966.

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Chapter 4

ACTION THERMODYNAMICS Spontaneity in natural processes Enthalpy and action resonance Spontaneous processes and work potential Free energy and action potential Action field gradients in spontaneous reactions Classical versus action thermodynamics

4.1.

Spontaneity in natural processes

One of the main tasks of thermodynamics has been to predict in which direction and how far a spontaneous reaction will proceed, given a defined set of initial conditions. As already discussed in Chapter 3, the second law of increasing entropy (and increasing action) sums up our experience. In general, physical and chemical reactions take place in the direction that allows the system to minimise its energy, by achieving more stability. It will be shown below using action resonance theory that these processes act to provide more variety in the dynamic complexes between molecules and energy quanta. By using the maximum number of ways of distributing the radiant energy on molecular surfaces, the rate of impulses from quanta can be minimised, generating the lowest pressure possible consistent with the temperature. Furthermore, positions of equilibrium, will also involve the least action possible while exhibiting the minimum energy requirement. The tendency towards equilibrium, irrespective of whether it is reached or not, indicates the role of the turning forces exerted by quanta generated in collisions between molecules, to generate action. The potential of each different chemical species as molecular units to do work throughout the system is then at a minimum and as equalised as possible. This book on action theory will provide a basis to examine the transient rates at which such reactions or molecular rearrangements take place. Indeed, the physical model that the action resonance theory provides should enable the kinetics and dynamics of thermodynamic processes to be examined much more easily. A case will be made that most thermodynamic states in ecosystems are not at equilibrium at all. In fact true equilibrium is characteristic of completely isolated systems, perhaps of academic interest only, such as those prepared in laboratories. Such isolation is certainly not found in ecosystems. In reality, the rate and extent of readjustment of action states needed is controlled by the intensity of the energy flux in ecosystems. Continuously varying rates of energy input and output, diurnal and seasonal, force the generation of appropriate action and entropy states in the ecosystem’s molecules. States of greater action are sustained only as long as the density of quanta is maintained and the necessary dispersive forces can be sustained. Indeed, this dependence of action on energy provides a new, concise, definition of sustainability. If the intensity of the forcing potential changes, so will the position of transient or steady-state equilibrium. This intensity can be recognised in physical processes such as the boiling of a kettle. As long as sufficient heat is applied, the water will boil at the rate

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appropriate to the heat flux, doing work against gravity by lifting the lid, evaporating and expanding the humidified atmosphere - thus cooling. If the heat source is switched off, there will be insufficient energy flux to sustain the system and progressively, an equivalent amount of water will condense, the atmosphere will slightly descend in the gravitational field and the former state will tend to be resumed. The seasonal and daily variation in intensity of sunlight will also provide a variable forcing potential, resulting in different positions of transient equilibrium. Because of the limited rate at which molecular systems can respond to energy inputs, these readjustments will lag behind states theoretically possible. The magnitude of the energy flux provides a variable density of energy as quanta, tending to alter the relative distributions of reactant and product molecules as a means of minimising the total stress of the system. With an increased density of quanta, the position of equilibrium of a reaction will tend to evolve towards the production of molecules or arrangements of molecules needing more quanta to sustain them at the temperature of the system. This will satisfy the tendency to provide least action by minimising the pressure and temperature. Thus, the new equilibrium states predicted in ecosystems must be considered as metastable and are probably never quite attained. The direction of increased entropy (and action) following energy inputs either from the exterior or from internal chemical reactions has often been called the direction of increased disorder during the past 150 years since Clausius defined entropy. But as was pointed out in Chapters 2 and 3, this may be far too pessimistic a point of view of the nature of entropy. From the action resonance theory described in Chapters 2 and 3, it is clear that adding more energy as quanta to a system – always an entropy increase by Clausius’ definition - will spontaneously generate more action, because of the increased rate of impulses and greater exchange of momentum possible. The final extent of readjustment after such an addition is usually characterised as the system spontaneously reaching a state of minimum overall energy. Can this characteristic be better explained? In this chapter, the limits of spontaneous readjustment in natural processes as the result of the operation of thermodynamic forces will be examined to see if action resonance provides a simpler explanation. However, at the outset it is stressed that the increase in entropy possible in such processes is strictly limited by the amount of energy added at a given temperature. This is implied by Clausius’ definition of entropy as the capacity for heat absorption at a given temperature and also by the Boltzmann definition, if for the latter case it is accepted that greater redundancy of energy states and greater probability also means greater action as proposed in Chapter 3. Indeed, when considered as indicative of the generation of action by energy, it will become clear that the idea of entropy as disorder must be revised, because it has been quite misleading. We may profitably distinguish between the initial disorder as energy becomes available to the system from physical or chemical sources, before molecular entropy or action is generated, and the more relaxed situation when the system has rearranged. Although it may seem at odds with current understanding, a remarkable feature of the molecules at a transient hot spot is that their entropy initially increases dramatically from their increased molecular velocity. The subsequent reaction progress is one in which the entropy and action of these hot molecules then decreases to the minimum possible as their energy is redistributed. Radiant energy is simultaneously redistributed to other molecules of lower energy content and entropy in the system.

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It will also become clear in the following discussion that, despite Clausius’ injunction of the entropy of the world increasing to a maximum, the long term rate of entropy increase of molecules on earth is actually negligible or zero. Certainly, there are temporal, local, increases in entropy, but these always occur as part of reversible physical or metabolic cycles. Rather than having a general trend of increasing entropy, all the molecules in earth’s ecosystems are actually characterised by fluctuating entropy and action. Full consideration of entropy in this new light, linked to cooperative action, may even show later that the conclusion that the entropy of the world or universe is increasing to a maximum - so dramatically enunciated by Clausius - can also be revised. Indeed, it is predicted that action thermodynamics will allow a revision of our understanding of the second law itself so that even the generation of ‘order from chaos’ can be considered as the natural outcome of the second law. Chaos and disorder will then be seen as normal characteristics of transient unstable states, or states of continuous stress or steady non-equilibrium, rather than of the more relaxed state of dynamic equilibrium or order towards which the system tends to evolve. The spontaneous generation of states of increased entropy is still a matter of fact, but to consider this final state as the most disordered simply ignores the much more chaotic stage just following the initial point at which energy is added to the system. This increased energy content provides the impulses with which increased action and entropy are generated. So the second law really describes the trend to generate a relaxed state from a stressed state, quite the opposite of more chaos and disorder. In fact, the underlying principle involves the generation of more balanced order, where the stresses are, as far as possible, shared equally. We intend to show that such a sharing of the impulsive forces of resonant action actually favours growth and the development of complexity in ecosystems. This reversal of the meaning of chaos and disorder and a suggested constancy of molecular entropy, on average, does not mean that the apparent outcome of increasing entropy in the steady state operating in our part of the universe is incorrect. In fact, as the next Chapter will discuss, life on earth depends on a continuous amount of energy being emitted at high temperature from the surface of the sun, about 70% of which is initially absorbed in earth’s ecosystems, sustaining many work processes in the biosphere and the atmosphere. The increase in entropy1 results from the fact that the same amount of energy is emitted later from the surface of the earth but at a much lower temperature. The physical meaning of this is that a relatively small number of rays of sunshine of high frequency absorbed on earth is converted into a much larger number of rays of “earth 1

-∆S = Q/Tsun – Q/Tearth; 1.7 x 1021 ergs (Q) per second of sunlight emitted at 6000 K is intercepted by the earth and re-emitted at about 255 K from the top of the atmosphere (therefore the negative entropy consumed per second as sunlight on earth is about 1.7x1021/6000 - 1.7x1021/255 = -6x1018 ergs/K). This decrease in negative entropy or increase in entropy assumes an approximately balanced steady state in which the total radiation energy received by the earth from the sun must equal that radiated by the earth, although the latter is redistributed before emission. We must also have Q = Σnshνs = Σnehνe, where the mean frequency and energy of the solar energy spectrum hνs >>> hνe, the mean energy of radiation emitted from Earth . Therefore the number of quanta for total energy Q emitted on earth ne >>> ns,, the number emitted from the sun intercepted and absorbed by the earth although the total emission of actons from both must be the same. In fact, the earth generates some of its own radiation as a result of gravitational stresses (e.g. volcanoes) or radioactive decay, but this does not affect the validity of the argument given above.

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shine” of much lower frequency. But the total momentum of the quanta involved and the number of primary impulses as individual actons2 in solar radiation must be the same in the earth’s radiation, although the earth’s radiation can certainly be regarded as less ordered than the sun’s. From Clausius’ mathematical definition, this process of absorption of sunlight and its re-emission later at a lower temperature provides all of the increase in entropy necessary. However, the equation is only validated once the total energy emitted from molecules in resonant quantum or action states at the surface temperature of the Sun has equilibrated with the same total energy for resonant quantum or action states of molecules at the temperature on Earth. Thus, Schrödinger’s conjecture that life on earth feeds on the stream of negative entropy from the sun derives its validity. But sunshine is also the direct source of enthalpy or heat as radiant energy on earth, which provides impetus for nearly all life’s actions. An important bonus emerging from this revision of the second law using action theory is that no new general principle for generating biological order in the Universe other than the second law will now be necessary. The second law itself is a perfectly natural outcome of action resonance and the spontaneous flow of radiation and its momentum from hotter to colder molecules. We need look no further than to this revised version of the second law to find the basis for evolution of the most complex ecosystems and organisms on earth. We may even claim that the second law can be derived from the principle of the conservation of momentum exhibited in the recoil of molecules from the impulses of energy. 4.2.

Enthalpy and action resonance

4.2.1. Classical enthalpy Experience has shown that all chemical reactions are accompanied by either heating or cooling. The amount of heat evolved or consumed depends on the difference in the total energy content of the reactants and the products and whether work can be coupled to the reaction. The generation of heat initially raises the temperature and kinetic energy of the system. To the extent that a degree of freedom exists in the system allowing work to be done on the surroundings (e.g. expansion work of gases against the constant pressure of the atmosphere) less heat is produced and there is an overall cooling effect. Even at constant pressure such as atmospheric pressure, the reaction may take place without a significant change in the volume of the system. This is true of most biochemical or biological reactions occurring in the aqueous cytoplasm of living cells. Here, most of the energy released or consumed may appear either as heating or cooling of the system, but this is reduced by the extent to which this energy is coupled to some other work process requiring energy, such as chemical synthesis. In fact, in living systems the latter case is very common. The nature of such coupling agents, highly typical of living organisms, will be discussed in subsequent chapters. On the other hand, many nonbiological chemical processes conducted at constant pressure are not coupled to such 2

The acton was defined in Chapter 2 as the basic unit of impulse from energy. The dispersive force (rate of impulses) exerted by a quantum of energy made up of actons will depend on its resonance time or the radial separation of the interacting material surfaces divided into the speed of light.

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work processes and nearly all the energy change, initially at least, will act merely to change the temperature of the system. For chemical reactions that take place at constant pressure in vessels open to the atmosphere, the change in total energy content is equal to the change in heat content minus any pressure-volume work3 done. Because heat changes in reactions can be measured fairly easily, whereas measuring total energy change requires a calculation from other data, it has been convenient to define a thermodynamic property known as the enthalpy as the heat of reaction at constant pressure. Our interest in enthalpy is derived from its role in the description of physical and chemical processes that evolve or absorb heat, thus altering the temperature of the local environment from heat transfer by radiation or conduction. We will also be acutely interested in the possible use in ecosystems of the heat of reaction or enthalpy as a source of energy for work, in addition to any pressure-volume work. Chemical reactions taking place in an insulated reaction vessel of fixed volume, in the absence of energy coupling agents, will only change the temperature of the system. A rigid vessel of this kind also prevents work being done on the surroundings or by the surroundings on the system it contains. Under these conditions, the change in total energy of the system during a reaction is exactly equal to the change in heat content. When reaction has ceased and equilibrium is reached with no further temperature changes, the total heat evolved or consumed in the reaction can be measured. This is achieved by measuring the temperature accurately and knowing the heat capacity of the system, calculating the total change in energy of the system during the reaction. Such a rigid vessel equipped with accurate thermometers is known as a calorimeter and from many such experiments, tables can be prepared showing the change in energy content during chemical reactions. Most chemical reactions take place in vessels open to the atmosphere. In order to calculate the enthalpy, which includes pressure-volume work, a correction must be made (Morowitz, 1968). Thus, the enthalpy content can be measured experimentally, tabulated and then calculated for other reactions. These values allow the change in enthalpy content of the reactants and products of any chemical process to be calculated. This enables the amount of heat energy or the change in enthalpy needed to dissociate the atoms of a molecule, such as methane4 into carbon and hydrogen atoms, to be calculated. Exactly the same amount of heat would be evolved as quanta in the formation of the methane molecule, beginning with gaseous carbon and hydrogen atoms. The energy needed to dissociate a mole of bonds of a particular kind is considered as the bond energy, which indicates the strength and stability of the bond. To chemists, high bond energy in a molecule actually indicates the absence of a quantity of energy needed to break the bond. The greater the

3

From the first law, the change in energy E2 - E1 = Q – W (heat – external work) for a process in which subscripts indicate final (2) and initial states (1). The total change in energy content for a process at constant pressure with pressure-volume (PV) work = E2 - E1 = QP – P(V2 – V1). Thus, QP = (E2 + PV2) – (E1 + PV1) = H2 – H1 = ∆H, defining the enthalpy as H = (E + PV); then the heat absorbed or evolved in any chemical reaction at constant pressure is represented by the symbol ∆H: ∆Hreaction = ΣHproducts - ΣHreactants. 4 CH4 (g) → C (g) + 4H(g) ∆H = +1661 kJ/mol = 2.76 x 10-11 ergs/molecule Thus, breaking four moles of C-H bonds requires the absorption of 1661 kJ of energy or 415 kJ per mole of C-H bonds.

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bond energy measured, the more stable the bond is and the more energy is needed to dissociate it. The concept that the change in enthalpy is the sum of the change in internal energy plus any pressure-volume work done by the molecular system is quite logical. This is because heat must be absorbed not only by the molecular system during the dissociation of bonds as its temperature rises but more heat is needed if there is work to carry out on expanding the atmosphere even when the temperature does not change. This is obviously true during the dissociation of one mole of methane into one mole of atomic carbon and four moles of hydrogen atoms where the volume of the chemical system increases five times. This external pressure-volume work has a cooling effect on the system. We will return to this important point many times later in this book.

Fig. 4.1: The tetrahedral structure of methane (CH4) was suggested in 1874 by the 22-year old Dutchman, Jacobus van’t Hoff. At the apices of the tetrahedron shown in this model of the molecule, the four hydrogen atoms are as far apart as possible. This is accepted to be a minimum energy arrangement – one that is also consistent with minimising the repulsive action resonance exchange forces carried as the impulses of quanta between the atoms by maximising the path-length or transit time. In order to dissociate hydrogen atoms, a large amount of additional dispersive exchange force between the hydrogen atoms in the molecule must be generated; this is achieved by raising the radiant energy or heat content of the system to the point where the screening effect of the central carbon atoms and of associated electrons is sufficiently diminished by separation that release of hydrogen atoms can occur.

We also recognise a change in the enthalpy of water when it is vaporised. A considerable quantity of heat is needed first to dissociate the hydrogen bonds of each water molecule to the liquid phase and then to expand the water molecule from its

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condensed state in water to the vapor state in air. This process was already discussed in Chapter 3 in relation to the increase in entropy and action of water at vaporisation. In fact, by the Clausius definition of entropy, the change in entropy5 of the water is equal to the change in enthalpy divided by the temperature at which vaporisation takes place. An increase in entropy for each molecule is involved but the vaporisation will only continue as a substantial process if a heat source such as an electrical element is available to heat the water. Such a process is regarded as reversible near equilibrium. Just as in the breaking of C-H bonds of methane, we see that the change in enthalpy involves a change in the internal energy of the water molecules together with the pressure-volume work performed against the atmosphere. Organic chemical compounds may be burnt in a calorimeter charged with pressurised oxygen gas and the heat evolved or absorbed can be measured, yielding the heat of combustion for the reaction. In principle, this process of combustion is the same as food chemicals being consumed by the physiological process of oxygen respiration. Such data provide the basis of the Calories tables for establishing dietary requirements of energy foods popular some years ago. However, some of the available heat energy in food, or its enthalpy content when burnt in oxygen, may be conserved in organisms as chemical energy in biosynthetic products, or even used in physical work. Either of these outcomes would also have a cooling effect, compared to complete combustion with oxygen of organic compounds to carbon dioxide and water. The great significance of enthalpy for living organisms is encapsulated in the popular declaration by the pioneering biochemists of the early part of the 20th Century that “life is a pure flame”. This requires an understanding that the enthalpy change of molecules is the primary source of heat for many living systems, part of which will be needed for biological work and part of which is needed to raise the temperature. Clearly, an isolated flame is not enough for life, for which a complex apparatus of genetically specified coupling agents promoting biosynthesis and other physical work such as locomotion is also required. However, a continuous flow of energy, as implied by the idea of a flame, is essential for living organisms to operate in a sustainable fashion. 4.2.2. Enthalpy and action resonance The absorption of heat from the surroundings to increase the internal energy or the performance of internal pressure-volume work increases the enthalpy content of a molecular system. Both processes heat the molecules. Equally, the extraction of heat from a molecular system by the performance of external pressure-volume work or the decrease in internal energy of molecules by the flow of heat to the exterior decreases its enthalpy. Action resonance predicts that an expansion of the system increasing pressurevolume work requires energy as extra quanta just to sustain the expanded system of molecules in equilibrium with the increased gravitational potential of the atmosphere. A greater resonant space between the molecules while in a sustaining equilibrium with the external environment is predicted to correspond to the need for more quanta to maintain pressure. Equally, an increase in the bond length between the atoms of molecules as they dissociate increases the internal resonant space in molecules versus the external; the transit time for quanta between the material surfaces of the atoms increases, there is a reduction of material screening, more energy can be sustained by faster moving particles 5

The change in entropy involved in the vaporisation of water is: ∆S = ∆H/T.

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and hence the requirement for increased internal energy of the molecules increases as the temperature increases. Thus action resonance theory regards the enthalpy content as real radiant energy in a molecular system, required to sustain resonant action by the molecules within the system and by them with the environment. The enthalpy is field energy present as ground energy or quanta transmitted at the speed of light both within and between all molecules in the system. The content of quanta at a given temperature corresponds exactly to the requirement for sustenance of action by resonant momentum transfer between the material surfaces of the system of molecules. 4.2.3. The mass-energy equivalence and enthalpy The equivalence of mass and energy proposed by Albert Einstein in the theory of special relativity (1905) is not usually related to enthalpy. Indeed, the heat evolved or absorbed in chemical reactions is rarely mentioned in connection with Einstein’s definition6 of the equivalence of energy with mass travelling at the speed of light squared. Here, we invoke this concept to explain the source of the energy appearing as the enthalpy of reaction, such as in the reaction of hydrogen and oxygen to produce water. This reaction has a large negative enthalpy of reaction indicating that heat energy or pressure-volume work is transferred from the system as water is formed. Traditionally, the source of this energy or enthalpy of reaction is credited to changes in bond energy - in this case the exchanging of two hydrogen-hydrogen and one oxygenoxygen bond for four hydrogen-oxygen bonds. This energy is clearly not available from the store of heat needed to warm hydrogen and oxygen above zero degrees absolute to the ambient temperatures of ecosystems, although the heat energy experimentally required to raise the temperature of a mole of water from zero degrees is not greater than that required to warm hydrogen and oxygen to the same temperature. One must conclude instead that the energy as negative enthalpy of reaction is derived from the total massenergy field of the hydrogen and oxygen molecules, clearly including ground state energy associated with them at absolute zero. Then it follows that, in a reaction with a large negative enthalpy change where there is heat evolved to the surroundings, the massenergy of the products must be less than the mass-energy of the reactants equivalent to an amount of mass that can be estimated by Einstein’s equation. In chemical reactions, this change of mass would be extremely small. For example, the reaction of hydrogen with oxygen to yield water7 produces 5.7 x 1012 ergs of heat per mole of oxygen consumed. This is equivalent to a decrease in mass of 6.3536 x 10-9 g for each mole of water produced - only one part in 5.66 billion by weight of the water formed. This is much too little mass for known mechanical balances to measure accurately, but finding a means to measure such a small change in mass would allow this prediction to be tested. Of course, assuming the Einstein mass-energy equivalence is correct, the calorimeter is the most appropriate means to measure the change. Incidentally, the majority of the change in enthalpy is associated with internal bond energy rather than the pressure-volume work done in compressing two moles of hydrogen 6

E=mc2. 2H2(g) + O2(g) → 2H2O(l) ∆H = -5.71824 x 1012 ergs/mol of oxygen; m = E/c2 = 6.3536 x 10-9g The system’s volume decreases, at one atmosphere pressure, from 74.94 litres of gas to 36 mL liquid; therefore P∆V = 1x73,940 cm3 atm = 7.394 x 1010 ergs per mol of oxygen. 7

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gas and one of oxygen gas to 36 mL of water as liquid. The enthalpy change from this compression is only one percent of the total enthalpy change. The change in bonding energy results not only from the substitution of H-H and O-O bonds with covalent O-H bonds within water molecules but also by formation of the much weaker O--H hydrogen bonds between water molecules in clusters. Formation of the weaker hydrogen bonds when water condenses from the vapor phase and is cooled to 298oK contributes 16% of the enthalpy change, with the remaining 83% coming from the change in enthalpy of covalent bonding between oxygen and hydrogen atoms. Thus, there are many physicochemical changes that must be considered in understanding such changes of chemical state. A full understanding of this topic would require a much better appreciation of the true nature of mass-energy and the physical basis of inertial mass and momentum than we have mastered till now. The conclusions in action resonance theory that the incessant impulses of quanta sustain the Brownian motion of molecules and that heavier atoms and molecules require more quanta to sustain or elevate them in a gravitational field provides some basis for further analysis of the nature of inertial mass. We recognise that heavier molecules require a greater force or rate of impulses to alter their current state of motion, which may simply reflect the existence of greater rates of impulses already associated with their motion. This view of mass or inertia as a dynamic phenomenon related to impulses contrasts with the current static view. In the action resonance theory, for a reaction with a negative enthalpy change, one would conclude that the need for field energy including quanta in the case of the product molecules to achieve a given temperature is less than the field energy needed in the reactant molecules. This is rationalised as resulting from the changed velocity or screening of the matter within molecules, including changes in the configuration of the electrons. Less field energy is required to sustain hydrogen atoms and oxygen atoms as water molecules than when hydrogen and oxygen atoms are directly linked. The average velocity8 of molecules at the same temperature is inversely proportional to the square root of the mass, so that dihydrogen gas translates three times as fast as hydrogen linked in water as a gas, now in a higher action state. On the other hand, oxygen in water vapour will translate faster than oxygen in dioxygen by a factor of 1.333, altering the field energy required to sustain it when part of the water molecules. Oxygen in dioxygen will be screened, appearing almost as one atom on its axial dimension, also true for dihydrogen. Obviously, the possibility for screening of the material of hydrogen atoms and oxygen atoms is greater still in the condensed liquid phase. The change in enthalpy during the chemical reaction then is the outcome of all these factors and particularly of the physical changes associated with the geometry of electronic configurations. Some of these changes may increase the enthalpy capacity of the molecules concerned, cooling the reaction system, but more often in spontaneous processes they will reduce it, initially heating the system (negative enthalpy change). 4.2.4. The enthalpy of ATP hydrolysis - the energy currency of metabolism A reaction of great biochemical relevance is the potential for hydrolysis of adenosine triphosphate (ATP). This ubiquitous reaction occurring in living cells yields an enthalpy decrease about 2.0 x 1011 ergs of heat energy when a mole of ATP is hydrolyzed (Figure 8

KE = mr2ω2/2 = 3/2kT; so r2ω2 = v2 = 3kT/m; Therefore v = (3kT/m)0.5.

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4.2) under standard conditions at 36oC. The quantum of energy involved is equivalent to infrared radiation with an average wavelength of 5.983783 µmetres. This is also equivalent to a loss of 2.2516 x 10-10 g in the mass-energy of the products, a change much too small for practical measurement in a total of several hundred grams of reactants and products. ATP is a key metabolite found in the cells of all living species and its role in metabolism and bioenergetics will be examined in more detail in Chapter 6, later in this book.

Adenosine 5’-triphosphate (ATP)

Adenosine 5’-diphosphate (ADP)

Fig. 4.2: The ATPase reaction, hydrolysing ATP to ADP and inorganic phosphate. The standard free energy change (ǻG) in this reaction is -3.2 x 1011 ergs (0.5 x 10-12 ergs per molecule) and the standard enthalpy change (ǻH) is –2.0 x 1011 ergs. This corresponds to –32 kJ and –20 kJ per mole respectively under standard conditions of 25oC as 1 kJ (kilojoule) is 1010 ergs. Since (discussed later in this chapter) ǻG = ǻH – TǻS, more than one-third the spontaneity of the reaction (-12 kJ) is a result of entropy increase (and much more action) in the products, mainly as a result of the increased radial separation of phosphate groups. ATPases occur in an inactive form in living cells because it is important to maintain the reactants and products of this reaction in a non-equilibrium state in order that other chemical and physical processes effectively carrying out this reaction can be coupled to the conversion of ATP to ADP. As discussed in Chapter 6, this non-equilibrium state is much more powerful than standard thermodynamic conditions (where all reactants and products have a 1 molal concentration) would suggest, since the free energy change possible is 57 kJ per mole (1.0 x 10-12 ergs per molecule), almost twice as much as under standard conditions.

Biologists stand accused, by physical chemists (Banks, 1970), of misunderstanding the function of ATP in metabolism - particularly when they refer to ATP as possessing “high energy” phosphate bonds. Conventionally, when chemists refer to chemical bonds as being of high energy, they mean stable bonds that require a large input of energy to break them. Conversely, one might say that forming a stronger chemical bond indicates a lower quantity of field energy associated with the atoms involved. Despite a high free energy of hydrolysis of ATP indicating spontaneity, a key property of ATP is its high stability when dissolved in water. In fact, the direct ATPase reaction given in Figure 4.2 occurs rarely if ever in living cells, except as an overall result when coupled through special agents to some other work process such as muscle contraction. There are numerous biochemical reactions that are coupled to this negative change in free energy and enthalpy in the reaction between ATP and water, yielding ADP and inorganic phosphate. And from the holistic point of view of action resonance theory the biochemists’ intuition that ATP hydrolysis is associated with the breakage of “high energy” bonds may, paradoxically, be correct. However, this must be understood in

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terms of higher field energy of ATP plus water providing energy quanta that can be released when ATP molecules are broken into two, forming ADP and inorganic phosphate. More resonant energy is contained in the action field of the molecules of ATP and water than in their products, ADP and inorganic phosphate and in this positive sense the phosphate bonds of ATP are, indeed, high energy bonds. The action resonance theory predicts that, when an ATP molecule reacts with water and disappears, reappearing as ADP and inorganic phosphate, there is a decrease in the resonant energy needed to sustain the ATP-water system and an increase in the resonant energy needed to support the ADP-inorganic phosphate system. But the increase in the latter is less than the decrease in the former, providing an excess of field energy over that required in the products. We may note that, immediately after the hydrolysis of one ATP, the individual ATP molecules now have slightly more volume to act in than previously and that they are slightly more separated. That is, they have greater action at the temperature of the system and therefore are in a higher quantum state and have greater entropy per molecule. But the system can release a quantum of sustaining energy because there are fewer molecules (by one) in the system (note that the same effect would be achieved locally inside the cell if one molecule were to leak out through a pore). On the other hand, both ADP and inorganic molecules are now in a lower action or quantum state than before and have lower entropy per molecule than formerly. The size of the quantum of energy released is the net outcome of all these decreases and increases in the sustaining energy needed in the system. There are two possibilities regarding the fate of the quantum of energy released into the system. The quantum can be used to do work either inside or outside the system, provided there are efficient coupling agents such as enzymes, contractile tissue or membrane transporters present. These are required to capture and transfer the quantum of excess energy. Alternatively, the quantum of energy can be dissipated in causing extra kinetic energy in the molecules, raising the temperature of the system. This thermal radiation can then flow to the surroundings or it can be used to perform pressure-volume or gravitational work. Effectively, this increases the entropy of the surroundings to the extent of heat added at the temperature of the surroundings9. A mixture of these two outcomes would occur if the quantum of work performed is less than the quantum of energy available. We then say that the efficiency of coupling is less than 100%, which is the most probable outcome. 4.3.

Spontaneous processes and work potential

4.3.1. The Gay-Lussac expansion One of the most important conceptual experiments ever performed in thermodynamics was that carried out by Gay-Lussac (1807) in France. Two chambers in an insulated box were connected as shown in Figure 4.3. One chamber contained air while the second was evacuated and a stopcock between the two opened, allowing the gas to expand spontaneously into the second chamber. Thermometers in each chamber recorded the temperature. When all gas flow had ceased, no significant difference was observed between the temperature in both chambers, although the caloric fluid theory of heat, then 9

dS = dQ/T.

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popular, predicted that the temperature should drop because of the greater space the fluid caloric would now occupy. Mayer was intrigued by this result, which had been largely overlooked, and explained it (1842) as follows. In the usual expansion of a gas against a piston, work is done in pushing the piston. The temperature of the gas should fall as some of its internal energy is converted into external work. In Gay-Lussac’s experiment, however, no work needed to be done during the expansion into the vacuum. From our perspective, this is an irreversible process where action and entropy is apparently generated only as a result of the special initial conditions. In establishing these improbable initial conditions, expansion work had already been done in preparing the vacuum and the energy needed to sustain the system in either configuration had already been provided.

Fig. 4.3 The Gay-Lussac experiment. Flask 2 connected to Flask 1 is evacuated and the connection between both flasks is opened. The entire apparatus allows the temperature change, if any, following the expansion to be measured. The conclusion, despite technical difficulties of measurement, was that there is no such change in temperature. Classical thermodynamics indicates that the change in entropy is ∆S = Nkln[(V1 + V2)/V1], where N is the number of molecules. Action resonance theory considers the whole system and proposes that both compartments contain equal densities of ground state energy but that the density of quanta (fluctuations in energy above ground state as a result of relative motion) is greater in Flask 1 as shown, according to the difference in pressure. During the expansion, molecules in Flask 1 do work on those in Flask 2, compressing them decreasing their entropy and action while those in Flask 1 expand, increasing their entropy and action. The position of equilibrium when all flows have ceased and temperature has re-equilibrated through the system is the position of least action, resulting from a threedimensional least-cubes plot of molecular distribution, minimising the pressure differences and the impulses from exchange forces in the system. .

In fact, according to the statements of the action resonance theory (Chapter 2) the ground state field energy required to sustain the molecules in the system at a given temperature after expansion, even when there is initially a large pressure difference between the two

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compartments, was already present. As long as no external work is performed during the expansion, except by the high pressure gas on the low pressure gas, there will be no change in temperature. It is true that there will be fewer detectable quanta in the compartment with fewer molecules, but these will still carry sufficient momentum to generate the torques needed to maintain the same temperature as in the first compartment at higher pressure. The quantum state and action of the set of molecules in the compartment with a lower pressure will be greater per molecule than in the compartment with higher pressure, but the kinetic energy of the molecules will be the same in both. From the field energy point of view, there is no relative vacuum at all in the low pressure flask and the ground state energy per molecule must be greater than the gas at higher pressure. For the action resonance theory, the ancient adage of Aristotle that “Nature abhors a vacuum” can be considered as true after all. In such a system, only if net work is done either inside the system or externally, will any temperature change occur. However, despite this equality of the density of ground state energy in both flasks, the pressure resulting from the energy fluctuations of the quantum exchange forces is very different and the once the connection between both flasks is opened, a flow of molecules from the high pressure to the low pressure results. This flow will continue until action exchange forces are equalised. Although it is customary to calculate an increase in entropy for the system in terms of the increase in volume, in fact there is an increase in entropy per molecule only in the first flask. In the second flask there is a compression of molecules as the expansion from the first continues and the increase in entropy (and action) in the first flask is matched by a decrease in entropy (and action) in the second. So the process of expansion (and compression) is actually one of optimisation of entropy and action during the irreversible process. Action resonance theory predicts that there will be transient heating as gas molecules are accelerated into flask 2, but that this heat will be required to counter the cooling effect of the increase in action states of molecules in flask 1. In a paper published in Annalen der Chemie and Pharmacie edited by Liebig, after it had been rejected by a more prestigious physics journal, Mayer boldly went further. He reasoned that the extra heat required in heating a gas in a container at constant atmospheric pressure compared to heating the same gas in a rigid vessel at constant volume was consumed in doing work of expansion10 against the constant pressure imposed by the surrounding atmosphere. We discussed this concept earlier in section 4.2.1 in this Chapter, in considering the pressure-volume work included in the enthalpy, but Mayer provided the original idea. This extra heat is the difference between the heat capacity at constant pressure versus that at constant volume. This reasoning enabled Mayer to calculate the mechanical equivalent of work and heat. Joule in the United Kingdom had determined the mechanical equivalent of heat independently, by using the opposite method of measuring the small rise in the temperature of water following mechanical work being performed on it after its randomisation as molecular motion. 10

In modern classical terms, if W is the work done by a gas in an expansion, then: W = œPdV = RTln(V2/V1) For a pressurised gas in an insulated box doing adiabatic work through a moveable partition against the atmosphere, the final gas would cool by an amount decided by the work done and the heat capacity of the gas. An enclosure is called adiabatic (Buchdahl, 1975) if the equilibrium of a system within it can only be disturbed by mechanical means. It follows that no heat can be transferred into or out of the system, so that any work done by the system must be equal to the change in its internal energy.

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4.3.2. Expansion and work from a gradient in chemical potential A useful extension of Gay-Lussac’s model experiment would be to insert a turbine as coupling agent between the two chambers using a pure gas in the first chamber. The turbine could then act as an agent to couple impulses from the flow of gas into the vacuum of the second chamber to the performance of mechanical or electrical work. In this case the temperature in the second chamber, when the gas flow had ceased with the pressure in each chamber now the same, would be less than the initial temperature. The fall in the heat content of the gas indicated by the fall in temperature would be equal to the work performed. This form of heat engine may seem artificial, but in living organisms the performance of biological work will be seen in Chapter 6 to be quite similar in principle to this model. One important difference is that biological systems normally allow analogous expansions to take place in the steady state, so that the concentration of the molecules in the first compartment relative to the second remains fairly constant. In this model, the work11 possible for the transfer of each molecule of gas from one chamber to the other depends on the difference in what is called the chemical potential of the gas in the two chambers. The chemical potential12, a concept introduced by Josiah Willard Gibbs at Yale in the USA, is defined as the partial derivative of free energy (the potential to do work) with respect to change in molar concentration, holding temperature, pressure and the concentration or activity of all other components constant. As an alternative to this mathematical definition, we may use a physical model similar to that discussed above by defining chemical potential as the change in the capacity of a chemical system to do work as a result of the removal (or addition) of a molecule of a chemical substance. Its value can then be expressed per mole of such molecules, simply by multiplying by Avogadro’s number for one mole. So the work possible from the transport of one molecule from one compartment to another is equal to the difference in the chemical potential between the two compartments. The work possible for each successive molecule transferred will stay the same only if the relative concentration or activity of the chemical substance in the two compartments remains the same. In living cells, to have such a steady state in the relative concentrations of a chemical substance is a common occurrence. For an irreversible flowing system such as in the Gay-Lussac experiment and many industrial chemical reactions performed in batches, the average concentrations of the gas in each chamber varies with time and the theoretical capacity to do work will depend on the current ratio of concentrations. This ratio will be greatest at the earliest times, depending on the degree of vacuum, eventually declining to a point where the concentration or pressure is the same in both compartments and the capacity to do work will be zero. The Gay-Lussac model can be discussed further as a model for other systems. Although it is possible to conclude that the capacity to do work by such a system simply depends on the pressure difference between the gas in the two chambers, this would be a 11

Work potential = µ2 - µ1 = ∆µ = kTln(C2/C1), where µ indicates the chemical potential of the gas per molecule. 12 Chemical potential is the differential change in the capacity to do work relative to a differential change in the activity of the chemical substance: µi = (∂G/∂ni)T,P,n.

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false conclusion. If the second chamber, instead of a vacuum, contained another gas (i.e. a different chemical species) at the same pressure or concentration as the gas in the first chamber, the same capacity to do work by the first gas still exists. Furthermore, to this can now be added an equal work potential arising from the reverse expansion now possible of the second gas into the first chamber. However, a specific turbine or coupling agent selective for the second gas and unaffected by the pressure of the first gas would be needed for this second system to perform work. Obviously, we must conclude that the pressure exerted by each gas or its kinetic energy cannot be the source of the extra work potential. These should now be balanced in the two chambers, since both gases are at the same pressure and temperature. We must conclude that the chemical or work potential is a specific property of the particular chemical species. Another remarkable property of such gradients in chemical potential in doing work is that the magnitude of this potential depends only the relative concentrations in the two compartments. The work potential per molecule is independent of the absolute concentrations of the chemical species making the transit. Thus, a gradient of millimolar to micromolar concentrations has the same potential to do work as a gradient of micromolar to nanomolar or nanomolar to picomolar, each molecule experiencing the same ratio of concentrations of one thousand-fold for its passage. Of course the total capacity to couple this work potential would be affected, since the rate or frequency of passage of molecules would probably be affected by the absolute concentration. The total capacity to do work is the change in chemical potential per molecule times the frequency of transition possible. Furthermore, there is no need for the fluid in this development of the Gay-Lussac system to be a vapour. A solution of a gas or of any other chemical species in water would have exactly the same total chemical work potential for the same gradient in concentration. Here, an irreversible process of diffusion would occur, until the concentration of each chemical species was the same in both chambers. But for a denser system, such as a liquid, the time taken to reach equilibrium would clearly be much greater than for a gas. Later in this book, the ability of gradients in proton concentration or pH to do chemical work will be discussed. These are now recognised as of primary importance in life processes, providing a means of storing chemical energy in special organic substances containing phosphorus. It will be shown how the action resonance theory can explain the mechanism by which energy is stored, as protons move through special ion channels in proteins embedded in biological membranes. Each time a proton moves from an action field where it is present in higher concentration to a field where it is at lower concentration, a quantum of energy is made available, allowing the performance of biochemical work13.

13

An article in New Scientist in 1998 described the phenomenon of mysterious sound waves generated when pressurised liquid helium molecules near absolute zero were allowed to pass through a pore in the wall of the container to liquid helium at lower pressure. However, this process is the same in principle as the forceful passage of protons through the ion channel of the membrane enzyme ATP synthase (see Chapter 6), resulting in the synthesis of ATP. In fact the quantum of energy released as sound (and presumably heat) as helium atoms are accelerated by action resonance into a zone of lower chemical potential is much more usefully exploited in living systems when protons are accelerated through the pore in the molecular motor, ATP synthase. We can humbly observe that nature learnt to put this phenomenon

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4.3.3. Action resonance as the source of chemical potential What is the physical source of this chemical work potential? The current operational response to this question is usually to state its source as the gradient in chemical potential between the two chambers, effectively dealing with this query mathematically. Here, in employing action resonance theory, extra detail can be provided by the proposal that specific impulses of the action field referred to in Chapter 2, provide the driving force we recognise in the chemical potential of each species. From the impulses of action resonance, the two fields of the same kind of molecules would experience a thermodynamic force and pressure14 of a magnitude dependent on the local concentration of the specific molecule. A molecule about to make a transition from one chamber to the other, could experience impulses or momentum exchanges from specific quanta directed from both chambers. But the imbalance between the fields of quanta from the two chambers would provide a net force on the molecule in the direction of declining chemical potential, allowing the performance of work. The magnitude of the force can be estimated, since the maximum amount of work possible in a transition would be the integral of the product of force x distance through which the force acts on the moleculecoupling agent. Thus, the capacity to do work is a thermodynamic property of a system of particular molecules and the existence of a thermodynamic gradient. Once the concept is grasped, it seems inescapable that the mechanism of energy transduction requires such a physical process, changing the action of each molecule during its transition from one chamber to another. Action theory, in which the force between molecules results from the momentum exchange possible by exchange of quanta, must therefore be refined. The action field is obviously specific for each set of molecules. This specificity can readily be achieved if the frequency of the quanta involved is specific for each set of molecules. This will automatically be so because the quantum state of each set of molecules differs, according to their action (which is proportional to concentration and temperature as discussed in Chapter 2). All molecular sets at equilibrium or in the steady state involve distributions of material particles (electrons and nuclei of atoms) in which there are periodic recurrences of particular complexions with particular frequencies. It is proposed that there will be corresponding sets of quanta in the molecular fields, of an intensity characteristic of the temperature and pressure, which provide specificity of the energy field. This spontaneous equilibration between matter and specific quanta is a basic statement of the action resonance theory and is considered to be the source of specific spectra for different elements and other substances. Even in dense mixtures of different sets of molecules, this sorting of sustaining quanta by matter will ensure a sufficient degree of specificity in the energy-action field, because most quanta readily penetrate deeply into the molecular field before interacting with molecules, as most of the volume is space. Thus, in terms of specific frequencies of quanta the energy of the action field is quantised as proposed by Max Planck. As a result of the capacity of these specific quanta to provide a significant number of impulses by simple resonance, a dispersive

for converting chemical potential to work, only recently shown with liquid helium, to good use several billions of years ago. 14 This molecule-specific thermodynamic pressure can be considered as similar to that referred to as fugacity, or the escaping tendency.

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thermodynamic force or torque can be generated, which must be eq ual for all sets of molecules in a system at equilibrium. Wherever there are gradients in concentration or action of particular kinds or sets of molecules there will be an action potential (difference in action state) providing chemical work potential. This disparity in force is proposed to provide the mechanism for the expression of chemical potential as work. As in case of permanganate ions in solution discussed by Schrödinger and mentioned in Chapter 2, the action resonance theory extends the assumptions of statistical mechanics on this point. Statistical mechanics involves a mathematical treatment of molecular systems using Newton’s equations of motion to model random collision processes between molecules. However, it lacks any mechanism for generating specificity in the forceful interactions of a particular set of molecules and assumes that molecular processes are time invariant so that reactions can run in either direction in time with equal facility. By contrast, the action resonance theory is strictly asymmetrical with respect to time. It proposes that the gradient in numbers of molecules in the field providing the action potential also provides a real diffusion force acting to drive the chemical species from a high concentration region to the low concentration region. This is not spontaneously reversible and it clearly challenges the well-known conjecture of Poincaré that a dynamical system will eventually return to any particular configuration given sufficient time, however improbable. Poincaré’s conjecture suggests that the gas molecules in the Gay-Lussac experiment will spontaneously all return to the first flask leaving a vacuum in the second flask if only we were patient enough to observe the system for a sufficiently long time. Such a statistical conclusion is based on the concept that the number of possible states or ways of arranging the molecules in space can be calculated and the probability for any particular state estimated. The inference is that the system will be arranged in a certain way for a proportion of the time corresponding to its probability, requiring the time invariance of Newtonian mechanics. But the quantum exchange forces of action resonance theory ensure that such time reversal cannot occur without violating the principle of conservation of momentum. Therefore, Poincaré’s conjecture will be refuted, except for minor statistical variations related to the Boltzmann distribution near equilibrium, if action resonance theory is valid. This conclusion is relevant to the discussion to be conducted in Chapter 7 on the genotype x environment interaction and the probability of the origin of life and of subsequent evolution operating by blind chance. Action resonance theory concludes that simply waiting long enough for a thermodynamically improbable event to occur is an irrational procedure and can never produce a sustainable outcome. The direction of time is uniquely determined by the impulses from actons. However, if energy quanta sustaining the Brownian motion of the molecules are withdrawn from one flask by insertion of a probe or heat sink kept near the absolute zero of temperature, the dispersive forces can be eliminated and all of the gas will eventually return to the colder chamber. The connection between the two compartments can then be closed, fulfilling Poincare’s prediction. It was asserted strongly in Chapter 2 that numbers of molecules alone cannot provide a directed force, merely as a statistical outcome or as the result of a game of chance. However, the complementary but obligatory nature of matter and quanta proposed in action resonance theory makes it

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impossible to test the behaviour of matter with and without quanta present except by changing the temperature. For the moment, the reader must test this proposal by the use of common-sense, the explanatory power of the action resonance model and the simple predictive logic involved. For example, quanta (and the capacity to generate force) can be removed from matter by the act of cooling. In principle, a gradient in concentration or chemical potential would lose an increasing part of its power to do work as the temperature approaches absolute zero. At absolute zero, even the most intense gradient in concentration cannot result in a force without the requisite quanta being present. Clearly, at this temperature, all statistical arguments fail. It is anticipated that the action theory will be most severely tested because of its power to predict factors controlling the efficient performance of work and the influence of molecular geometry on this power. In particular, predictions about the nature and physical structure of biological coupling agents for achieving work, such as enzymes, whose structure and function are suggested here to depend on the complementarity of matter and resonant quanta, will also provide critical tests of the theory. 4.4.

Free energy and action potential

In the 19th century, Helmholtz in Europe and Gibbs in the United States proposed the concept of free energy or the potential to perform work soon after the concept of entropy was defined by Clausius. Helmholtz introduced the work function, relating the work possible to decreases in internal energy of a system and increases in entropy. The Gibbs free energy15, defined for chemical reactions was important because it allowed a mathematical definition of the existence of spontaneity and the potential to do work at a given temperature and at constant atmospheric pressure. The potential change in Gibbs free energy or electrochemical work potential at constant temperature and pressure consists of any enthalpy difference between the reactants and products of a reaction and any difference in entropy between the reactants and products. If the enthalpy change is negative and the entropy change is positive, the capacity to do work will be maximised, depending on the magnitude of each. So a negative value for Gibbs or Helmholtz free energy change indicates spontaneity. The fact that the performance of work always involves a decrease in Gibbs and Helmholtz free energies in the system must be kept clearly in mind. This is particularly so in understanding the fact that the estimate of work potential using Helmholtz free energy is always greater than that estimated by Gibbs free 15

Free energy was defined by Gibbs (G) and Helmholtz (A) respectively, in terms of functions of state that change during a chemical process at a given temperature (T), energy (E), enthalpy (H) and entropy (S) as: G = H – TS and A = E - TS Since H - PV = E, A = H – PV – TS; then A = G - PV More importantly, since the absolute values of these factors is never used: ∆G = ∆H - T∆S and ∆A = ∆E - T∆S -∆A includes expansion work together with any other chemical, electrical, osmotic and photochemical work. -∆G is called the useful work potential, since it excludes the work of expansion necessary against atmospheric pressure, P∆V; it is assumed that must be done in any case. If the reaction is carried out at constant volume rather than at constant atmospheric pressure, the potential to do work is ∆A and more work of other kinds can theoretically be done.

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energy, the difference being the amount of external pressure-volume work that must be performed in systems equilibrating with the atmosphere. Since this pressure-volume work is inescapable in open systems such as ecosystems, able to equilibrate with atmospheric pressure, Gibbs free energy is usually the appropriate function to use. These definitions provide descriptions of the direction of reaction only, related to changes in energy and entropy. Using action theory in explanation of the direction of reaction, one must consider the magnitude of the action resonance exchange forces involved. Any imbalance in the action or quantum states of the field of reactant and product molecules for the temperature of the system would lead to imbalances of the respective action resonance forces. In general, reactant molecules at high concentration, relatively low action per molecule but a high density of resonant quanta would tend to evolve into product molecules with lower density of quanta but of higher action state. Provided interconversion can take place, transitions would be expected to occur spontaneously, until the point is reached where the forces generated dependent on the magnitude and density of the quanta for both reactants and products balance. In addition, one can imagine that excess quanta generated in a chemical reaction would raise the density of quanta, the kinetic energy and temperature/pressure of the products; subsequent external work of some kind would then tend to cool the system towards the original temperature. In view of the direct relationship between entropy and action proposed in Chapter 3, it might be thought that a spontaneous process simply requires that the change in action be positive. Thus, the absorption of a quantum of energy by a set of molecules so that the total action and entropy of the set has increased is one such spontaneous reaction. But it must be remembered that the theory suggests that collisions also lead to emissions of quanta, so that the action of molecules can also decline. The deliberate removal of heat from a mixture of gas molecules, to the temperature where some of the gas molecules condense or freeze, also decreases the action and entropy of the mixture, although that of the cooling agent must increase. In fact, it should now be clear that any spontaneous evolution of physico-chemical systems is directly the result of resonant exchange forces exerted by quanta generating action and performing work. It is by examining these processes involving momentum exchanges and balancing of forces that spontaneity can best be explained - although a final outcome that the total action and entropy has increased, because of irreversibility, may be helpful information in predicting the outcome. But the fact that real-world processes never reach equilibrium because of continual fluctuations in environmental conditions argues in favour of approaches to this problem that will focus on the forces of action resonance. The Gibbs and Helmholtz free energies can then be considered as action potentials indicating the capacity for a molecular system to evolve, with resonant radiant energy driving the redistribution of matter. Work can be done in a chemical process if the enthalpy of the products is less than that of the reactants, in which case there will be less heating as the action exchange impulses of the quanta released are now required to sustain the work done. Or if the entropy of the products is greater than that of the reactants; in the latter case, to the extent that work is done, heat will be needed from the surroundings to sustain the new configuration that amounts to the work. In both cases, it is the “springiness”of the action exhange forces and the freedom of the overall system to adjust its configuration, thus relieving the stress from impulses, that provides the spontaneity of reaction.

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4.4.1. Entropy – disorder or not? It is most unfortunate that the suggestion of increasing disorder or molecular chaos has been so consistently linked to increasing entropy. The analysis made possible by action resonance theory shows that all spontaneous work processes driven by quanta correspond to increasing action and entropy. All increases in the state of motion of molecules as radiant energy is absorbed by molecular systems increase their action and entropy. But the notion of increasing disorder implied by Clausius’ brilliant definition of the second law, as increasing entropy, is a dismal view. Conversely, the order it extols is that of complete inaction and the timelessness of the absolute zero of temperature, where no change exists. Indeed, changelessness at absolute zero is the most obvious philosophical and practical conclusion of the third law of thermodynamics - that the entropy of a perfect crystal at zero degrees is zero. Unfortunately, we have not sufficiently understood Born’s definition of the third law to provide an effective antidote to the pessimistic viewpoint of entropy as disorder. When Planck (1913) developed the theory of quanta a century ago he pointed out that the absorption of a quantum of radiant energy always corresponded to an increase in entropy of the molecular system. But who will decide if the free quantum of energy in transit from one molecular system with its associated package of impulsive momentum and an unexcited molecule in another system is less disordered than the second system following the absorption of the radiation? Is a hydrogen atom with its electron excited to a higher energy orbital, where its kinetic energy is actually less by an amount equal to the quantum of energy absorbed more disordered? A case can readily be made that the excited hydrogen atom with its electron at least temporarily in a stable orbital has a higher state of order. In this process, we can more logically assert that the most disordered, chaotic, state existed at the instant when the quantum of energy is just being absorbed and about to disrupt the motion of the electron from the lower energy orbital. Action resonance theory assumes that such impulsive exchanges of radiation are essential for molecular motion and action to occur. Spontaneity in these cases essentially involves decreases in free energy and increases in entropy. All machines and life itself depend on the existence of entropy and action, but neither too little nor too much. All increased motion is increased entropy, even that generated in coherent objects such as locomotives, motor vehicles or aircraft. The fact that the steam locomotive moves, rather than the resonant energy setting it in motion being dissipated instead as internal motion in its molecular structure, results from the fact that the bonding between the iron molecules in steel is too strong and rigid. A path of least action is preferred and the locomotive moves as a coherent object rather than melting where it stands. This path occurs spontaneously and not mysteriously, as a direct outcome of the resonant action forces, using the least resistant degrees of freedom to motion in the system. A rigid structure, its rigidity itself being a function of its temperature, must have the property of transmitting the action exchange forces exerted by quanta resonating between all the structure’s molecules in a coherent fashion. Any lack of rigidity or inelasticity in the structure will reduce the efficiency of generating this coherent motion, generating friction and heat. But inelastic molecular collisions continuously mitigate this tendency to increased action, by also stimulating the emission of quanta. Furthermore, the analysis in Chapter 3 indicated that the extent of the increases in action and entropy is strictly limited by the space and the density of quanta available. Indeed, it was conjectured that the position of

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equilibrium achieved, because of the tendency for equalisation of the rate of impulses or thermodynamic forces three- or four-dimensionally, would be that providing least action for the whole system. This is true for the Gay-Lussac expansion when considering the changes in the whole system, but also for any chemical reaction. Considered from the viewpoint of the exchange forces generated by action resonance, the state of greatest disorder or stress must actually be that existing at the point when radiant energy first becomes available to the molecular system. This is independent of whether radiant energy is provided from outside (as in a steam engine), or it is internally generated by chemical reactions (as in an internal combustion engine), or from physical reactions such as molecular collisions. Thus, if the initial molecular state corresponds to the state of maximum free energy, the state immediately subsequent when radiant energy is added corresponds to the stage where chaos and catastrophe theory most aptly apply and where action will occur spontaneously. There is now the greatest opportunity for rearrangements of the system, whether by chemical reaction or by physical processes such as in an atmospheric storm. As a result of resonant action, the outcome of the subsequent rearrangement is to equalise the stress throughout the system. This is no less true of biological systems and ecosystems, although the coupling agents that have evolved to help achieve this outcome, discussed in other chapters, may themselves be of extraordinary complexity and efficiency. The analysis possible by action resonance theory of the Gibbs equation or the work function of Helmholtz thus helps strip away the mystery with which these were formerly surrounded. By providing a simple, dynamic explanation of these thermodynamic concepts, it should now be possible to rapidly advance the application of thermodynamics to the study of the rates of transition processes in ecosystems. The simple principle that will guide this advance is that of least action, by which the most rapid and efficient processes will occur by routes involving the least requirement for energy by using spatial geometries of matter also minimising the action or quantum number of the route required. 4.4.2. The Carnot cycle for heat engines Sadi Carnot, in developing a keen scientific interest of his father, also recognised the significance of the Gay-Lussac experiment as a basis for rejecting the caloric theory of heat as a simple fluid. He then developed a brilliant theoretical model for analysis of the heat engine’s conversion of heat to work and to examine the efficiency of this conversion. This model introduced the concept of the reversible process as an ideal where no energy losses occurred. A process is said to be reversible if it can be performed in both directions with no change in the availability of energy for work. The concepts of reversibility and its converse, irreversibility, where the energy may lose part of its ability to do work – more characteristic of the real world – appear frequently in this book. He also employed the concept of the adiabatic process, during which mechanical work may be done, such as pressure-volume or gravitational work, but in which no heat is transferred into or out of a molecular working fluid. While it may seem unnecessary to consider the Carnot cycle here in great detail, it will be seen later in this book that the cycle actually provides an excellent model for analysing aspects of the performance of work on earth using radiant energy from the sun. This model, in its action resonance form, has special value for analysis of the greenhouse

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effect. Indeed, analysis of the greenhouse effect will be shown to be an important illustration of action in ecosystems, with some surprising results. The fully reversible Carnot (1824) cycle consists of the following four stages or processes: • an isothermal expansion of a piston at the temperature of a heat source during which heat is transferred from the source to the working fluid and external work is done, • an adiabatic expansion of the working fluid to the lower temperature of a heat sink during which further external work is done, • an isothermal compression at the temperature of the heat sink during which work is done on the working fluid and heat is transferred from the working fluid to the sink, • an adiabatic compression during which further work is done on the working fluid as it is restored to the original temperature of the source. This is an idealised system16 for a perfect gas requiring, alternately, efficient heat flow during isothermal processes at constant temperatures and perfect insulation during adiabatic processes when no heat flows. All heat input to the cycle is considered to be at the temperature of the source while all heat rejected is considered to be at the temperature of the sink. It was recognised that it is impossible in such a cycle for all the heat taken from the hot source to be converted to external work. For a cyclic process restoring the system to its original state, it is essential that the entropy of the working fluid, as a 16

In stage 1, for an ideal gas at constant temperature, ∆E = 0, and Q = -W using the 1st Law of conservation of energy that ∆E = Q + W. For a reversible process of expansion, the heat (Qsource) transferred from the source and work performed (W) in stage 1 of the Carnot cycle are equal: Qsource (1) = -Wrev (1) = nRTsource ln(V2/V1); And ∆S (1) = Qsource (1)/Tsource The heat provided by the source is used to do work, part of which may be external to the heat engine (shaft work) and part on the engine itself. For an irreversible process of expansion, where the expansion is not perfectly coupled to external work and there are frictional losses, Wirrev and Qirrev will be smaller in absolute value. In stage 2, the fluid continues to expand doing external work at the expense of the heat content of the fluid, its temperature falling to Tsink but with no heat flow and hence no change in entropy of the fluid: nR ln(V3/V2) + Cv ln(Tsink/Tsource) = ∆S = 0 = nR ln(V4/V1) + Cv ln(Tsource/Tsink) Stages 2 and 4 of the Carnot cycle are an adiabatic expansion and an adiabatic compression, so that Qrev (2) = Qrev (4) = 0. In stage 2, the gas expands without heat flow doing external work and in stage 4 an equal amount of work is done on the gas raising its temperature without heat flow as it is compressed. Stage 3 involves a reversible isothermal compression using inertial forces in the engine, raising the pressure as the volume is decreased but not the temperature because heat is reversibly transferred to the sink: Qrev (3) = -Wrev (3) = nRTsink ln(V4/V3); And ∆S (3) = Qrev (3)/Tsink Finally, work is done by the piston on the gas during adiabatic compression, raising its temperature, using potential energy stored in the engine from inertial forces. The total change in heat then is equal to: Qtotal = nRTsource ln(V2/V1) + nRTsink ln(V4/V3) From the perfect gas laws: Tsink/ Tsource = (V2/V3)nR/Cv (step 2) Tsource/ Tsink = (V4/V1)nR/Cv (step 4) By inversion and elimination of a common exponent, V2/V3 = V1/V4 and V4/V3 = V1/V2 Thus, the total heat change for the cyclic process = nRTsource ln(V2/V1) - nRTsink ln(V2/V1) = Qsource - Qsink Qtotal = nR ln(V2/V1)(Tsource - Tsink ) And the total change in entropy of the working fluid: ∆Stotal = nR ln(V2/V1) - nR ln(V2/V1) = 0 = Qsource (1)/Tsource + Qsink (3)/Tsink.

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property of state, be restored to its original value, which requires a certain amount of heat depending on the temperature. This would be true whether or not a reversible path were found. Then the efficiency of the reversible process can be calculated17 by taking the ratio of the work done (equal to the difference between the heat transferred from the source and that transferred to the sink) to the heat initially absorbed by the working fluid from the source. Thus, the lower the temperature of the heat sink (commonly atmospheric temperature) and the higher the temperature of the heat source (e.g. a flame) the greater the efficiency of the heat engine. This is because the lower the temperature of the sink, the greater the work that can be performed during the adiabatic cooling step in the cycle. Only if the temperature of the sink was zero degrees Kelvin where the entropy of the working fluid would be zero, or if the temperature of the source was infinite, could all the heat added from the source be used to do work - when the efficiency would be perfect. In practice, the working fluid of a heat engine does not cycle ideally between these two temperatures because of the limited speed of temperature equilibration between the heat source or sink and the working fluid. The ideal Carnot cycle is the most efficient possible because heat is transferred reversibly and isothermally only while the working fluid is at the same temperature as the source or the sink. 4.4.3. Action resonance interpretation of the Carnot cycle The Carnot cycle seemed to offer a reason for the limited power to convert heat to work, although no molecular model was available to validate this conclusion. Action resonance theory can provide such a model. Initially the working fluid absorbs heat at the temperature of the source, providing the resonant energy needed to sustain the molecules of the fluid in performing external work. The resonant momentum of the quanta added as heat from the source exerts exchange forces, to be considered as torques acting on the numerous couples of molecules, sustaining their motion and maintaining their temperature. This is necessary because the isothermal expansion during which shaft work is done exerts reverse torques on the gas molecules as a result of the forces exerted on the external environment, cooling them. Thus additional resonant energy, added as heat and exactly equivalent to the work done externally, must be added to the working fluid to maintain its temperature. In effect, the quantum state of the sets of molecules is adjusted so that the same torque is exerted but on longer trajectories. Because of the increasing volume, the transit of quanta between molecules now takes longer and the rate of impulses on molecular surfaces is reduced, corresponding to reduced pressure. It is important to note that this heat would not be required if the isothermal expansion occurred irreversibly into a vacuum, as in the Gay-Lussac experiment, because there would be no need for the molecular system to provide a sustaining force doing work on the external environment during the expansion. In fact, this was accomplished earlier, when the vacuum was prepared. No momentum is transferred from the system. The irreversible expansion is therefore a result of the special initial conditions and no extra radiant heat is needed to maintain the temperature because no reverse torques from 17

Efficiency = (Qsource - Qsink))/Qsource = -Wrev/ Qsource = { nRTsource ln(V2/V1) - nRTsink ln(V2/V1)}/{ nRTsource ln(V2/V1)} = 1 - Tsink/Tsource.

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outside the system are experienced during the expansion into a vacuum. The torques needed to generate the extra action during expansion and maintain the temperature will be unopposed. The pressure must fall, however, just as when work is done, because the trajectories of quanta are longer, the resonance times increased and the rate of impulses and momentum transfer is reduced. Carnot had proposed that heat can flow at this primary stage of the ideal cycle into the working fluid only from the source, and none into the sink. In the second reversible stage, no radiant heat can flow from the source nor any heat into the sink. But the gas driving the piston continues to expand doing external work, driven by the greater pressure or resonant action forces of the working fluid as a result of its greater initial temperature. External work is now performed at the expense of the heat content of the working fluid, which cools. In this adiabatic phase, the action and entropy of the molecules remains constant as a result of the effect of decreasing velocity of the molecules on their action being exactly matched by greater radial separation. The differential decrease in action, due to reduced velocity of the molecules as momentum is transferred out of the gas from reverse torques doing external work, equals the differential increase in action of molecules as a result of their increasing radial separation. Thus, the gas molecules remain in the same action or quantum state and require no more energy. The expansion and work can continue just to the point at which the temperature of the working fluid molecules falls to the temperature of the working surfaces, which in an ideal heat engine will be equal to but no less than the temperature of the heat sink. At this point, the force and torques exerted by the resonant action of the working fluid is just equal to the backforce and torques exerted by the resonant action of the molecules in the sink. No heat can be transferred to the sink at this common temperature. The lower the sink temperature, the more work can be done but once the temperatures of the working fluid and the sink are the same no more external work can be done. In the third stage of the cycle, there is an isothermal compression at the temperature of the sink during which work is done on the gas by the inertia of the heat engine, effectively exerting forces and generating torques in the gas molecules, which in return exert forces and generate torques in the molecules of the sink - the sink thus extracting heat energy from the gas molecules equivalent to this work done on them by the engine. According to action theory, this process clearly results in a decrease in action and entropy of the gas. At the constant temperature of the sink, the velocity of the gas molecules does not change but the radial separation and the action are reduced. But the temperature of the gas is less than it was in the expansion phase, when heat flowed from the source. As a result, the magnitude of the quanta transferred as heat to the sink associated with decreases in volume would be less than the magnitude of the quanta utilised in supporting work during the expansion. The difference between the total energy flows as quanta in these two stages represents the net work possible. Indeed, this difference in magnitude of quanta and the associated quantum exchange forces is the only reason that external work is possible in a heat engine at all. The final stage of the Carnot cycle involves an adiabatic compression during which the temperature of the working fluid is restored to that of the source by the work done on the gas, with the sink no longer extracting heat. But during this process, the tendency to increase action and entropy arising from the increased temperature and velocity of the molecules is exactly matched by the decreased

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action and entropy from a smaller radial separation. That is, there is no change in action or entropy in this stage. This analysis18 of the Carnot cycle in terms of action theory is possible because of the relationship between action and entropy discussed in Chapter 3. Thus, during step 1 where heat transfer is occurring during an isothermal expansion, an entropy increase in the gas is accompanied by an equivalent action increase as each molecule obtains more space and the action radius lengthens, although the average velocity remains the same. The one-dimensional action increases in direct proportion to the radial separation. In the second step of the ideal cycle, the adiabatic expansion while doing work on the environment, there is no entropy change and there must also be no change in action, despite the change in volume and temperature. Thus, any increased separation in the adiabatic expansion must be exactly balanced by reduced velocity as a result of the cooling of the molecules, keeping the action constant. This analysis based on physical action contrasts with the descriptive idea that negative free energy changes can predict the direction of spontaneous reaction, providing a correct mathematical formalism. True, the work processes on the external environment and in the heat engine during the isothermal and adiabatic expansion stages of the Carnot cycle clearly correspond to increases in entropy (stage 1) and decreases in enthalpy (stage 2). These are both indicators of negative free energy change, but no molecular mechanism for achieving these outcomes is obvious from the classical theory. On the other hand, the action resonance exchange forces acting at the molecular level clearly provide a mechanism or efficient cause for the direction the reaction will take. The ploy of reversibility does not conceal the fact that the quantum states of the particles of the working fluid will spontaneously proceed only in a direction that can minimise the stress of action resonance imposed by heat flow from the continuously heated source, by providing more space between the molecules of the working fluid and less radiant pressure. Of course, this requires mobility or degrees of freedom in the coupling agents to other processes that can absorb this work. In the subsequent stages 3 and 4, when the gas is now being compressed, the coupling agents or engine parts now hold the upper hand and the greater stress to dispose of, because of the inertia of the fly-wheels. The 18

As discussed in Chapter 2, the 3-dimensional action of a molecule (@3 = (mr2ω)3 = r3(mrω)3) is directly proportional to the volume at constant temperature, so that the ratio of the initial and final 3-dimensional action per molecule is equal to the ratio V3/V2. This is off-set by the reduced temperature of the molecules of the gas, which is proportional to the reduction in (velocity)2. Consequently, the reduction in 3dimensional translational action is proportional to T3/2. The changes in entropy in step 2 correspond to: ∆S (2) = nRln(V3/V2) + Cvln(Tsink/Tsource) Tsink/Tsource = (V2/V3)nR/Cv = (V2/V3)2/3 (ideal monatomic gas) So (Tsink/Tsource)3/2 = (V2/V3) (Tsink/Tsource)3/2 - (V2/V3) = 0 If V3/V2 = 10, then (Tsink/Tsource)3/2 = 0.1 So Tsink/Tsource = 0.2154467 Then the change in @3 due to the fall in temperature is x0.1. The change in @3 due to the increase in volume is x10. Therefore, the negative change in action due to the fall in temperature is just matched by the increase in space or volume, so there is no change in @3 in step 2. If Tsink = 215.45o, Tsource = 1000o If Qsource = 10000 units, then ∆S1 = 10000/1000 = 10.0 = nRln(V2/V1).

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working fluid now provides the lesser resistance, so work is done on it but the availability of a heat sink provides at least some respite by which it can relieve its stress by dumping heat. Deprived of a heat sink in the final stage of the cycle, it can only yield to the greater force and become heated to its original state at the beginning of the cycle. The resilience of the working fluid can only be marvelled at as the next cycle of many commences! Action resonance theory suggests that isothermal transfers of heat from the source at the maximum temperature possible would maximise the magnitude of the quanta to be exchanged and the resonant action forces that could be generated. Ideally, the magnitude of the quanta and their rate of availability from the source and then from the working fluid should exactly match those required in the work process. This would allow reversible energy exchanges so that no heat energy would be supplied to the system surplus to that needed for each molecular transition to new action states. In practice, such exact matching of the quanta transferred is obviously rarely achieved. The isothermal heat transfer and adiabatic cooling processes are not conducted reversibly and the temperature of the working fluid does not fall to that of the heat sink before the compression begins because there are inevitable losses of heat to friction. The work possible is also limited whether reversible energy exchange is possible or not because the temperature of the working fluid cannot fall below the temperature of the heat sink or surrounding environment. As a coupling agent, the heat engine and its working fluid must remain mobile. Given these restraints, it still seems probable that further developments of action resonance theory can suggest means of preparing more efficient heat engines. This can be achieved by bearing in mind the particular need to match the magnitude and the rate of transfer of the quanta produced in the working fluid to the rate of transfer that the work process can absorb. The use of special materials with matched resonant geometry in heat engines and drive trains, suitably insulated and designed with an efficient outcome in mind, will assist. By the current process of trial and error, this outcome has already been partly achieved, but efficiencies are still much lower than those achieved during work in biological systems, which we will see in Chapter 6 can approach 100%. 4.4.4. Free energy and action potential – real energy or not? No wonder students have difficulty in understanding and applying thermodynamics. The definition of so many different kinds of energy, except perhaps for specialists, has not helped the average student to obtain a clearer understanding. However, if the purpose of these extra definitions is clearly grasped, more scientists will find they can apply the theory. They should recognise that heat can readily be used to perform work, particularly if it is available at a high temperature, but only under certain stringent conditions. Heat can be used to do work if the free energy change in a process is negative. The Carnot cycle analysis above shows that this prior opportunity to perform work must exist. But the definition of work is rather arbitrary and can even include simply heating molecules if the purpose is to prepare a pot of tea. More usually, it an intermediate process of developing kinetic energy in a coherent object such as a motor vehicle, raising a weight in a gravitational field, or storing energy in a chemical reaction. All of these processes could eventually lead to dissipation of the stored energy in molecular motion at some subsequent stage.

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In fact, a negative free energy potential is equivalent (Porterfield, 1972) to a positive entropy change in the universe19 and in this sense, all work processes involve increases in entropy and action. The Helmholtz function can be written in almost tautological style indicating that the spontaneous total entropy change of the universe is simply the entropy change of the surroundings plus the entropy change within the system, all multiplied by temperature. The mechanism for spontaneity may then be interpreted as allowing action exchange forces to operate to carry out a work process, using enthalpy content as resonant quanta to provide the driving force. External work may result from either entropy increase in the system or the surroundings. This external work is matched by an inflow of heat to replenish the internal energy of the working fluid used to perform the external work. Therefore the free energy decrease or entropy increase provides the mechanism for the work to occur, but free energy decreases or entropy increases are not an inexhaustible means of doing work. In a cyclic process such as in the Carnot cycle, the maximum net work possible is the difference between the heat transferred from the hotter source and the heat transferred to the colder sink. The work done by the working fluid in the isentropic expansion stage 2 is exactly repaid to the working fluid in the isentropic compression stage 4, needed to restore the working fluid to the temperature of the source. Without a continuous supply of fresh heat, the work process would soon cease, as the system cools. Although the Carnot cycle and the theory of heat engines may seem rather distant from the thermodynamic function of living organisms and of ecosystems, the analysis that remains to be conducted in this book will reveal that this is not necessarily so. The ecosystems of the earth can be considered as operating between a heat source at 6000oK (the sun) and a heat sink at 255oK (the top of the earth’s atmosphere). Even within individual organisms, a role for heat in supporting life processes will be recognised. So that many of the essential features of the heat engine can be recognised in the function of essential processes in ecosystems such as photosynthesis. However, the subtlety of life systems, their ability to operate some processes with extremely high thermodynamic efficiency near one and the lessons they may hold for improving the efficiency of operation of our technological machines still remain largely to be revealed. 4.4.5. The heat pump and refrigerators If the Carnot cycle is operated in the opposite direction, heat can be absorbed by a fluid at a low temperature and rejected at a higher temperature. This enables a process in which heat is pumped from a source at low temperature and used to heat a space at a higher temperature. The heat energy that was converted to external work in the Carnot cycle above is now supplied from an external source (e.g. electrical storage) in order to operate this heat pump or refrigeration cycle. In this case, the relative amounts of heat flow and external shaft work will be the same as in the operation of the heat engine. For the Carnot heat pump, the heat absorbed from the colder “sink” plus the heat equivalent of the shaft work supplied by the external system is equal to the heat discharged at higher temperature. The analysis in the footnote20 indicates that a reversible heat pump 19

∆A = ∆E - T∆S can be written as -T∆Suniverse = -T∆Ssurroundings - T∆Ssystem. Using the same designation for the various terms: Qsource/Tsource = Qsink/Tsink = (Qsource - Qsink)/(Tsource - Tsink) = W/(Tsource - Tsink) We can describe this process with reference to the laws of thermodynamics as follows. 20

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operating an air conditioner to pump heat at 20oC to the exterior at 40oC could pump almost 15 times as much heat as energy to do work is needed. Equally, such a reversible heat pump could pump almost 14 times as much heat from the exterior of a dwelling at 0oC to its interior at 20oC as its electric motor does work. This remarkable result is not in conflict with the principles of thermodynamics because the total energy is conserved and the entropy change is zero (or greater than zero in an irreversible process). Unfortunately, such remarkable efficiencies by heat pumps are not achievable in practice. By good design, efficiencies enabling two to three times more heat to be delivered than work is required have been achieved, showing that the Carnot cycle predictions for a reversible system are a worthwhile guide to the value of a heat pump. As a result, a reverse cycle air conditioner can make an excellent heater in winter, providing at least twice as much warmth for the same amount of electrical power as direct electrical resistance heating. Note that this fact is consistent with both the first and second laws of thermodynamics, although at first sight it may seem to contravene them. Applying action resonance theory, similar considerations apply to the theory of heat pumps as to heat engines. Maximum efficiency in cooling will be achieved when the rate and magnitude of quanta transferred are best matched for the various processes involved. Just as action resonance theory was proposed to offer more efficiency in the design of heat engines, similar improvements in efficiency may be generated by better design of heat pumps. These possibilities for improved heat engines and refrigerators using action resonance theory will be examined in future publications. 4.5.

Action field gradients in spontaneous reactions

Chemical work potential or Gibbs free energy must be available in the chemical reactions catalysed in cells by enzymes, if organisms are capable of performing biological work. This infers a non-equilibrium state between the inputs and outputs of cells and the potential for spontaneous reaction, incorporating a mechanism to allow a significant proportion of the reactant molecules to reach the transition state for interconversion. It is possible to consider21 that activation of reactant molecules can be achieved simply by compressing them, until they reach a quantum state where the effective ∆E = Qsource + Qsink + W = 0 (1st law) ∆S = Qsource / Tsource - Qsink/Tsink = 0 (2nd law) Substituting Qsource = Qsink(Tsource/Tsink) into the 1st law expression yields W = Qsink(Tsource/Tsink - 1) Note that as Tsource approaches Tsink, Qsink/W becomes very large. 21 Thus, in the nonequilibrium reaction, A + B => P + Q we can consider that a proportion of the substrate molecules A and B exist in an activated complex (A*B*) of sufficient total energy that they are at the same chemical potential as a similar activated complex (P*Q*) of the product molecules P and Q. A + B => A*B* P*Q* => P + Q No work is done in the interconversion A*B* P*Q*, since these complexes must be of equal overall chemical potential or total quantum state. The trajectories of the reactant and product molecules may be considered as two activation and then two deactivation processes,

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concentration is such that the total chemical potential of both sets of reactants and products will be the same. The radiant energy quantum needed to sustain the reactant complex would then be equal to that needed to sustain the product complex. Transition between reactants and products can then occur spontaneously, although there will be a large difference in the size of the quantum of energy needed for the reactants to reach the transition state compared to the size of that released when the products are formed at their field chemical potential. Reaction will continue until the point is reached where these quanta have equal magnitude. Action theory, because of the phenomenon of resonance, allows for the possibility of arrangement of forces in such a way that transition states can be achieved other than by random collisions. In principle, equilibrium in all reactions which are chemically possible can be achieved by such a device. It is intriguing that the transition process, independently of the activation process for reactants and deactivation process for products, is also formally equivalent to the removal of reactant molecules to an infinitely low concentration, or a similar addition of product molecules - since one of each disappears or appears during the process. The definition of chemical potential is the change in Gibbs free energy of a chemical system per mole of substance (reactant or product) added to the system, with the important proviso that all concentrations of reactants or products and physical conditions must be held constant. Another means of adjusting the action or quantum state of a system of molecules to achieve a transition state is to adjust the temperature. If a suitable mechanism exists, these expansions could be coupled to work just as in the expansion of gas in heat engines Activations: A => A*, B => B*, Deactivations: P* => P and Q* => Q The activation processes may be simulated as compressions of A and B and the deactivation processes as expansions of P* and Q*. The ratio of concentrations of the products and reactants at the degree of compression needed to achieve a net change in chemical potential of zero would be equal to Keq. .In principle, the chemical potential of all the molecules of A and B in a system could be simultaneously changed to that of A* and B* by a set of impulses leading to adjustment of each molecule’s action state corresponding to compression (in which work is done on both of the molecules). Once this has been achieved, given an efficient mechanism able to orient A* and B* correctly with sufficient proximity, a spontaneous transition to P* and Q* in equilibrium with A* and B* can occur without the need for further work. The final reaction phase is equivalent to spontaneous expansions of P* and Q* to achieve the same chemical potential as that experienced by bulk P and Q. The available work potential per molecule of A and B reacted, considered as ideal action processes involving volume changes alone would be (Kennedy, 1984): δG = kT{ln([A*]/[A]) + ln([B*]/[B]) + ln([P]/[P*]) + ln([Q]/[Q*])}, And the work potential per mole (per molecule multiplied by Avogadro’s number, N): ∆G = RT{ln([A*]/[A]) + ln([B*]/[B]) + ln([P]/[P*]) + ln([Q]/[Q*])} = -RTln{([P*][Q*])/([A*][B*])} + RTln{([P][Q])/([A][B])} = -RTlnKeq + RT ln{([P][Q])/([A][B])} ∆G = - µA - µB + µP + µQ Incidentally, This corresponds to the quotients above, bearing in mind that all reactants and products would also be in equilibrium if infinitely diluted. If the reaction is conducted using equimolar concentrations of all reactants and products, arbitrarily set equal to 1 molal (the standard state), or any other combination of concentrations producing unity in the quotient then the second term becomes zero (ln(1) = 0) and the corresponding change in chemical work potential is known as the standard free energy change, ∆Go. Thus: ∆ Go = -RTlnK.

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discussed above. In fact, the work achieved during the expansion phase of a diesel engine is a practical example of such a work process, although transition is not instantaneous for all hydrocarbon and oxygen molecules but must occupy a finite period during which the reactant molecules can collide. The position of equilibrium is temperature dependent because the most probable distribution of action states of molecules is temperature dependent. Changing the temperature will change the relative proportions of reactant and product molecules at equilibrium because their heat capacity will not change at the same rate as change in temperature. In an aqueous solution, the much slower rate of the chemical reaction results from the lower frequency or probability that the reactant and product chemical species involved can achieve transition action states where the reaction can occur smoothly. A smaller proportion of the reactant molecules can achieve the activated action state at any one time. The role of catalysts such as enzymes is to increase the proportion of molecules that can achieve the transition state within a time interval. Once the transition to activated product molecules occurs, the final stage of the interconversion is formally equivalent in terms of varying chemical potential to an expansion of product molecules just as in a piston, but for work to be done other than heating, a special coupling mechanism will be required. 4.6.

Classical versus action thermodynamics

Action thermodynamics provides a new, highly physical, viewpoint regarding spontaneity in natural systems. It proposes that all spontaneous reactions result as action generated by inequalities in the resonant forces of dispersive interaction between molecules. These forces always involve the exchange of quanta, carrying momentum in proportion to the frequency of the exchanges of impulses. The quanta or primary actons providing an efficient cause for these forces, representing the total energy content of molecular systems, including both ground state energy which all sets of molecules have access to and the transient energy responsible for quantum transitions in the action states of particular sets of molecules. This ground state energy is usually ignored in thermodynamics since it is present as a constant background but it provides the energy appearing as new quanta during chemical reactions such as in a flame. All entropy increases or free energy decreases are driven by these dispersive forces. Entropy increases involve increased action in molecules, either by increased average velocity or increased radial separation of particular atoms and molecules. However, the dispersive forces generating molecular entropy can always be reversed. Coupling agents can couple other strong dispersive forces to provide compressive forces and decreased entropy. In principle, the rate of such compressions could be increased if the heating effect of compressive work could be ameliorated by a process providing rapid cooling. Statistical thermodynamics are completely consistent with action thermodynamics. These dispersion forces of action resonance are consistent with the randomisation of molecular species within physical compartments or states. They are also consistent with the generation of fractal patterns, resulting from complex binding reactions of different molecules that minimise dispersion forces. Statistical arrangements are related to multiple action states by the dynamic geometry of molecular complexes involving

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exchanges of quanta. The number of molecules that particular states can contain are limited by interaction between this dynamic geometry of molecules and the energy field. Analysis of the Carnot cycle using action resonance theory reveals more clearly the nature of efficiency in thermodynamic processes as a matching of the quanta available to those needed. But considering the Carnot cycle also reminds us of an important feature of thermodynamic processes – their cyclical nature. At any point in the cycle, the molecules of the working fluid have returned to exactly the same free energy and entropy content as they had at the same point in the previous cycle. This assumes that the working fluid is sufficiently robust. This observation is relevant not only for heat engines but, as we shall see illustrated later in this book, equally relevant for the thermodynamic cycles of ecosystems and for the whole global ecosystem. While the entropy of solar radiation received by earth is much less than the entropy of the same radiation emitted from earth, as a steady state phenomenon the total entropy of molecular systems on earth tends to remain constant. For every local process generating molecular entropy, there is an equivalent process elsewhere generating free energy and vice versa. This conclusion may be considered as one of the key elements of sustainable ecosystems, the focus of this book. Action thermodynamics are also consistent with classical thermodynamics, but allow more detailed insights into the nature of various thermodynamic functions. Thus, free energy clearly represents a potential to generate action. Systems highest in free energy are those of lowest entropy and action, characterised instead by inaction. However, it is insufficient for a system to possess high molecular free energy for work to be possible. Formally, molecules have their greatest free energy at zero degrees Kelvin - where no work is possible. So the system must have access to real radiant energy for work to be done. This radiant energy can be provided by radiation from an external source, such as sunlight, or by internal release of energy as the enthalpy of reaction, when quanta excess to requirements for the product molecules at a given temperature are produced in the transitions, by conversion of mass to energy. Perhaps work potential or action potential would provide better descriptive terms than free energy. Paradoxically, the highest values of Gibbs or Helmholtz potential actually indicate molecular states which are relatively energy free as exchangeable radiant energy. But they do indicate a state amenable for the performance of work once quanta are released from the ground state energy by molecular transitions. Internal energy, enthalpy and pressure-volume work easily find their place in action thermodynamics as real radiant energy needed to generate the resonant action forces causing all spontaneous changes. The total energy is now considered as real energy (ground state actons or quanta in transit) providing real impulses supporting the elements of material particles. So thermodynamics is merely the statistical average of the dynamics of individual molecules. Bonding energy denotes an absence of energy or enthalpy compared to the increased energy or enthalpy contained in the system at a temperature sufficient to break the bond. Stable chemical bonds occur in molecules with a dynamic geometry favouring a low need for radiant energy as quanta, using molecular screening to achieve energy-sparing resonance. Chemical reactions proceed until they achieve equilibrium at a point where the energy of the system is distributed in such a way that the action exchanges of reactants and products correspond to quanta of the same

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magnitude – a position of least action where the dispersive intermolecular exchange forces are approximately in balance.

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ACTION FROM SOLAR ENERGY

Solar protuberance photographed during an eclipse in June 1946, known as the “grand-daddy”. Solar storms driven by the nuclear furnace at the sun’s centre are capable of hurling huge quantities of gaseous matter 25 times the earth’s diameter spiralling into space. This chapter will argue that impulses from fusion energy generate action on this scale. However, the process is non-equilibrium, and gravitation results in eventual fall of the solar material onto the surface of the sun. The National Center for Atmospheric Research, University Corporation for Atmospheric Research, National Science Foundation, USA, thanked for permission to reproduce this photograph and Figure 5.2.

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Early sunspot observations from Scheiner’s Rosa Ursine sive Sol 1630. The Jesuit astronomer’s observations of sunspots convinced him the the sun must rotate once every 27 days. Aristotle had taught that the sun was a perfect body without blemish. Reproduced with permission from Penguin Books, The Face of the Sun H.W. Newton, 1958.

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Chapter 5

ACTION FROM SOLAR ENERGY Solar action Solar action and storms on earth Action resonance in the atmosphere Action modelling of global warming

5.1.

Solar action

The primary source of action on earth is sunlight. Reactions of nuclear fusion in the intense pressure of the sun’s interior convert matter to quanta, yielding internal temperatures of millions of degrees. Much later, this energy diffuses on a tortuous route to the surface of the sun, where the environmental conditions are still sufficiently hot at 6,000oK for the sun’s surface to glow incandescently. The characteristic solar emission spectrum has 95% of its photons falling in the energy range of 290 nanometres ultraviolet to 2,500 nanometres infrared wavelengths, centred on green light near the peak of sensitivity of chlorophyll and the human eye around 540 nanometres. More formally, we can state that the sun emits radiation with the spectrum of a perfect black body, characteristic of a surface temperature of about 6000oK. These emissions coincide with quantum transitions of the heated molecules at the surface. In terms of action resonance, we state that a proportion of the quanta constantly being exchanged between the molecules of the surface materials escape the molecular matrix of the sun, dispersing radiation in all directions into the relative vacuum of space. Travelling at the ultimate speed of light, quanta that could have taken millions of years to emerge at the sun’s surface squeezed from its crushing interior are absorbed just minutes later by the surface materials of the earth. Some of this energy even converts in the green cells of plants into sugar. We can measure the physical impulses of these quanta as molecular action on earth, not only in terms of their immediate momenta and dispersive force but also by almost every other physical and chemical event that occurs on the surface of earth. 5.1.1. Storms on the sun Do not make the mistake of considering that the process generating sunshine on earth is a benign or gentle phenomenon. It is no secret that the stormy sun-spot scarred surface of the sun is an extremely turbulent environment - capable of projecting huge streams of incandescent gases many times the mass of the earth spiraling hundreds of thousands of kilometres into space as shown in the frontispiece of this chapter. Solar radiation is nuclear radiation, initially emergent from matter as deadly gamma radiation, but considerably softened in the force of its quantum impulses by the gravitational work the rays of quanta perform on the molecules of the sun’s interior and its surrounding atmosphere. This redistributes the energy quanta of these gamma rays, eventually reducing their frequencies to that of the radiation emitted by the sun. This energy of lower frequency is nonetheless still capable of doing great damage as ultraviolet rays to

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unprotected living cells. These quanta are also capable of being utilised beneficially for many work processes on earth. The nuclear reaction that occurs at the immense pressure near the sun’s centre is the fusion of hydrogen to form helium1, giving rise to intense emissions of quanta equivalent to the mass lost in the fusion process. Direct observation of these processes near the centre of the sun from earth is impossible, but it is considered that nuclear fusion in the sun involves the consumption of four protons and their associated four orbital electrons, replaced in an intense explosive reaction by a single helium nucleus (or alpha particle) and two electrons, products which must be lighter in mass equivalent to the radiant energy released as gamma rays (Figure 5.1). The new helium nucleus consists of an association of two protons and two neutrons, remaining dissociated from its two orbital electrons in the extremely hot pressurised plasma that exists near the centre of the sun. The action resonance theory outlined in Chapter 2 discounts the causal role of the positive and negative charge of protons and electrons in single atoms as a binding force. Instead, it attributes the ‘attractive’ binding of unlike charges to a steady state field phenomenon resulting from reflective screening of quanta by nucleons and electrons and the detailed balancing of internal and external forces on atoms by the impulsive exchange of quanta constantly transmitted between all of the molecules in the field. In the sun, the crushing 900 million atmospheres pressure of its vast mass readily contains the plasma and is the primary cause of the compression, generating the plasma and the chaotic fusion process in the first place. So intense is the frequency of energy exchange and internal transfer of momentum that nuclei are constantly denuded of electrons; all the recognisable particles are forced to behave independently as if each formed part of a gaseous Brownian fluid with all its particles moving at a significant fraction of the speed of light. The confining walls of all the sun’s outer matter provide a natural vessel of sufficient density and strength in which fusion can readily occur. The rate of the process of fusion is limited, in part, by the rate of diffusion of quanta from the interior since the density of quanta in the zone of fusion might be anticipated to control the rate of coalescence of nuclei. From the viewpoint of action resonance theory, the key primary

1

411H => 42He + nΣhνi The solar fusion process was originally proposed by Bethe of Cornell University to occur in a carbonnitrogen-oxygen cycle involving successively 126C (+ H+), 137N + e+ + hν, 136C + hν (+ H+), 147N (+ H+), 15 + 15 + 4 8O + hν + e and 7N (+ H ) => 2He as intermediates (Mendelssohn, 1946), a process now considered as restricted to more massive, short-lived stars. To achieve the process of fusion using deuterium, the heavy isotope of hydrogen, has been the subject of extremely costly research seeking to employ nuclear fusion as a more or less unlimited source of heat energy. The main problem in conducting the process of nuclear fusion on earth has been the difficulty of containing the highly volatile plasma that is generated when matter has reached the temperature considered necessary to effect fusion. Fusion is achievable on earth for just a few moments in a thermonuclear explosion. But intense action exchange forces from the interaction of a high density of quanta with matter would be expected to disperse the particles appearing in the plasma; efforts to contain the hot plasma such as the use of magnetic fields might be futile. An external field matching the internal dispersive action field at high temperature is clearly required and the onset of fusion would so elevate the internal dispersive force as to defy practical containment, except perhaps in vessels with dense walls many kilometres thick.

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factor in the action process of nuclear fusion on the sun must be pressure, not temperature. The high temperature is a result of the fusion process, not the cause!

221D+ + 2e+ 2[H+ + H+] => + 2H+ => 232He + 2ν 2e+ + 2e- => 4γ 3

2He

+ 32He =>

4

2He

+ 2H+

411H => 42He + Σhνi Fig. 5.1 Solar fusion of protons on the sun. The massive pressure at the centre of the sun causes the mutation of four separate protons into helium nuclei, consisting of two protons and two neutrons, releasing huge quantities of radiant quanta.

The transmission of energy from the interior of the sun occurs in part as outward diffusion of quanta between the interstices of matter, increasing the temperature and action of the particles it encounters by resonant impulses, but also as mass transport of vast quantities of the sun’s coherent matter. Turbulent rising streams of super-heated hydrogen impelled to rotational action by resonant impulses - cooling as it rises in the gravitational field with the absorption of quanta - are matched by plunging streams of relatively cooled material that heat spontaneously as they descend, re-emitting part of their potential energy as quanta. The relentless transfer from the sun’s interior of energy, momentum and action by radiation, collision and convection eventually results in the turbulent action of the matter at the surface of the sun. Here, where the granular fine structure of the sun’s surface is visible from earth in the heads of myriads of local storms (Figure 5.2), the molecular quantum processes producing the spectrum characteristic of a body near 6000oK occur. This radiant energy of sunlight, temporarily freed from interaction with matter, is transmitted in 499 seconds at the speed of light (2.9979 x 1010 centimetres per second) through the relative vacuum of space intervening between the sun and the earth. At the earth’s surface, where only a very small fraction (a proportion of 0.4544 x one-billionth) of the total sunlight falls, the solar energy is either directly reflected as light, or absorbed and re-emitted later as rays of energy of much lower frequency. This book seeks to analyse the action in ecosystems that is initiated from the moment these photons are absorbed by molecular systems at the earth’s surface. The energy received by the earth involves the continued annihilation by fusion of 1.95 kilograms of matter each second, equivalent to the total radiation emitted by only 690 hectares or 6.9 square kilometres of the sun’s surface. (In fact, any place on the earth receives radiation from the entire orb of

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the sun since its radiation is transmitted in all directions.) To enable this intensity of sunlight (1.374 x 106 ergs per cm2 per sec) to fall on the surface of the earth requires the total annihilation of 4.3 million tonnes of the sun’s mass each second. Fortunately, the sun’s total mass is so great that this process can probably continue unabated for at least another five billion years.

Fig. 5.2: Turbulent conditions on the sun’s granular surface and at a sunspot. Varying temperature of the surface matter is indicated by the relative brightness.

5.1.2. Solar action on earth Two major action processes caused by the impulses of solar radiation and essential for the operation of earth’s ecosystems are examined in this book. The first of these processes is meteorological, affecting the earth’s atmosphere and includes the generation of the daily weather, climate and the greenhouse effect. The second process is photosynthesis by green plants, where actinic impulses are utilised to catalyse actions that result in the synthesis of bio-organic chemical products. Photons in sunlight are intercepted at the earth’s surface with an intensity depending on the angle of incidence. Thus, on average through the year, sunlight is most intense at the equator, amounting to the receipt of about 1.374 x 106 ergs per square centimetre per

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second2, while at the north and south poles it is at its lowest intensity, because of the more glancing angle of incidence. The earth has an overall albedo of 0.30; this indicates the total proportion of this light that is directly reflected without change in spectral quality is about 30%. This will be highest wherever the most reflective surfaces occur (e.g. at snowfields, in mountainous areas or from clouds). At the equator, this direct solar radiation is equivalent to an incident force of 4.58 x 10-5 dynes exerted on each square centimetre. This is a very small force indeed3. But we shall also see that when its distribution is considered as focussed on the surface of molecules so as to dissociate electrons, amplified by action resonance, the impulses delivered by this energy can have the most profound significance for life on earth. 5.1.3. The Crookes radiometer One way to illustrate the force exerted by quanta is to examine the function of the Crookes vacuum radiometer (Figure 5.3). This fascinating toy, rarely studied in physics courses, is generally regarded as a novelty and of little significance. In this book the radiometer is considered to provide an excellent example of the power of action resonance and the dramatic role this phenomenon can play in nature. The radiometer is able to develop rapid rotational motion of the cross-vanes when suitably illuminated. It can do so only if two critical conditions are met. Firstly, the vanes must have contrasting surfaces, one a white surface or a mirror reflecting light and the other coated with lightabsorbent carbon black. Maxwell’s electromagnetic theory predicted that light could exert a pressure (see Chapter 2). Crookes’ original theory formulated in the late 19th century should have predicted from the principle of conservation of momentum that the vanes would rotate with the reflecting surfaces receding. Maxwell reasoned that the change in momentum for a photon interacting at the surface would be twice as much when reflected on the mirrored surface as on the black surface where photons are simply absorbed. But the radiometer rotated in the opposite direction with the black surfaces receding when illuminated! The second critical condition is that there had to be a low pressure of gas in the radiometer - but not too low. This was found essential to obtain any rotation at all – another fact not predicted by Crookes’ original hypothesis. With too high a vacuum, rotation ceased! An alternative explanation was then devised that involved the hotter black surface heating any impinging gas molecules by conduction, thus delivering more recoil momentum when they were ejected from the surface in collisions. However, the mechanism by which this might occur is by no means obvious. Just how a molecule will 2

Considering the cross-sectional area of the earth (r = 6.2712 x 108 cm) is 1.275241241 x 1018 cm2, the non-resonant radiation force of sunlight for an albedo of 0.3 can be calculated as 7.5933 x 1013 g.cm.s-2 (dynes). This amounts to a total (non-resonant) impulse per day of 6.5606172 x 1018 g.cm. For the earth’s mass of 5.975 x 1027 g, this is only a minute impulse. The instantaneous acceleration would be only 1.2708 x 10-14 cm sec-2, about 10-17 times less than the gravitational acceleration at the surface of the earth of 981 cm sec-2. Thus, if this force was unopposed, it would take 2.49 million years to accelerate the earth to a velocity of 1 cm sec-1 away from the sun and 2.5 billion years to reach 10 metres sec-1 (although this would be a displacement of more than three thousand km per year). However, we need have no concern that such a minute force is about to disturb the earth’s orbit since it is minute compared to the balancing force of gravity impelling the earth towards the sun and these forces are already in dynamic equilibrium. 3 Non-resonant force = i1Σhνi/ct.

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be heated on the carbon black surface of the vane, imparting extra motion to the vane, is not clear and the explanation rather begs the question.

Fig. 5.3: The Crookes radiometer. The low-pressure radiometer provides a model of action resonance theory, involving resonant exchange between the warm black surfaces and absorbent molecules of air (CO2, H2O), impelling the cross-vanes to rotate. A schematic diagram at the right indicates, on a short time scale of events around 10-15-10-17 seconds, how action exchange forces from radiant energy or quanta, can generate a dispersive force on matter, by mutual recoil from impulses. The diagram can also be considered to model greenhouse theory and the motion of asymmetric molecules in the gravitational field (see Chapter 5).

Action resonance theory provides a simple explanatory mechanism. The action theory agrees that the black surface will become heated by comparison with the white or silvered surface as a result of its absorption of quanta. The high frequency quanta absorbed by the black carbon become trapped internally and this energy is redistributed as rays of heat quanta with lower frequency of impulses, travelling at the speed of light, within the tortuous internal molecular structure of the black material. By increasing the internal torques exerted on the internal molecular structure the black material becomes warmer as the frequencies of the quanta harmonise with the molecules of the black material. This results in greater radiation from the black surface than from the white surface. We can also conclude that there will be more points of emission of quanta from the black surface than of the initial absorption, each ray being of lower frequency than the incident radiation reflected unchanged from the opposite surface once the apparatus equilibrates with incident radiation. At this point, the total density of momentum emitted

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from the surface must equal that received. Furthermore, the probability that quanta will experience multiple or resonant reflections between gas molecules and the black surface is evidently much greater than in the opposite zone near the reflecting white surface where fewer, higher frequency, quanta are emitted. In any case, most of these reflected high frequency quanta will leave the radiometer immediately by transmission through the glass. By contrast, the lower frequency heat quanta from the black surface are reflected and retained by molecular interaction within the glass vessel; these can undergo resonant reflection at the speed of light (3 x 1010 cm per sec) between molecular surfaces, when separated (for example) by one centimetre, more than 10 billion (1010) times a second. Such action resonance amplifies the dispersive force in direct proportion to the rate of reflections. As a consequence, a much stronger force is predicted by action resonance theory to be generated at the black surfaces than at the white because the rate of momentum transfer is much greater. In effect, gas molecules near the black surface will be impelled by resonant impulses to stream away from the black surface and an exactly equivalent though opposite momentum will be imparted to the rotating vanes. So it is no mystery that a wellconstructed radiometer in strong sunlight can develop an extremely rapid ‘whirring’ spin of the vanes of many cycles per second. From the onset of sufficient illumination to overcome inertia and initiate motion, the rate of rotation of the vanes will soon reach a steady or transient-state equilibrium; here the total flux of incident energy generating the resonant impulsive force and the reverse forces resulting from exchange of quanta associated with collisions of gas molecules on the whitened surfaces match one another. This action resonance model also predicts that the density of gas molecules will be slightly greater near the cooler white surface than near the warmer black surface. This difference, increasing at first with the rate of spin, ensures that eventually equilibrium will be reached because of an increased rate of collision with molecules and back pressure. This limiting rate of rotation can only be sustained as long as the same intensity of incident radiation is maintained. The actual rate of rotation of the vanes reached will be a complex function of a number of factors. These include the mass or inertia of the rotating assembly, the gas density, the nature of the gas molecules and their resonant frequencies, the range of frequencies and intensity of the incident radiation and the temperature of the system to begin with. The fact that even completely randomised illumination of the radiometer still leads to directed motion is one of its most significant properties, providing a model for the behaviour of asymmetric molecules. A serious experimental analysis of the action of the Crookes radiometer would offer a means of testing these aspects of the action resonance theory. Not only does the action resonance theory explain the phenomenon of the Crookes radiometer - it also provides an efficient cause for a heated molecule being able to impart greater momentum to the vane when accelerated from the warm surface than when initially colliding with the blackened vane as a cooler molecule. A warming molecule will exchange quanta at a greater frequency during the collision with the vane’s surface, transferring more momentum and generating more action and kinetic energy. We shall see that the radiometer can also provide an excellent model of greenhouse warming and the capacity of action resonance to do motive work on the molecules of the atmosphere.

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5.2.

Solar action and storms on earth

5.2.1. The meteorological cycle From material already discussed in this book (Chapters 2 and 3) it should be clear that there is a good potential to apply action resonance theory to the various problems concerned with the weather and climate. Generally, scientific discussion of the earth’s meteorology is heavily descriptive, addressing in turn each of the phenomena involved in generating the weather, but without a coherent basic theory that can also explain the many processes involved. The very complexity of these processes may seem to require this operational approach and has no doubt discouraged the search for such a theory. Although it is well beyond the scope of this book to provide a revision of climatology, the action resonance theory may provide such a useful theoretical model, enabling description, explanation and prediction of these phenomena at the same time. A test of this proposal will be advanced here in connection with some aspects of the greenhouse effect and global warming. The rational bases for this ambitious claim are three-fold: • The basic statements of the action resonance theory (Chapter 2) coupling energy to the development of action provide an efficient mechanism for the development of motion by the molecules of air. This is simply the logical extension of Einstein’s Brownian model of energetic impulses of resonant quanta interacting with the momentum of molecules. The varying flow of solar energy provides the basis for all of the phenomena of the meteorological cycle. Inputs of this energy and momentum create the chaotic initial conditions needed by setting up gradients in temperature from differential heating of the earth’s surface leading to the increased action. The spontaneous processes of distributing this energy to space leads to the more or less orderly motions of molecules and systems of molecules in air, consistent with the second law of thermodynamics discussed in Chapter 4. Thus, the development of convective (vertical) and advective (lateral) action by cells of air is the natural outcome expected from stress-releasing changes of state seeking equilibrium. Although equilibrium is rarely if ever achieved, the characteristic rotational motions of air of cyclones and anticyclones displayed in the weather are therefore a natural prediction of action resonance theory. These dynamic cells of air are nature’s coupling agents providing a steady state solution to the problem of the redistributing chaotic stress to all of the available material surfaces accessible by means involving the generation of least action. • Microscopic changes in the action and entropy of water resulting from the exercise of action exchange forces generated the exchange of quanta can provide a basis for the hydrological cycle.

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All of the processes of vaporisation, transport and precipitation of water as rain in ecosystems known as the hydrological cycle can readily be accommodated in the action model. Changes of state between solid (ice and snow), liquid and vapour involve changes in action state, also constantly seeking solutions to the problem of redistributing stress for all three at the same temperature (see Section 3.1). Thus, the structure of ice, the various shapes of snow crystals, the viscosity of water, the humidity of air are also determined by action exchange forces spontaneously distributing and diffusing themselves through these different action states. The melting of arctic and antarctic ice as fresh water, the loading of heating air over sunwarmed oceans or land with water vapour by vaporisation, the cooling convective and orographic uplift of air, the resultant condensing of the water as aggregated droplets in clouds as the thermal quanta are translated to sustaining more gravitational work, the eventual precipitation to land or sea surfaces as raindrops once the droplets are so large and the action exchange forces too small to sustain them in the gravitational field - all of these processes can be explained as successive action states for water molecules, using the action resonance model. Of all the greenhouse gases, water occupies the most prominent role because of the very significant absorptions or emissions of radiant energy that are involved in its frequent changes of physical state during the hydrological cycle. • Storms are spontaneous states of coherent rotational action of the molecules of the atmosphere developed when local gradients of temperature and energy content become too great for the orderly dispersion of energy. If the steady state influx of solar energy could be redistributed to space by very rapid processes, there would be no weather at all because temperature and energy gradients could be maintained as very small. However, the rate of energy flow through space is limited by reflection from screening molecules. The resultant weather cycle provides the means of energy dissipation. This process spontaneously couples coherent motions of air to the process of energy dissipation. In effect, the threedimensional action and entropy generated in this way exercises a degree of freedom involving a change of scale at which action can be generated. This additional scale of more macroscopic action provides another dimension of mobile surface requiring the exchange of energy to sustain it. The additional energy sustains a work process that does not result in an increase in the molecular temperature. At the microscopic level, quanta heat molecules and increase their action states by exercising torques on individual molecules. However, the flow of energy in the atmosphere is not isotropic but asymmetric, depending on where sunlight is absorbed, its intensity and the physico-chemical nature of the absorbing surface. Therefore, directional flows of energy can exercise torques on coherent groups of molecules leading to the rotational motion of cells of air many kilometres across. The actual speed of rotation of these cells will depend on how long the torques are maintained, the generation of back torques on nearby bodies of air opposing the motion and the generation of frictional eddies where these air masses meet, dissipating the rotational action into smaller cells

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of air. Action resonance models can help explain the development of hurricanes involving large masses of air but also of localised tornadoes. The speeds of rotation reached would be correlated with the initial torques generated, but also with the mass and inertia of the air cells. Since the action resonance theory provides a simple basis for the conservation of angular momentum based on resonant exchanges of impulses it also provides the basis for conservation (and dissipation) of angular momentum in storms. Obviously, any decrease in the space available for the rotating body of air will result in an increase in its rotational speed as the potential energy of large scale angular motion is converted to kinetic energy of small scale motion. As a consequence, very large variations in the distribution of the energy density or pressure can be generated. The development of intensely varying action exchange forces in air rotating at extremely high velocities near the speed of sound - the limiting rate at which energy can diffuse through air – results in such high local energy density and exchange forces that the stabilising influence of gravity is readily overcome and the disintegration of structures depending on gravity for stability is often a spontaneous result. There are many points of detail related to other effects of action resonance theory and the degree and direction of rotational motion on earth, such as the Coriolis effect, which shall be discussed in future work. However, some aspects of the action resonance theory particularly relevant to the greenhouse effect will be further examined. 5.2.2. The normal greenhouse effect It is estimated4 that the greenhouse effect, caused by polyatomic gases in the earth’s atmosphere with three or more atoms per molecule results in the globally averaged temperature at sea level being +15oC rather than –18oC, expected with no atmosphere or an atmosphere of argon. If true, this increase in surface temperature of more than thirty 4

Current greenhouse theory uses the following approach. From the Stefan-Boltzmann law, back-radiation from the earth would be proportional to the fourth power of the temperature: Ee = σTe4.(4πr2) (i); Ee = energy emitted, σ = 5.5597 x 10-5 ergs sec-1 cm-2 K-4, Te in degrees K, 4πr2 = surface area of the earth emitting radiation Ei = S(1-A)( πr2) (ii); Ei = energy input, S = solar constant = 1.367 x 106 ergs sec-1 cm-2, A = albedo of earth = 0.31, πr2 = area of the flat disc (being the earth) intercepting sunlight By equating (i) and (ii) since energy input should equal energy output, we have: σTe4 = S(1-A)/4 and Te should be 255.2 K or –18oC It is argued (Schnoor, 1996, p. 636) that this calculation is in error, because it fails to consider backradiation absorbed by water vapor and carbon dioxide (peaks at 12 µm and 15 µm respectively). When a factor for opacity or emissivity (e), the proportion of the back radiation that is estimated to escape the earth’s atmosphere (ca.0.615), is included, a new equation is generated: eσTe4 = S(1-A)/4 and the average global temperature Te is now 288.2 K or 15oC, 33oC warmer. Incidentally, the theory of black-body radiation recognises that only radiation emitted from the interior of a heated cavity (i.e. via a window) obeys equation (i) exactly. Whenever the intensity of radiation from the surface of a heated body is considered, an emissivity factor less than 1.0, which is different for different materials, must be introduced (Halliday and Resnick, 1977, p. 1093). Whether this application of the Stefan-Boltzmann law to explain the degree of heating of the earth’s atmosphere is legitimate, or merely represents a cyclical argument or tautology can be examined by using action resonance theory.

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degrees is obviously crucial to the sustainability of most life on earth. Apart from raising the average temperature of the biosphere well above the freezing point of water, such a change in the average surface temperature of the earth would be expected to profoundly affect all global processes, by changing their rates and positions of equilibrium. Historically, the first mention of the basic principles involved in generating the greenhouse effect was made by the French physicist and mathematician, Joseph Fourier (1824), quoted by Crawford (1997) in a well-researched article on Arrhenius’ 1896 model of the greenhouse effect. As discussed by Crawford, he distinguished between heat associated with light from the sun (chaleur lumineuse) and the dark heat (chaleur obscure) reflected back to the atmosphere. He also recognised that the latter was less able to pass through the atmosphere, drawing on the experiences near Mount Blanc of H.B. de Saussure of the University of Geneva, who had observed that light absorbed by blackened cork in a sealed glass box heated the air inside the box and that this heating effect was independent of altitude. Pouillet (1837) extended this approach by establishing an equation for thermal equilibrium of these light and dark rays. Arrhenius quoted both Fourier and Pouillet, as well as Tyndall who had drawn attention in 1861 to his laboratory data on the differential ability of carbon dioxide and water molecules to retain the heat emitted by the earth, 15 times as strongly as oxygen or nitrogen molecules. Sunlight passes through the earth’s atmosphere on its initial journey from the sun without significant absorption since its action spectrum does not contain quanta with frequencies matching allowable quantum transitions in the gases present. However, about 30 per cent of the energy of sunlight is directly reflected or scattered into space from the earth’s surface. Such scattering is particularly strong from the white surfaces of clouds in the atmosphere or from snowfields and icefields, but also occurs from air molecules and other non-absorptive materials, with little or no change in the frequency of the quanta involved. In other cases such as from forests, deserts and the ocean, the colour of light emitted is changed, because of selective absorption. The proportion of such direct reflection of sunlight (0.3) is the earth’s albedo. Since humanity tentatively began its new exodus to space in NASA’s Apollo program, inspired by the vision (and the promise of funding) of the USA’s President John F. Kennedy in the 1960s, we have become used to the splendid photographic images of the earth generated by focussing the light of this albedo. However, all the remaining 70% of sunlight is said to be absorbed by molecules at the earth’s surface on land and water, such as by the chlorophyll of photosynthetic plants. The quanta of sunlight equilibrate with this superficial matter on earth, to be eventually re-emitted as radiation with quanta of lower frequency or of longer wavelength than in sunlight. As shown in Figure 5.4, the peak frequency of the radiation emitted by the earth’s surface into space is about twenty times less than that of sunlight. This is almost exactly in agreement with the ratio of surface temperatures on the earth and the sun, as predicted by black body theory. The much cooler molecules at the earth’s surface gradually redistribute the impulses of the quanta of sunlight into new quanta corresponding to allowable action resonances at the temperature of the earth. From action theory, these transient changes or oscillations in the energy state of molecules in ecosystems represent the superficial changes in energy levels that we sense as quanta and not the far larger bulk of relatively unchanging energy that underlies and provides the

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action impulses that sustain them. They are like the frothy waves on the surface of an extremely deep ocean - so deep that we never think to measure it. The temperature that the earth will reach, given the spectrum and flux density of quanta shown in Figure 5.4, is a complex function of the composition of its surface, the extent to which energy may be retained by action resonance and work processes within the systems of molecules there present. Because the time taken for this dissipation process of hot sunlight into the spectrum of a much cooler body is finite and not instantaneous, there is a warming effect on the earth. Nevertheless, many of the processes retaining energy on earth involve work, thus limiting the heating effect, at least in the short term. Overall, the flux of radiant energy and impulses as momentum leaving the earth must equal the flux of energy and momentum received by it, allowing for much smaller effects of radiaoactive decay or gravitation such as tides or vulcanism. The earth does not accumulate radiant energy and the rate of arrival of actons must equal the rate with which they leave. This equality defines the nature of the overall solution required and prospective environmental changes on earth such as global warming. Without changes in the absorptive properties of the earth’s surface and its albedo, there can be no change in the earth’s true surface temperature, because this temperature defines its radiant output. However, this is not to say that the temperature at the terrestrial surface cannot change even if the temperature at the top of the atmosphere remains the same. As long as the temperature of the atmospheric zone where radiation is emitted to space remains the same (taking into account any change in its surface area as a result of change in atmospheric altitude) the total emission should remain the same. At sea level we are really dealing with an internal zone or shell of the earth where the temperature can obviously be much greater. A completely black surface at the earth’s surface can even reach the boiling point of water in equilibrium with the maximum rates of insolation possible near midday at low latitudes, as shown by the success of solar heaters. For that reason, unless a window can be placed in the atmosphere, the temperature of the earth’s surface measured from a satellite in space using infrared emissions may be less than that measured using a thermometer on earth, unless appropriate corrections are made. The space satellite will also see the infrared emissions corresponding to the quantum transitions of cooler air molecules of the troposphere in the gravitational action field as well as some of those from nearer the surface, but with decreasing probability as sea level is approached. Considering the theory of black body radiation, this corresponds to the difference in temperature seen between the surface of a body emitting radiation and its much brighter interior as viewed through a small window cut in the surface. Radiation emitted directly into the interior (and escaping through a small window) is in equilibrium with the internal molecular temperature whereas the surface is at least marginally cooler than the interior, because it is currently emitting heat energy irreversibly to cooler surroundings. The dissipative 20-fold decrease in the peak frequency of the quanta of sunlight to that of the peak of energy re-emitted on earth from all latitudes, day and night, provides the driving force for the generation of nearly all the action processes of living ecosystems. The contemporary view of the greenhouse effect is that certain atmospheric gases, particularly carbon dioxide and water, absorb lower frequency, longer wavelength, radiation emitted from the surface of the earth. Thus, the atmosphere acts as a blanket

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that then returns part of the heat radiation by emission back towards the surface of the earth, from where it is eventually re-emitted – a recycling process that effectively retains more heat energy in the soil, water and atmosphere. This increase in the density of radiation of wavelengths able to be absorbed results in a warming effect so that the earth’s surface and atmosphere is sustained at a higher temperature than if there was no atmospheric absorption and all surface radiation was merely emitted directly to space. To the extent that this radiant energy is retained for a longer time by the molecular systems in the biosphere and the atmosphere than if it were directly reflected into space without change in wavelength, its residence time on earth is increased. We shall see that the residence time of the total radiant energy of sunlight on earth is directly related to the sustainability of life systems on earth. The richer and more diverse the ecosystems on the earth’s surface and the greater the biomass present, the greater is the ratio of the energy that is retained on earth, albeit temporarily, to that continuously arriving as sunlight.

6000 K Shortw ave

287 K Longw ave

RELATIVE FLUX DENSITY

0.1

1

10

100

WAVELENGTH (micrometres)

Fig. 5.4: Spectra of solar and terrestrial radiation, normalised for peak flux density (adapted from Reifsnyder and Lull (1965)). The total number of actons or impulses received by the earth must equal the number it emits, to maintain energy and momentum balance.

The mathematical model previously given in the footnote uses the Stefan-Boltzmann law to estimate the earth’s temperature by equating the energy input from the sun known as the solar constant to the energy emitted from the earth. By introducing the additional concept of emissivity, one is able to calculate a temperature for the surface close to that observed on earth, using a modified equation and the relationship involving the fourth power5 of the temperature. A higher temperature in the atmosphere is inferred as 5 The variation of the radiancy of a black body with temperature is based on a mathematical theory of Boltzmann (1884) that employs radiation as a working substance in a Carnot cycle; he shows that the energy as radiation per unit volume at any temperature should be proportional to the fourth power of the absolute temperature. Planck (1913, p. 62) advanced a thermodynamic argument based on the entropy of radiation in an enclosure, where pressure was one-third the radiation energy (U) density (p = u/3, where u = U/V). Then dS = (dU + pdV)/T = Vdu/T + 4udV/3T and the differential rates of change of entropy of

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necessary because of the opacity introduced by greenhouse gases. However, this formal mathematical solution is less than fully convincing because the nature of the physical mechanism is unclear and it introduces a factor (the emissivity) for which the logical basis is obscure. Any inference that water and carbon dioxide, by absorbing quanta can trap energy indefinitely, preventing its eventual emission, is not credible. However, resonant exchange of infrared quanta between molecules of water or carbon dioxide in the biosphere can certainly delay the emission to space of this energy, increasing the transient state density of these quanta in the lower atmosphere and specifically raising the temperature (by torque exerted) of the absorbing molecules. These greenhouse gases can even remove a part of the infrared spectrum from the earth’s surface emissions as the energy absorbed by water, water vapour and carbon dioxide, but this energy must be passed kinetically to nitrogen and oxygen molecules by collisions in the atmosphere, as air temperature equilibrates. The total inwards and outwards fluxes of energy must be in balance. The total momentum of the energy quanta arriving on the earth’s surface must also equal the total momentum leaving, although it is obvious that the total number of quanta leaving the earth’s atmosphere must be much greater that that of those arriving in order that this equality can be met. It will be seen below that the action resonance theory can provide a credible mechanism for greenhouse warming. 5.2.3. The greenhouse analogy As discussed above, Arrhenius (1896) is given credit for popularising a century ago the concept of the earth’s atmosphere acting as a greenhouse. Like the earth’s atmosphere, the glass covering a greenhouse is similarly completely transparent to sunlight and the near infrared. But it is relatively opaque to much of the radiation of longer wavelength around five to ten micrometres emitted from plants and other objects contained within the greenhouse that have absorbed the sunlight. This has the effect of raising the temperature of all the contents of the greenhouse because molecules in the air in the greenhouse or the glass itself absorb this radiant energy of longer wavelength or lower frequency. Radiation trapped within the glass walls and ceiling bounces from glass surface to glass surface until it is all absorbed by molecular systems within the greenhouse including the glass. Eventually, the whole system reaches a transient state temperature that depends on the intensity of the incident sunlight, the difference between the internal and external temperatures of the greenhouse, the wind-speed and the rate at which energy escapes from the greenhouse by radiation and conduction from the glass and other structures. Since most greenhouses leak, the air pressure inside and outside will tend to equilibrate so that the greenhouse will actually contain slightly fewer air molecules per unit volume than the exterior air. The warmer, speedier, molecules inside generate the same pressure at a lower density than the cooler molecules outside. In action theory, the space density of impulses from energy must be equal inside and outside if the pressure is to be the same. Because warmer molecules need more energy to sustain them (keeping radiation in an enclosure were (∂S/∂T)V = V/T.dU/dT and (∂S/∂V)T = 4u/3T. From this, dU/dT = 4u/T and u = aT4. The pressure must also vary as the fourth power of the temperature. In the Endnotes/Glossary under black body radiation, we advance a simple argument for T4 dependency based on the relationship between three-dimensional energy density as quanta required to maintain pressure as the temperature (or torque) and volume increase.

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gravitational potential constant) there must be fewer molecules per unit volume for the energy density and pressure to be the same. A greenhouse completely sealed and then allowed to warm up will have a higher internal pressure than the air outside, in accordance with the gas law formula relating pressure, volume and temperature (PV/RT = 1). This higher pressure is consistent with high frequency energy as light being able to enter through the glass, but when re-sorted by molecular interaction into longer wavelength as heat quanta, less able to leave through the glass. The same amount of total energy in the greenhouse with the molecules closer together than in a leaky greenhouse means that the rate of impulses of actons with molecular surfaces will increase even more, so that both pressure and temperature (or molecular torque) must increase. The solar energy within the greenhouse is partitioned between all the degrees of freedom of molecular vibration, rotation and translation, resulting in a transient state temperature characteristic of the environmental conditions and the material structure. At this point, the energy received by the greenhouse from sunlight and other nearby sources will be in dynamic equilibrium with that radiated by the greenhouse and transmitted directly by conduction to the soil or to the air. However, if there is net growth of plants in the greenhouse, the rate of loss of radiant and conductive energy by the greenhouse will be reduced by the amount of sunlight energy used in photosynthesis by plants in the greenhouse. This energy of sunlight is needed to do major work of the biosynthesis of macromolecules from carbon dioxide and water as well as simply raising and supporting the matter in the plants extracted from the soil against the force called gravity. To the extent that biological and gravitational work is done, there is a cooling effect in the greenhouse analogous to that of evaporative cooling. If the air in the greenhouse is also de-humidified and the heat of condensation exported, there will also be considerably extra work involved in uptake and transpiration of water by the plants and in direct evaporation of water. In terms of its initial transmission and absorption of sunlight and subsequent retention of longer wavelength radiation, the greenhouse provides a very good analogy for what occurs in the atmosphere, although there is one important difference that we will now consider. Some authors of popular books and textbooks on the greenhouse effect have concluded that the greenhouse analogy is a poor one (Henderson-Sellers and Blong, 1989), suggesting that the glasshouse is warmer because it prevents convection and advection (wind generation), shown by the results of Wood in 1907 (see Jones and Henderson-Sellers, 1990). This is an interesting point of view, originally based on a criticism of Fourier and Pouillet by Langley (1889) for employing the analogy of the glass “hot-bed” when referring to the heating of the atmosphere, and only part of the truth. Langley’s careful physical measurements on the infrared spectrum of the moon to determine its surface temperature with a bolometer had provided the main basis for Arrhenius’ greenhouse model published in 1896. It is true the cooling effect of convection and advection will not be available to the air contained in the glasshouse. But it is still because of the transparency of glass to sunlight and its relative opacity to long wave infrared radiation that the glasshouse warms up in the first place and then retains heat. A glasshouse with half its roof removed would still have at least part of its volume warmer, but it would not be as effective in warming. We suggest that the conundrum posed by Langley a century ago still contains an important message for predictions about

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global warming that, surprisingly, may have been misunderstood. We will see that the action resonance theory automatically indicates a major role for the cooling effects of convection and advection in the atmosphere, which is not possible in a glasshouse. Molecules in the atmosphere will absorb and re-emit quanta of lower frequency in the concentric layers of gas molecules, forming a glass wall that becomes progressively thinner with altitude. A monatomic gas in the atmosphere such as argon contributes least to the greenhouse effect, because its heat capacity involves quanta associated with translational motion of much lower frequency than most of the infrared quanta that are radiated from the earth’s surface, heated by sunlight. Diatomic molecules such as the major components of air, nitrogen and oxygen, have a larger heat capacity than monatomic gases, but also absorb infrared radiation relatively poorly, exerting a much lower greenhouse effect than molecules such as water, carbon dioxide and ozone containing three atoms. These polyatomic molecules have stronger absorption bands for frequencies in the infrared region, and can be readily excited to higher quantum or action states by radiation emitted by the earth’s surface. Therefore, they increase the residence time of radiant energy in the atmosphere by recycling quanta between molecules, thus amplifying the overall action exchange forces between molecules. Multiatomic molecules such as hydrocarbons and chlorinated fluoro-carbon compounds (CFCs) have even greater greenhouse effects. The paradoxical result of the presence of only small amounts of these polyatomic molecules is that the earth’s surface receives much more radiation than it would if there was no atmosphere between it and the sun. Thus, resonant exchange of radiation results in a greater rate of momentum transfer or radiation pressure to the earth’s surface than would a non-resonant radiation of heat from the surface of a planet with no gaseous atmosphere of polyatomic gases. 5.3.

Action resonance in the atmosphere

5.3.1. An action explanation of the greenhouse effect From the action resonance theory given as testable statements in Chapter 2, gases in the atmosphere will require a density of quanta greater that the minimum (corresponding to zero entropy) present at absolute zero, according to their heat capacity and their current temperature. For a particular gas to be suspended in the atmosphere at a certain temperature there must be present adequate radiant energy to sustain the motion of all its molecules, their action and their kinetic energy. The more atoms a gas molecule contains, the more radiant energy is required to sustain the interacting gas molecules, though screening effects will reduce the density of ground-state energy required by polyatomic molecules, equivalent to the bonding energy. On the other hand, monatomic gases such as argon exchange fewer quanta, equivalent to their lower total heat capacity, between the molecules. There are no internal degrees of freedom of motion that would provide more reactive surface for reflection of quanta, so their heat capacity per molecule is less. As explained earlier, polyatomic molecules with more action need more energy per molecule to support their motion. Because greenhouse gases such as water and carbon dioxide absorb radiation efficiently and are directly excitable to higher quantum or action states by the heat

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radiation emitted by the earth to the atmosphere, they can act as primary agents for heating the atmosphere. Initially, as a group they will absorb infrared heat radiation causing intramolecular and intermolecular recoil by the principle of momentum conservation, adding to their average kinetic energy and momentum. Collisions with other molecules in the air, from action theory, will then result in the absorption of energy from the general action field of secondary gas molecules such as nitrogen, oxygen and argon, accelerating their motion in proportion to the collision rate. As a result of these collisions, equilibration between different gases in the atmosphere will tend to arise, so that the heated carbon dioxide and water molecules will then heat up nitrogen, oxygen and argon molecules. Subject to the same radiative turning forces or torques on their reactive surfaces (electrons and nuclei), all gases will tend to reach the same temperature as the quanta are redistributed and a new ground state distribution is established. However, the distribution with height of each set of different gas molecules in the gravitational field will be that giving least action for the complete system. Thus, heavier molecules travelling with less speed but requiring a greater density of field energy to provide sufficient impulses to sustain them will distribute in a manner giving the highest concentration and least separation nearest the surface of the earth, but falling off more rapidly with altitude than lighter gases. Action resonance also ensures that there is a continuous tendency to achieve an equilibrium distribution of molecules with height. This vertical distribution of molecules in the gravitational field is exponential6, just as the equilibrium vertical distribution established by Brownian movement of natural resin particles suspended in water on a microscope stage studied by the Nobel laureate, Perrin, described in Chapter 4, was found to be exponential. Of the natural gases in the atmosphere, carbon dioxide is heaviest, with a molecular weight of 44, and, theoretically, its relative concentration will fall off most rapidly with height. Argon, oxygen, nitrogen and water, in that order, are progressively less concentrated as a proportion of their total content at lower altitudes in the atmosphere, because of their decreasing molecular weight. Gases such as hydrogen and even helium are so light that, subjected to the action field, their Brownian motion is so great they may reach escape velocity at ambient temperatures of the upper atmosphere, leaving the earth’s gravitational field. As mentioned above, gases such as carbon dioxide and water are said to be greenhouse gases because of their ability to exchange quanta in the infrared. Nearly everyone has observed that a clear, dry, atmosphere results in the most rapid cooling of 6

According to Laplace’s 18th century derivation, the barometric formula for the atmosphere gives the relative number (n) of molecules of a gas of mass m in unit volume at an altitude h greater than ho sea level (or any other reference level): nh = noe-mgh/kT However, this equation infers constant temperature with height, which is not observed. The adiabatic lapse rate of about 10oK per kilometre change of altitude in the atmosphere dictates that the correct equation for an equilibrium distribution cannot assume constant temperature with height. Currently, the theory explaining the distribution and lapse rate of atmospheric temperature with altitude is poorly developed, despite the well known effects of the phenomenon on climate in alpine regions. A rudimentary action resonance analysis of this problem is presented in the Endnotes, but a more complete theory is needed.

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the earth’s surface at night by radiation to space, sometimes leading to frosts. Quanta emitted from water on the earth’s surface find little water in the dry atmosphere with which to exchange and the probability of resonance is reduced. When quanta are returned by reflection or emission to the atmosphere, they take longer to do so because of a longer mean free path, a reduced rate of surface impulses and hence generating a lower kinetic energy or temperature of water. Remember that the kinetic energy and action of the water molecules depends on action resonance between molecules mediated by quanta. As a result, freezing of surface water as frost is more likely. In fact, greenhouse gases are not completely characterised by their ability to exchange quanta in the infrared. All molecules exert some greenhouse effect because they will absorb and exchange more energy if their concentration increases. A distinguishing feature of those with pronounced greenhouse effects is the ratio of the heat capacities at constant volume and constant pressure, a variable factor governed by the magnitude of the heat capacity for a particular molecule at constant volume. A simple molecule like argon with only three translational modes of motion has the largest ratio of heat capacity at constant pressure to that at constant volume (5/3 = 1.67). This indicates that a greater proportion of any heat added to achieve a given temperature for argon molecules is used to do cooling pressure-volume or gravitational work rather than providing internal energy, just raising its temperature, than is the case for more complex molecules such as carbon dioxide. For the diatomic molecules like nitrogen and oxygen, the number of modes of motion is greater, so that a higher proportion (7/5=1.4) of the heat added is retained by the molecules and not used to do gravitational work. For carbon dioxide, water and other polyatomic molecules, the proportion of the energy added that does gravitational work on the molecules is even less than about 1.3. Obviously, polyatomic molecules require more energy for their sustenance than simpler molecules, but all kinds of gaseous molecules involve the same amount of pressure-volume work per mole so that the proportion of the energy needed for expansion decreases as molecular size increases. In a closed volume of gases unable to expand to greater altitude, no cooling from gravitational work is possible and all the heat absorbed raises the internal energy content and temperature of the molecules. This would be the situation in a sealed glasshouse. It should be noted that the heat capacity of gases for a marginal change in temperature depends on the number and distribution of the atoms they contain, rather than their mass. Thus the noble monatomic gases helium, neon and argon at ambient temperatures all need about the same amount of thermal energy to raise their temperature one degree Kelvin. This may mean that the quanta of energy needed to change their action state are matched at any given temperature. Denser atoms screen one another more than lighter atoms at a given concentration, so that the transit time for energy between reflecting surfaces would be shorter. Offsetting this, larger atoms move at slower speeds at a given temperature, inversely proportional to the square root of their mass and therefore interact with fewer other atoms. As a consequence of balancing such effects, the radiant energy needed to sustain their motion at a given temperature becomes equal. However, their distribution in a gravitational field will differ, with a higher proportion of the lighter gases being found higher in the atmosphere. Using action resonance theory, we can conclude that the gases distribute themselves at a given temperature according to

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their action state. Heavier polyatomic molecules require a greater energy density to sustain them in the gravitational field. A greater rate of change in concentration with height implies greater change in chemical potential and hence of the size of the quantum of energy involved in changes of gravitational potential. However, a greater mass implies a greater mutual celerity (see Glossary/Endnotes), and a greater change in potential energy and kinetic energy associated with the relevant quantum transitions. Matching these two changes in action state implies that heavier molecules will decrease in concentration more rapidly with height than lighter molecules. In action resonance theory, quantum effects result in part from screening effects by atoms and also from the effect of this on the rate of interaction with energy. Heavier polyatomic molecules also have a greater mass to surface ratio (since mass depends on volume and surface to radius squared), implying they will need a greater energy density to separate them or to provide sufficient impulses to keep them sustained in the gravitational field. Very importantly, it should also be noted that these quantum relationships infer different responses for different molecules under different environmental conditions. Thus the relative distributions of different gases in the gravitational field should vary with the base temperature at the earth’s surface. We need also to recognise that the ability of some polyatomic gases to trap more radiant energy does not directly raise the temperature of air. On the contrary, their greater heat capacity and mass causes the temperature to rise more slowly with added radiant heat. But their larger heat content also provides a larger buffering capacity against cooling, so that greenhouse gases slow down the rate of temperature change at night or from one season to the next. Not only does the heat stored by raising the temperature of greenhouse gases provide buffering, but so do all the gases in the system, because temperature equilibration by molecular collisions ensures that the heat capacity of each gas contributes to the buffering. Thus, a humid, overcast, atmosphere cools more slowly at night. The probability of resonance is increased by the greater concentration of water in the atmosphere and the resonance time is reduced because of the lower mean free path of the quanta concerned. Others may have shared a similar experience to the author who, on the shores of Lake Michigan in 1967, suffered the most severe sunburn on the shins, even though conditions were cloudy and overcast with little or no direct sunlight. 5.3.2. Convective cooling as an action process A feature of the temperature of the atmosphere is that it cools rapidly with height or altitude. The relief to be obtained at mountain resorts or hill stations like Murree in Pakistan from the oppressive heat nearer sea level, is well known. As an approximation, the air is naturally cooler by 1oK for every 100 metres increase in altitude, although heat released on condensation of water vapour can reduce this rate of cooling with altitude to about two-thirds this value for humid air. It can be concluded that the equilibrium distribution involves equivalence between the increased potential energy of gas molecules in the gravitational field with increased height and decreased kinetic energy and Gibbs free energy with height. For the air molecules, each gas is distributed with its concentration decreasing exponentially with height, according to its mass and the temperature. The total energy of a particular gas molecule and its capacity to do work

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will tend to be the same at all heights. Therefore the kinetic energy and temperature of gas molecules will increase if they are falling in the atmosphere, accelerated by gravity. This is the meaning of equilibrium. Considered dynamically, if a parcel of air is heated (e.g. by being in contact with a black surface illuminated by sunlight), it now has greater total energy and density of quanta than the surrounding air. Because of the gradients established, there is a new tendency to heat up the surrounding air as a result of more frequent collisions and the associated diffusion of quanta. The most rapid degree of freedom for dissipating this asymmetric stress is to achieve cooling of the parcel of air by vertical mass transport. The extra radiant field energy in heated air can support the gas molecules in the gravitational field at a higher altitude but only at a lower temperature, so that work of expansion of the air against the overlying atmosphere occurs spontaneously. As the air rises, the individual molecules also have the freedom to separate slightly, because of the greater volume available in the sphere obtained with increased height or distance from the centre of the earth. This spontaneous flow to fill a vacuum is, to some extent, analogous to the flow into a vacuum discussed earlier as the Gay-Lussac experiment. But in contrast to flow into a vacuum at the same gravitational potential, work against gravity and the consequent pressure of the overlying atmosphere must be done, so that now a cooling effect must occur. One may consider that the density of quanta needed to sustain the air molecules at a higher temperature at lower altitude can only support the same number of air molecules at higher altitude at a lower temperature. This follows since the resonance time between molecules of the quanta involved is now greater as a result of the greater radial separation of molecules. As a consequence, the frequency of impulses and the kinetic energy is less for gas molecules at higher altitude. This vertical flow of air in the gravitational field is the phenomenon of convection. The author’s first scientific physics experiment at school, at the age of 13, was to make an apparatus to demonstrate convection. This involved constructing a cardboard chimney containing a light bulb at the base to heat air, with smoke introduced through a basal intake to demonstrate the phenomenon of convection of heated air. This occurs spontaneously in a chimney erected over burning logs in a fireplace. It is important to note that the initiation of this process of convective cooling of the air depends on the state of non-equilibrium in the energy content of the atmosphere, comparing one level or altitude with another. This results from the local chaotic state caused by a local source of heat such as sunlight being converted efficiently to quanta resonant with at least some of the molecules in air at a black, absorptive, surface. If the black absorptive materials are replaced by reflective white, or if the intensity of sunlight declines, the radiation pressure within the lower altitude air will decline – just as observed earlier in the Crookes radiometer. The transient state distribution of air will change and cool air will descend, heating up as it falls in the gravitational field and the resonance time for quanta decreases. Thus, as heat is radiated into space as a net process after sunset, there would clearly be a tendency for the atmosphere to contract towards the earth’s surface, slowing the rate of cooling as air molecules gain kinetic energy as their state of inertia decreases. Cooling during expansion work is called adiabatic when there is no input of heat into the system. In an insulated cylinder separated from the atmosphere by a piston, a heated

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gas undergoing a reversible adiabatic expansion will retain constant values for its entropy and action per molecule as the gas cools in doing work against the atmosphere - as discussed in Chapter 4 (Section 4.4.2.). Decreased molecular action resulting from decreased temperature and molecular velocity will just equal the increased action resulting from increased radial separation of the molecules. The decline in heat content of the working fluid will be exactly equal to the energy needed to sustain the expansion work done. For expansion work against atmospheric pressure, where the cooling is known as the Joule-Thomson effect, the heat consumed is equal to the increased gravitational potential of the atmosphere. However, it should be noted that the decrease in kinetic energy of the air molecules as they expand to higher altitudes only provides half of their increase in potential energy. According to action resonance theory7, an equivalent quantity of radiant energy will be needed to sustain the molecules at greater height. 5.3.3. Implications of convective and advective cooling for the greenhouse effect Implications for the greenhouse effect from action theory are profound. The capacity of heated air to spontaneously cool by convection and the need for radiant energy to sustain it imposes a buffering capacity on the extent to which the temperature of the atmosphere would be expected to increase as a result of the greenhouse effect. This buffering effect would also apply to heating of the ocean and the predicted rise in sea level. Any thermal expansion of the ocean has to involve a transient increase in field resonance energy 7

Action resonance theory (see Chapter 2 and Endnotes) proposes that potential energy (U) in a system maintained in dynamic equilibrium (even as a transient varying state) is given by the following equation: U = mc2 – mv2 and ǻU = -ǻmv2 A gas molecule elevated reversibly in the gravitational field loses kinetic energy (i.e. becomes colder) but also must absorb the quantum of energy needed to sustain it at its new elevation in the system, equal to the decrease in kinetic energy. Thus the increase in potential energy of the system is equal to the size of the quantum of energy plus the loss in kinetic energy. Therefore, reversible convection as a result of pressure differences in the atmosphere requires not only the kinetic energy of the molecule but also an equivalent amount of radiant energy. This radiant energy will be provided from the heated parcel of air. However, since quanta are continuously dissipated by radiation from the upper atmosphere to space, the energy required to sustain the elevated molecules may soon disappear unless replaced. After the peak intensity of radiation at noon, the previously rising atmosphere will now commence to fall. In their fall, molecules will regain kinetic energy equal to the radiation lost (i.e. they warm up without needing extra heat), so the change in potential energy remains consistent with the above equation. This may seem to conflict with the common opinion that the decrease in potential energy during the fall of a body in the gravitational field is equal to its gain in kinetic energy. In fact, the latter case applies only for falls as irreversible processes from stationary positions relative to the earth. In this case, there is initially insufficient field energy available to provide impulsive force to sustain the matter of the body in an elevated position. In action theory, such sustenance in the gravitational field occurs during orbital motion, or as a result of the cooperative Brownian motion of the atmosphere. The fall of Skylab from orbit near Balladonia in bush country while the author and his family were travelling across Australia’s Nullarbor Plain in 1979 involved a loss in potential energy twice that which would have been involved for its direct fall from a stationary position, were this possible. The Endnotes show that the difference in potential energy of air molecules with height is equal to that for particles of the same mass in orbit at the same two heights and that the change in kinetic energy is half this value of opposite sign. However, because of the greater intensity of impulses available from energy quanta at the density of the atmosphere as a result of cooperative action the air molecules can be sustained at a much lower kinetic energy and velocity than required for independent orbital motion.

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sufficient to elevate water molecules in the ocean as well as the entire atmosphere above it against the force of gravity. This radiant energy requirement for water will also exert a strong cooling effect and provide a buffer against temperature increase. Increased carbon dioxide dissolved in the ocean as its level in the atmosphere increases will also increase the heat capacity of the ocean since more field energy as quanta will be required to maintain a given temperature in the ocean. It is now generally accepted that carbon dioxide is increasing in concentration in the atmosphere, as the long-term trend for measurements taken at the Mauna Loa observatory in Hawaii show (Figure 5.5). Action resonance theory predicts that seasonal variations in solar intensity will cause a seasonal oscillation in carbon dioxide concentration, since the whole atmosphere is more elevated and less dense in summer and less elevated and more dense in winter. This prediction is in agreement with seasonal variations observed in Hawaii of just under two percent. The current explanation that the oscillation results from the imbalance of increased rates of photosynthesis of carbon dioxide in summer in the northern hemisphere and faster degradation of soil organic matter in winter (Henderson-Sellers and Blong, 1989) has always seemed intuitively unlikely to the author of this book. Degradation of leaf fall and plant detritus and associated biological nitrogen fixation where there is a high C:N ratio is highly temperature dependent, being much faster in summer.

[CO2] ppmv

Year Fig. 5.5: Increasing trend of atmospheric carbon dioxide concentrations. A more pronounced annual oscillation in concentration is shown for Mauna Loa in Hawaii than at Cape Grim in Tasmania. Action resonance theory suggests that the oscillation is caused by seasonal convective effects for greenhouse gases rather than imbalance of photosynthesis and mineralisation of organic carbon. Reproduced with permission from Figure 11.3 in Schnoor (1996).

It is true that the magnitude of photosynthesis is such that a significant imbalance between carbon dioxide fixation and carbon dioxide formation should result in some fluctuation in the atmospheric concentration of carbon dioxide near sea level. This effect is observed above crops conducting rapid photosynthesis, but direct evidence of such a

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global imbalance is lacking. Also, similar seasonal oscillations with maxima in winter are observed for other gases such as methane (see Schnoor, 1996), which is not consumed in summer by photosynthesis. Action resonance theory predicts an annual oscillation in the density of both carbon dioxide and methane, as a result of convective dilution as the barometric redistribution is established. This effect is predicted from the action resonance theory to be most effective with greenhouse gases such as carbon dioxide, since they are selectively elevated in the gravitational field by specific quanta. If all gas species behaved ideally like the noble gases and were elevated simultaneously at the same temperature instantaneously at equilibrium and correctly distributed in the gravitational field, no seasonal oscillation would be expected. This conclusion is also conditional upon carbon dioxide concentration being expressed relatively as the ratio of the total number of molecules (ppmv) rather than the absolute mass per unit volume (density), for which there will be daily and seasonal change. Although carbon dioxide is significantly heavier (MW=44) than oxygen (32) or nitrogen (28), there might ideally be no seasonal variation in the relative proportions of the different gases because the vertical distributions of each could be affected equally by changes in temperature. However, there is no evidence that the different gases are distributed in the atmosphere as predicted by Laplace’s ideal barometric distribution. On the contrary, no physical meteorologists expect this to be true. Varying and chaotic conditions in the atmosphere could also maintain nonequilibrium distributions – a constant feature of the real world. This is predicted by the theory of action resonance, which would not involve equal accelerations for all chemical species. Nor is it likely that ideal behaviour will be observed by all the different gases. Carbon dioxide in particular is known to behave anomalously with change of temperature and pressure, more so than nitrogen and oxygen, reflecting real variation in its quantum state. All these predictions of action theory regarding seasonal oscillations and other effects are subject to experimental testing and there may already be sufficient data to perform these tests. An associated cooling from the expansion work against atmospheric pressure and gravitational potential would be expected to occur. In principle, this explanation suggests a large buffering capacity for the absorption of extra heat as carbon dioxide and water levels in the atmosphere increase. This buffering results from all of the readjustments of the atmosphere, including the elevation of non-greenhouse gases such as nitrogen and oxygen. Such a redistribution will increase the heat capacity of the atmosphere. This prediction of the action resonance theory can readily be tested, by measuring carbon dioxide concentrations (as well as that of nitrogen, oxygen and argon) at sea level and at various altitudes above so as to contain most of the atmosphere. If there is a gravitational dilution near sea level as a result of upwards action resonance, the gradient of concentration with higher altitude should be less than observed in cooler conditions. However, the integral of the concentrations with altitude would remain the same. Any imbalances in the rate of carbon dioxide consumption and production by biota would mean that this integral over altitudes would vary between summer and winter. The action resonance explanation does not suggest that there will be no change in temperature from an increase in atmospheric greenhouse gases, as a result of the spontaneous conversion of extra heat trapped to gravitational work. These re-adjustments

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take time to establish new transient equilibria. To initiate the adjustments, marginal increases in heat content and local temperature near the earth’s surface would be required as carbon dioxide concentration rises (1-2 vppm per year), before there will be an adequate gradient of action forces (pressure) to generate mass convection. The current state of the atmosphere represents the outcome of all the resonant exchange forces, pursuing a steady state equilibrium, but its actual state depending on a large number of kinetic factors. These include the rate of receipt of energy at the earth’s surface, the composition of the atmosphere and its capacity for energy and the rate of re-radiation of energy into space. Dynamic greenhouse models seeking to predict the rate of temperature increase as the concentrations of gases increase in the atmosphere need to consider the cooling effect resulting from gravitational redistribution of materials such as soil, water and air, as the energy associated with sustaining these materials at higher altitudes increases. Effectively, an increase in carbon dioxide concentration causes the residence time of energy in the atmosphere to rise, making possible more gravitational work and a partial dissociation of the earth’s atmosphere from the surface. As a result, the extent of the temperature increase will be less than expected in the absence of convective cooling. Increased action resonance in the lower atmosphere from more carbon dioxide, water or sunlight intensity will allow the atmosphere as a whole to be sustained at a higher altitude. This variation in density of the atmosphere as a result of increased energy content should be observable and is predicted to have practical consequences in affecting the drag exerted on artificial satellites orbiting close to the earth. Recent studies in this area (Fraser, 1998) show that solar energy as sunlight is not the only factor involved in raising the energy content of the earth’s atmosphere and the gaseous density at higher altitudes. The ejection of high velocity protons, electrons and other material particles from the sun into the solar system contributes to storm-generating conditions in the atmosphere during solar storms. The year 2000 is anticipated to be of above average turbulence. These high energy particles can have serious consequences for the operation of communications satellites, sometimes leading to serious technical breakdowns (Fraser, 1998). Mobile telephony requires satellites to be placed in relatively low orbits to reduce transmission times and annoying voice delays. The drag factor is a significant consideration in establishing the lifetime of satellites; an increase in drag could be another consequence of the greenhouse effect. When the extent of action resonance declines, after noon, at night or in winter when the intensity of incident sunlight is less, the atmosphere will contract. As a result, one would expect the density of gas in the atmosphere to vary with seasons at different altitudes. Zones of variable gases like ozone, found mainly at the top of the atmosphere where ultraviolet radiation is most intense, would be expected to become marginally thinner as summer approaches. This would occur as a result of a fixed amount of ozone molecules expanding into a zone of greater surface area at greater altitude. The net result on the physics and chemistry of such materials would plainly be highly complex, but the seasonal pulsation in concentration from convective elevation or fall needs to be included in models of such processes. Just as convection leads to cooling of heated air, so does the advective generation of winds. The whole weather cycle can be seen as an expression of the relief of stress by

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action exchange processes and the generation of mass movements of air as in cyclones and anticyclones. Since pressure in action resonance theory is considered to reflect the density of quanta (Chapter 2) and the rate of resonant impulses, these movements in air masses are predictable using the theory. Turbulence is a natural outcome of such action exchange processes and a means of relieving the stresses most rapidly. Because of the differential speeds of rotation of the atmosphere at different latitudes, there will also be heating and cooling effects resulting from the movement of air masses between the latitudes. This can be predicted from the definition of inertia in action theory and conservation of momentum. Air masses travelling northward in the northern hemisphere and southwards in the southern hemisphere will automatically heat up just as Chinook winds do with descending altitude. Thus, the temperature of such air masses will be greater than predicted from ambient temperatures at their source. Air masses travelling in the contrary directions will automatically cool. Exactly the same principles are involved in the movements of the ocean and effects on temperature such as warming of the Gulf Stream Current. A full exploration of the meteorological, hydrological and thermal consequences of these predictions of the action resonance theory and their relationship to the Coriolis effect would require far more space than is available in this book. 5.3.4. Thunderstorms and lightning as action processes Oscillations in the extent of action resonance in the atmosphere associated with acccelerations and decelerations of air masses can explain the origin of lightning in thunderstorms. Heated zones on the surface of the earth where sunlight is absorbed more efficiently or where there is more carbon dioxide or water in the atmosphere will result in mass vertical air flows by convection. This will reduce the surface pressure and cause cooling of the ascending air as molecular kinetic energy is converted to gravitational potential energy. Subsequently, compressive collisions between air masses and descending flows of increasing pressure, because of their greater radiant energy content and increased molecular kinetic energy, will set up the chaotic conditions needed for violent storms. Where collisions of air masses are particularly acute because of very rapid descents, or where there are very steep temperature gradients, action resonance theory suggests the energy density will greatly exceed that needed to sustain the molecular systems at the current temperature in the gravitational field. Once these energies exceed dissociation levels for electrons, the excess energy will then be dissipated as electronic quanta, exciting a chain reaction of excitation, dissociation and emission of electrons, propagating along paths of least action. Effectively, electrons will be bumped from one molecule displacing another in the next molecule. Cooperatively, these events will appear as lightning strikes between air masses or between an air mass and the earth’s surface. This viewpoint does not conflict with the electrical viewpoint that lightning is associated with charge separation resulting from friction and the generation of potential gradients or voltages. Frictional processes correspond to compressive collisions, which will amplify action resonance forces and lead to emission of more quanta from the general ground-state energy field. As noted above, these forces are anticipated to dissociate electrons from molecules in collisions, setting up imbalances in electron and

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proton distribution or charge separation. This action resonance theory identifies charge separation as an effect and not a cause. 5.3.5. Action thermodynamics of the Greenhouse effect It has been pointed out that geological records do not support some of the major predictions of greenhouse models (Crowley, 1993). On both Pleistocene and tectonic time scales (during which continental drift is observed), changes in climate are positively correlated with greenhouse gas variations. However, the prediction of the models that tropical sea surface temperatures will increase is not well supported. Geological data also suggests that winter cooling in high latitude land areas is less than predicted by the models (Crowley, 1993). These predictions are a common feature of the current models. It is noteworthy that both these outcomes, contrary to current greenhouse theory, would result naturally from the action resonance theory. The greater transient rate of impulses from radiant energy needed to sustain gravitationally the ocean raised radially by one metre, remembering that the whole atmosphere must also be raised, would buffer against temperature increase. The total mass of water and air to be raised one metre is equivalent to 100 grams of water plus 1.00 kilogram of air per square centimetre, or a total of 11 tonnes of air and water per square metre. The energy needed8 to lift and sustain this much water and air would be equivalent to 1.079 x 108 ergs per square centimetre or 1.079 x 102 kilojoules per square metre. This equates to the trapping on earth of about 79 seconds of continuous solar radiation – by no means an insignificant amount of extra energy to be retained in the earth’s ocean and atmosphere. This extra energy as redistributed quanta would need to provide the vertical thrust needed to support the weight of 1.10 kilograms per square centimetre one metre further from the centre of the earth. The same amount of energy somehow absorbed in a closed atmosphere of constant volume would produce an insignificant temperature increase of only 0.00235oC in an equivalent parcel of water and air remaining at the gravitational potential at sea level or about 0.01oC if all the heat was applied to the air. In fact, the cooling effect of

8

The equation relating energy input needed for the gravitational work of raising 11 tonnes by one metre (100 cm) is E = mgh; thus E = 11x106 x 980.7 x100 = 1.07877x1012 ergs. This calculation assumes that g, the acceleration (rω2= 980.7 cm.sec-2) due to gravity remains constant, which is approximately true since most of the atmosphere is concentrated near the surface of the earth; g varies in inverse proportion to the relative surface area of the sphere of radius r cm from the centre of the earth because the celerity Ca= a3ϖ2 = (m1+m2)G (see under endnotes); thus rω2 = (m1+m2)G/r2 = Ca/r2 for any gravitating body is similar for other bodies in this orbital system. Incidentally, the isobaric heat capacity of the atmosphere is 1.0x1010 ergs cm-2 K-1 (Szilder and Lozowski, 1996). At 00K, all the atmosphere would adhere to the earth’s surface as a thin layer of frozen gas just a few metres deep with almost zero entropy and action. If we assume that the heat capacity of air remains constant between 0oK and 288oK (which is not true), the total heat sink represented by the earth’s atmosphere would then be equivalent to about 3-4 weeks of solar radiation. It would be instructive to establish the true heat capacity of the atmosphere (Cv) at the surface and then to correlate this to the vertical distribution of the atmosphere, including any additional heat energy needed to raise the atmosphere and the total potential energy involved. This analysis would confirm the relationship between thermal and gravitational energy, showing that the atmosphere is a non-equilibrium structure in which addition of thermal energy both heats the atmosphere and then sustains it in the gravitational field.

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lifting one kg of air 100 metres would require the same amount of energy as heating by 1oC or oK. We cannot exclude the soil and other surface materials of the earth from such calculations. All these vertical motions of air, water and even surface earth materials will buffer against temperature change in either the heating or the cooling phases of daily or annual cycles, to the extent of the heat capacity and the gravitational masses involved. Consider carefully how action theory provides a more dynamic view of energy as a continuous need in the physical world to sustain its current geometric state and morphology. Calculating energy changes is no longer merely a static exercise in bookkeeping about virtual processes but directly involves the extent of dynamic balancing by dispersive forces between materials and provides the forceful mechanism by which all changes in action states occur and are sustained. Raising the molecules of air in the gravitational field using the impulses of quanta on one hand decreases their action by the cooling effect but increases it by their greater separation and by the scale change of greater gravitational rotation or spin. Both water and soil will also be affected by these exchange forces and these spontaneous motions in the landscape could have serious and chaotic consequences when the energy fluxes involved are unusually high. We can predict that any increase in greenhouse energy trapping will result in marginally increased mobility of air, water and earth and of all three at the same time. This is simply nature’s way of dissipating energy and relieving stress at the microscopic level, as predicted by the action resonance theory. The fact that the result while energy is rapidly dissipated may be devastating landslides such as occurred in recent years in Guatemala and in Vietnam, leading to whole villages being swept away, illustrates that humanity’s choices for sites of habitation may sometimes be injudicious or that more prudent precautions may be required as time goes by. Although classical thermodynamic discussions are usually restricted to ideal systems of molecules acting independently of each other, action thermodynamics is inclusive of all the dynamic phenomena observed in the earth’s atmosphere discussed above. All coherent motions of systems of molecules such as convection, as well as the lateral motion of cyclones and anticyclones, are naturally included in action resonance thermodynamics. It will normally be the case that these different modes of motion are actually mixtures of vertical and lateral components. Since there is no difference in principle between the impulsive role of quanta in initiating action or wind in a coherent set of molecules and their role in generating Brownian motion in individual molecules there can be no reason for excluding meteorological or geophysical effects from action theory. Indeed, one scale of motion is a prerequisite for the other. Thus the whole atmosphere, the ocean and all of the earth’s surface can be considered as an interacting thermodynamic system, subject to local fluctuations in action with changes in energy content, temporarily and spatially. Increases in action and entropy as net outcomes of the atmosphere and the earth’s surface materials will occur on daily and seasonal cycles as the energy content increases on daily or seasonal cycles. Decreases in action and entropy of the atmosphere and the surface materials will occur as energy flows out of the system as a result of radiation into space. The speed of motion of molecules and systems of molecules is the outcome of fluctuations in the energy density in space and the sudden withdrawal of energy creating a gradient in the force field is equally likely

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to generate molecular motion as the injection of energy from elsewhere. In such a dynamic system as the atmosphere continuously subject to fluctuating radiation intensity, equilibrium can never be reached and the concept of transient equilibria only would seem more appropriate. To the traditional molecular degrees of freedom of motion such as electronic, vibrational, rotational and translational we must therefore add these other coherent motions of the biosphere at greater scales simply because there is no logical reason not to do so. Indeed, denying this interacting hierarchy of levels at which energy can act is bound to cause problems and result in inaccuracy of our descriptions of the real world, because energy is constantly dissipating itself across such boundaries as a simple result of the dynamic geometry involved. This is unavoidable. Such spontaneous redistributions of energy and action are involved in the development (and disappearance) of turbulence in water and air, providing a mechanism for the generation of extreme forces in tornadoes and other cyclonic storms. Excluding these additional modes of motion when considering the transient-state thermodynamics therefore has no rational foundation. Indeed, in the action resonance theory it would be inconsistent to set such boundaries because the theory is designed to be universal in its application. All modes of extra motion can potentially provide a means of relieving stresses from the impulses of energy on primary particles. Every additional scale of motion will effectively increase the surface that the primary particles interacting with quanta can trace out. Indeed, the transfer of energy into large scale motions of relatively lower recurrent frequency has the advantage that the transit time for recurrence of quanta is greater and the energy capacity of the system at a given temperature will increase accordingly. 5.4.

Action modelling of global warming

5.4.1. Greenhouse modelling Having described and interpreted the meteorology of earth’s atmosphere from the point of view of action resonance theory, some interim conclusions involving prediction are called for. While it is considered that accurate predictions will need new action models to be developed based on the theory, there are some qualitative conclusions that can be made now, which can form tests of the theory. To the extent that current models fail to recognise that extra residence time for energy in the earth’s atmosphere does not necessarily mean an equivalent temperature increase, it is likely that many of the predictions of temperature rise are excessive. This chapter has shown how energy may be dissipated by doing work, either gravitationally by raising the whole atmosphere, increasing its density at higher altitudes, or through the vortices of the weather cycles. Simply adding heat by increasing greenhouse gases in the atmosphere does not necessarily mean that temperatures will rise as if the atmosphere was a static structure held at constant gravitational potential and unable to generate winds. The temperature-sparing effect of global gravitational uplift of the atmosphere is not discussed specifically in any of the models now being run on super-computers (e.g. Bengtsson, 1997; Slingo, 1997). Nor have the modellers concluded that the oscillation in CO2 concentration is a result of differential global uplift and fall for different gases in the

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atmosphere. In action resonance theory, differential effects on different gases will be anticipated for different temperatures as a result of quantum effects when coupling temperature responses to gravitational effects. While the governing equations (Haltner and Williams, 1980) used for numerical prediction of meteorology do correctly recognise transformation between kinetic and potential energies with changes in altitude, the atmosphere is often regarded simply as a uniform bulk gas of mass 29 in the predictions made with these models. The general circulation models (GCMs) are becoming increasingly sophisticated, including more and more aspects of the processes of the weather cycle - which does not necessarily mean they become more accurate. The advent of access to radiation measurements from artificial satellites since the 1960s has enabled data obtained on the earth’s surface or from aircraft to be checked. This has revealed an interesting possible discrepancy regarding atmospheric solar absorption amounting to 8% of the incoming sunlight (Ramanathan, 1997) which could have important consequences in predictions of the rate of global warming. Apparently water vapour, either in clouds or in the clear atmosphere, may be capable of more scattering of radiation in the visible and near infrared range of wavelengths to space than predicted by laboratory measurements. Furthermore, there is an acknowledged discrepancy between the surface temperature of the earth as measured from space using infrared spectra compared to actual measurements of air temperature using thermometers. Most discussion of possible deficiencies in the current models dealing with the enhanced greenhouse effect is addressed to topics such as the feedback of energy by variations in cloud formations (Szilder and Lozowski, 1996). The “radiative-convective” model developed by Manabe and Strickler (1964) did go some way in recognising the role of convection in heat transfer from the earth’s surface to the upper atmosphere (Manabe, 1998). The role of local convection in cooling the atmosphere leading to condensation of water vapour and local release of latent heat is also well recognised (Slingo, 1997). Arrhenius’ estimates of probable global warming of +5.7oC for a doubling of carbon dioxide from the burning of fossil fuels involved very large numbers of calculations in the range 10,000-100,000 (no doubt he had some hard-working assistants). But the addition of convection processes to the models has led to a substantial increase in the predicted global warming (Henderson-Sellers and Blong, 1989) rather than a decrease predicted by action resonance theory. Arrhenius was aware of many of the factors now incorporated into the modern models, including carbon dioxide buffering by the ocean, water vapour and he referred to the possible effects of changes in cloud cover. But neither he a century ago nor the modern modelers seem to have adequately considered gravitational cooling from global convection or uplift of the atmosphere, despite the cryptic clue given by Langley. The fact that each of the modern computer models has been used to perform billions more calculations than even the prodigious efforts of Arrhenius will be of little consolation if these calculations have overlooked any significant factors that need to be considered! 5.4.2. An action resonance model of the greenhouse effect An action resonance model of the greenhouse effect, still needing preparation, would focus primary attention on the cooling effect of global uplift of surface materials and of

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vorticity, emphasising that this occurs as part of the local daily and the seasonal fluctuations. All cyclic coherent motions of air, whether horizontal or vertical or combinations of the two, will increase the energy or heat capacity of the atmosphere, as cooling work. An action model would also recognise the possibility of different responses of different gases to changes in temperature and altitude in terms of their action state. Equality of temperature requires that the torques from the impulses of quanta on all species of molecules should generate the same total effect on kinetic energy, however changes in gravitational potential and pressure may significantly modify the relative responses of different gases. Once this question is resolved by theory and experiment, adding in the effect of an increasing extent of greenhouse retention of degraded solar energy should then only require simple adjustments to the basic explanatory model. The role of polyatomic greenhouse gases would be examined using action resonance principles, coupling the specific absorption and heating effect to the reiterated recycling of energy between the surface and layers of the atmosphere and then, including molecular collisions, to the impulsive uplift of the entire atmosphere and its cooling. Obviously, this dynamic sink for heat must result in a much greater need for energy to be retained by greenhouse gases than if all the extra energy was used to heat air at sea level. Fortunately, it is a simple matter to relate the potential for cooling to the utilisation of heat by gravitational uplift (see relevant footnotes and text earlier in this chapter and the Endnotes). It is anticipated that Fourier methods should be helpful in the analysis of the model, particularly with respect to energy flow. The model must include recognition of the transient, non-equilibrium thermodyamic control involved. This is significant because it indicates a role for variable kinetic factors. These factors include the rate of arrival of solar radiation at the earth’s surface; the rate of absorption leading to resorting of the wavelengths of the quanta; the surface emission spectra and the degree of matching to absorption bands of greenhouse molecules in the atmosphere; the concentration of greenhouse gases including water; the rate and degree of phase transitions for water, carbon dioxide and other greenhouse molecules; the rate of transfer of energy to non-greenhouse gases; the rate of gravitational uplift; and the eventual rate of long-wave radiation to space. These are all action phenomena. What are the kinetic relationships between transient heating of a column of air at its base and the rate of gravitational uplift, thus raising the heat capacity of the column and reducing its average temperature? This is plainly amenable to experimental testing, as part of the analysis of the kinetic factors mentioned above. According to the rough analysis given earlier, sufficient heat to raise the air temperature one degree Kelvin without gravitational uplift would be about two hours and 11 minutes of sunshine, with all reverse radiation from earth blocked. This could alternatively raise the air column an average of 100 metres if the gravitational work could be performed with 100% efficiency. Of course, daily and seasonal variation in insolation is considerably greater than this (2030oK), providing the driving potentials for the weather and climate cycles. Still, a global effect of this magnitude might appear to be no trivial matter, even giving a marginal advantage to alpinists. Adding enough heat to the atmosphere to raise the temperature ten degrees Kelvin could also make it possible to climb Mount Everest without oxygen

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masks in summer or to fly in a Boeing Jumbo jet with less pressurisation, assuming this prediction of action resonance theory is correct. Oxygen, on average, would be redistributed upwards, its density falling at ground level but increasing at higher altitudes as a proportion of the total. However, completely efficient uplift is unlikely to be possible in such a loosely-coupled system. Uplift may also increase the rate of convective transport, diffusion and emission of radiant energy to deep space. Molecules subjected to uplift must cool (shown as reduced kinetic energy) by an amount just equal to the extra radiant energy absorbed by the molecular system supporting them. There is now an opportunity, using action resonance theory, to re-examine the relevance of the Stefan-Boltzmann radiation model in determining the surface temperature of the earth. We need to distinguish carefully between cause and effect with respect to radiation and to understand what is essential and what is optional. The basic simplicity of the dependence of radiative flux on the fourth power of the temperature by black bodies is appealing. But the need for a emissivity factor indicates that the energy flux as radiation is actually occurring at a lower temperature than the ideal black body at the temperature of the interior. This results from non-equilibrium in temperature between the heat source and the radiating surface, as a result of the cooling effect of the radiative flux. The only absolute requirement is that the rate of arrival of energy on the earth must match the rate of its dissipation to space. In principle, it would be possible to dissipate the incoming radiation in various ways, with different consequences for surface temperature, as long as there the overall balance between absorbed radiation from sunlight and re-emission of this energy is achieved. From action resonance theory, different kinds of matter resort quanta into radiation of different frequencies. If less of the radiation from the earth’s surface was resonant with the greenhouse gases of the atmosphere there would be less greenhouse heating of the atmosphere. Adjusting the spectrum of the radiated emissions from the earth’s surface towards white, green or longer wavelengths in bands not resonant with materials in the atmosphere would be an advantage. This means that cooling of the surface needs to involve radiation from materials not found in the atmosphere. It might also be possible to harness some of the large energy sources available, at the same time modifying the spectra of emissions or directly benefiting from turbulence by harnessing its energy to drive versatile windmills able to store energy. Considerable attention has already been given to the physical role of heat energy in developing the entropy and action of water vapor from water (see Chapter 3), another cooling process involving the support of the configurational dynamics of the system by energy. Indeed, it was emphasised that the vaporisation of water is partly the same process (work against gravity) as global gravitational uplift, at least in the gaseous expansion phase. In principle, the uplift involves a differential increase in the radial separation of every molecule in the atmosphere, amounting to a global change in its quantum or action state. The obverse to this argument of global atmospheric uplift providing a strong buffer against temperature increase, is that the atmosphere will necessarily become more turbulent. The weather cycle has the potential to become much more violent if additional greenhouse gases are added, even if only equivalent to a one degree Kelvin increase in temperature under isobaric conditions. The global convection currents resulting will be

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significantly greater than at present because of the greater temperature gradients established and the system’s stronger need to transfer energy. It is anticipated that this greater turbulence will be exerted in aquatic and soil systems as well, leading to greater mobility of these structures. In these processes, energy can be regarded as a lubricant, even facilitating to some degree the uplift and lateral movement of these liquid and solid materials in ecosystems. 5.5.

Climatology and agricultural production

While the focus in this chapter has been on storms on the sun and on earth, it should be recognised that these events comprise their normal weather cycles. Weather plays a key role in the mass transport of matter and energy, speeding up their transfer compared to processes of molecular or radiative diffusion alone. Storms are nature’s response to chaotic conditions created by periodic injections of energy. No less than windmills for pumping water or storing electrical energy, dynamic storm cells represent coupling agents for work in ecosystems. They allow the mixing of air masses; the carriage of water vapour from oceans to land and mountains; the transfer of heat energy from low to high latitudes and vice versa, influenced by the Coriolis effect9 of the rotation of the earth; and the development of daily weather and seasonal climate. The problems of the enhanced greenhouse effect from emissions of polyatomic gases do not present any unique features not already part of the weather cycle. For example, the daily weather cycle - characterised by storms in the afternoon and evening can be predicted from the action resonance model. Solar energy is accumulated in the soil, water and atmosphere after sunrise. All molecular systems adjust their action states in response, expanding physical structures including the atmosphere. From true noon on, the intensity of radiation declines and the process of contraction of air, water and soil commences, inducing kinetic heating of molecules as they fall in action fields as a result of the emission of the quanta previously sustaining them. These processes induce storms, including the emission of lightning as discussed above. The dynamic cellular structure of the atmosphere is also part of this process of dissipating energy by generating action. Low and high pressure zones, cyclones and anticyclones, their direction of rotation by hemisphere and their paths on the earth’s surface are become explicable in terms of the action resonance model. Instead of employing empirical methods based on past experience, prediction could be made more reliable using the action model. A range of phenomena becomes amenable to study, including the development of the shapes of clouds themselves. Action resonance exchange forces would be expected to disperse condensing water droplets as resonant quanta are evolved, yielding the bubble-like cauliflower structures we see in convectocumulus clouds. Even the control of weather and climate may seem possible, when their action mechanisms are better understood. 9

The Coriolis effect is a result of the inertial effect of different speeds of rotation of the earth’s surface with varying latitude, generating an apparent force. The Coriolis effect emerges quite naturally as a direct physical consequence of the action resonance theory, providing a basis for the direction of circulation of air or ocean currents in different hemispheres and the motion of artillery shells or ballistic missiles.

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Other features of climate also seem more predictable, using action theory. For example, the onset of the monsoon (which the author experienced as a massive thunderstorm with downpour one memorable night after 2 am in December 1987, while touring with two of his sons near Katherine in Australia’s Northern Territory) can be more strongly linked to changes in the intensity of incident radiation. When the sun is sufficiently vertical in its daily transit, the elevation of the atmosphere will lead to a chaotic convective force causing uplift and cooling leading to precipitation of water and sustained rainfall, from an atmosphere well charged with water vapour. So the annual monsoon is not caused by the arrival of a general front of winds (as traditional geography maps often suggested) but is the result of the intensity of radiation at the boundary of a chaotic surface zone exceeding a necessary value. Only then will the action states of the atmospheric system have increased sufficiently to generate the monsoonal rains as a result of cooling uplift. Obviously, there will be relevance for agricultural ecosystems of new knowledge and a better explanatory model for the weather. Better prediction is essential for farming decisions such as when to plant particular crops and when to harvest. The el niño may now become understood as a zone of naturally uplifted and cooling dry air over the cooled south-eastern Pacific near Peru and a descending zone of dry, heating, air over south-east Asia and north-eastern Australia. It may also be possible to rationally reexamine some of the myths about rain-making and to re-analyse the data generated in extensive experiments by CSIRO in Australia, on the artificial seeding of clouds using nucleating agents such as silver iodide crystals. Could anecdotes related to the author such as the accidental burning of a large sugar-cane crop by “the kids” on a farm near Bundaberg, Queensland, followed an hour later by a torrential downpour, fortunately extinguishing the last of the fire, be found to have a scientific explanation other than coincidence. In other words, thermal events in the landscape should have a bearing on the weather. If so, landscape design might be undertaken in future on a global scale with respect to the location of farm-lands and forests, estimating and modifying the probability of rainfall by modifying the colour, texture and composition of the earth’s surface. Then chaos, understood as described in Chapter 4 as the precursor to more relaxed states of greater action and entropy, may be used to our advantage – just as demonstrated in generating the action of the Crookes radiometer.

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PHOTOSYNTHETIC ACTION - rH and rP

Adenosine triphosphate (ATP), found in all living cells, is known as the “energy currency of metabolism”. Its reversible cycle of synthesis and breakdown by hydrolysis and resynthesis of the phosphate groups in cells provides the energy and impulses needed to carry out all kinds of biological action.

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“But the (earthen) vessel had never received anything but rain water or distilled water, …….. In the end I dried the soil once more and got the same two hundred pounds (weight) that I started with, less about two ounces. Therefore, the one hundred sixty-four pounds of wood, bark and roots arose from the water alone." Van Helmont, Belgian physician and alchemist, concluding around 1600 that water must be the principle of vegetation, quoted in R.A. Dutcher and Dennis E. Haley, Introduction to Agricultural Biochemistry, John Wiley, New York, 1932

“All explanations of chemists must remain without fruit and useless because, even to the great leaders in physiology, carbonic acid, ammonia, acids and bases are sounds without meaning, words without sense, terms of an unknown language, which evoke no thought and no association.” Justus von Liebig (1840), the “Father of Agricultural Chemistry”, passionately promoting the theory of photosynthetic carbon dioxide assimilation from air, in support of the data of Theodore de Saussure (1804) and Jean Baptiste Boussingault (1830s). In Chemistry in Its Application to Agriculture and Physiology, Report to the British Association. The agricultural chemist J.H. Gilbert, one of Liebig’s former students, joined John Lawes at Rothamsted north of London in 1843 to begin a life-long collaboration on research at the Experiment Station, one of the first established and the oldest still in operation. .

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Chapter 6

PHOTOSYNTHETIC ACTION - rH and rP Storms in green plant cells Oxidation-reduction potentials and the rH value Biochemical phosphate transfer potential (rP) Action parameters and the life force

6.1.

Storms in green plant cells

Just a small fraction of the energy from the sun reaching the earth is absorbed by green plants and used directly to support their growth. Most of the solar energy is dissipated from heated vegetation, soil and water directly to the atmosphere, as described in Chapter 5. The light-absorbing green plants include all of the world’s food crops, such as the carbon-rich Gramineae – rice, wheat, barley and oats, maize, sorghum and sugar cane, as well as the nitrogen-rich Leguminosae – lentils, peas, peanuts, beans, soybeans, lupins, the pasture legumes such as lucerne, clovers and medics ņ and a cornucopia of fruits. Additionally, plants include the rich and far vaster array of the species of the world’s forests, grasslands and deserts – trees, ferns, creeping plants, succulent cacti, carnivorous insectivores and many thousands of other species including microscopic plants only the size of bacteria ņ far too diverse of nature to mention here. In all these living organisms, resonant impulses from light of wavelengths around 600-700 nanometres are absorbed by photosynthetic pigments such as chlorophyll contained within the cells of green plants. Indeed, wherever conditions of moisture, temperature and nutrients are even remotely favourable, the resilient green plants will be found growing, covering most of the terrestrial globe with the thinnest film of living vegetation, scarcely visible from space. Yet this fuzzy, fragile, layer is the very foundation of the earth’s biosphere, its ecosystems and its civilizations. 6.1.1. Action from photons, electrons and protons In this chapter, the utility of the action resonance theory will be illustrated by applying it at the scale of photochemistry and biochemistry. This will be done in the context of the organisation of basic driving forces existing in the living cells of green plants. This choice of green plants is justified by the relatively simple nutrients needed for plant growth, all simple inorganic substances in chemical nature, such as carbon dioxide, ammonia, water, metal cations such as potassium, magnesium, calcium and ferrous iron or anions such as nitrate and phosphate (Kennedy, 1992). Plants represent versatile living organisms, known as autotrophs, which are completely reliant on simple chemical substances found in their environment, derived from non-living processes. By comparison, the animal kingdom is made up of species always requiring some organic inputs derived from some other living species. Relevant basic statements regarding action resonance theory and plant growth are: •

The primary processes of photosynthesis involve the resonant absorption of quanta from sunlight, resulting in photochemical action as a result of the momentum and impulses of these quanta.

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How does sunlight elicit this remarkable response in plants? Part of the answer to this question is the fact that impulses from the quanta of these wavelengths or frequencies generate chaotic conditions but in the highly ordered environment of the light-harvesting apparatus. Just as for the photoelectric effect of quanta on metals, explained as a result of their particle-like nature by Einstein (1906), the impulses of these quanta displace electrons and protons from water in green plants, or from hydrogen sulphide in photosynthetic bacteria. Removing these particles is a remarkable chemical feat, particularly in the case of the dissociation of water, a molecule of great stability. Not only are electrons and protons separated from water, but the pairs of oxygen atoms also released1 join, forming the dioxygen (O2) of the atmosphere. This is a substance with special qualities2, essential for most life on earth. •

Action processes in photoelectron transport establish proton gradients in plant cells, providing thermodynamic gradients as exchange forces, able to force the synthesis of ATP. Together with chemically reduced compounds produced as a result of the photoelectron transport, the energy of sunlight is made available to synthesise bioorganic matter such as sugars, proteins and DNA essential for life. Thus, in the photosynthetic Calvin cycle described in any textbook on plant biochemistry, the electrons and protons released from the lysed water molecule are used in a process converting carbon dioxide derived from the atmosphere into sugars and fats - compounds much more electron rich and reduced than carbon dioxide

1

In present-day photosynthesis by green plants characteristic of most ecosystems on Earth, the remarkable reaction to the absorption of the impulse carried by photons is the lysis of the water molecule, yielding oxygen, protons and mobile electrons: ⇒ O2 + 4H+ + 4e(bio-photolysis) 2H2O + nhν The electrons (e ) released from the forceful lysis of water molecules do not exist as free species (except extremely transiently), but are bound to an organised sequence of biological electron carriers. Equally, the protons released into the cytoplasm are dynamically bound to water as H(H2O)n+. A similar reaction can be achieved in an electrolytic cell with an anode and a cathode, using a potential gradient derived from a battery or generator to provide impulses from quanta, achieving electrolysis of water (as a solution of a non-reactive salt such as Na2SO4) to hydrogen and oxygen gases: 2H2O + nhνi ⇒ O2(g) + 4H+ + 4e(anode electrode reaction) 4H2O + 4e ⇒ 2H2(g) + 4OH- + mhνj (cathode electrode reaction) In action theory, the linear momentum of a flow of electrons in a conducting material such as an electrical circuit must be matched by the net linear momentum of quanta or actons in the opposite direction (sinθΣhνi,/c =Σmev). Obviously, the number of electrons extracted from water and absorbed into the electrical circuit at the anode producing oxygen (O2) just balances those extracted from the circuit at the cathode producing hydrogen (H2). If the electrolyte solution containing the two electrodes is mixed, the H+ and OH- produced, which give red and blue colours respectively if litmus is added to the separated solutions, will neutralise each other to form water: 4H2O 4H+ + 4OH- ⇒ Thus, the sum of the reactions at the anode and cathode is: ⇒ O2 + 2H2 (electrolysis). 2H2O 2 Bonding in O2 is anomalous; the molecule is paramagnetic, containing two unpaired electrons indicating a single two-electron bond between the two atoms, although the high dissociation energy suggests the possibility of two additional three-electron bonds (Cotton and Wilkinson, 1962).

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itself. Carbon dioxide in the atmosphere represents the most oxidised form of carbon present in ecosystems. The main role of sunlight in photosynthesis, then, is to convert strongly oxidised carbon compounds, such as carbon dioxide (CO2), into reduced carbon compounds. It also converts oxidised nitrogen compounds (e.g. nitrate, NO3-, from soil or water and, more rarely, dinitrogen, N2, from the atmosphere) into more strongly reduced nitrogen compounds like ammonia, much more useful for life on earth. Reduced nitrogen compounds play key roles in the various organisms of ecosystems, as proteins or as nucleic acids. The various processes involved in making these more strongly reduced compounds are the subject matter of the discipline known as biochemistry, successfully established during the early to mid-part of the 20th century. In this book, we suggest that these biochemical processes may be considered as resulting from storms in cells, although a biochemist might rightly insist that these are very orderly storms, since their outcomes are rather predictable. Furthermore, storms in the atmosphere usually involve action exchange forces acting between stable molecules not involving chemical changes (although the reaction of nitrogen and oxygen gases caused by lightning provides a notable exception, Kennedy, 1992). Nevertheless, we will continue to claim that the main difference is one of scale and that photochemical reactions in green plant cells have the same general character of the storms in the earth’s atmosphere. In both cases, the forceful momentum of the impulses of energy from the sun is dissipated in performing work, rather than in simply raising the temperature. Furthermore, the biochemical pathways by which molecules essential for life are formed involve the lessening of the stresses set up by the energy-action field, just as in atmospheric storms. Far from being arranged in the neat columns and cycles seen in books on metabolic pathways, the molecules in living cells have to continuously run a gauntlet where they are buffeted to and fro in Brownian processes from one instant to the next. There is only a finite probability of arriving at a particular metabolic destination or even of continuing in the same pathway from one encounter with an enzyme molecule to the next. However, as will be discussed in more detail in Chapter 7, the information content of DNA expressed in green plants ensures that the probability of functional action is greatly increased. The outcomes of these chaotic processes, just like the processes in the atmosphere that generate all of the turning actions of the hydrological cycle - even turning the sails of the windmills of the Netherlands - are essential for the everyday action in ecosystems that constitutes the activity of the biosphere. In fact, the more fully reduced, electron rich, molecules generated by all photosynthetic organisms can be thought of as turning windmills, though on a truly ultra-microscopic scale. All of these reduced compounds act as windmills, requiring higher frequency field energy to generate the torques needed to sustain their molecular motion, as their electron clouds and nuclei spiral through space, than would be needed to sustain molecules of the compounds from which they are derived, carbon dioxide and water. The field energy that these molecular windmills exchange to sustain their torques, characteristic of the particular temperature, represents a store available in future to support other processes. Just how much energy as quanta is needed to fix each carbon dioxide molecule has been the subject of keen interest (Rabinowitch, 1956), a problem known as defining the quantum yield for each light photon absorbed. There is no doubt that the intensity of

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high frequency quanta is an important factor in initiating electron transport in photosynthesis. But action resonance theory also points out that high frequency quanta absorbed by plants are redistributed through interaction with molecules in living cells as quanta of much longer wavelength. These low frequency quanta are required to support the Brownian movement (translations and rotations) of molecules, organelles and all other structures in living tissue. This energy, which is part of the overall flux of quanta through green plants to the surrounding environment, is just as essential to metabolism and growth as the sunlight itself. It provides the dispersive impulses needed to set molecules in motion, cause cell division and growth. Indeed, without this energy field to support the action exchange process, structures in plants and the plant itself would collapse. 6.1.2. The photosynthetic reaction centre Spinach chloroplast Outer membrane

Stroma

Thylakoid disks and membranes

1 µm Fig. 6.1: Photoelectron transport and photophosphorylation by thylakoid membranes of chloroplasts. A transmission electron micrograph of a spinach chloroplast is shown. Quanta from sunlight raise the potential energy of electrons bound to photosynthetic pigments, dissociating them and allowing protons to be pumped across the membrane, setting up a pH gradient across the thylakoid membrane. The imbalance in action resonance exchange forces in the two fields of protons on either side of the membrane leads to the forceful pumping of protons in the channel of the ATP synthase enzyme embedded in the membrane.

From the point of view of action resonance theory, the photosynthetic reaction centre is considered as a zone where resonant impulses from quanta perform work on the electrons and the protons of the water molecule (Figure 6.1). Four electrons from pairs of water molecules are transferred in an orderly sequence to reducible molecular centres nearby, as well as dissociating four protons from the oxygen atoms to the surrounding solution. These processes involve transient increases in free energy and then more relaxed states of greater action and entropy of the electrons and protons involved. During the subsequent process of energy harvesting, electrons flow spontaneously through an ordered series of electron carriers - a process in which protons are pumped from the stroma of the chloroplast into the thylakoid space, setting up a gradient in pH across the membrane of the chloroplast with the stroma. To dissociate an electron from each carrier requires a quantum of energy to generate the action required to enable the transfer. At

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each subsequent binding of the electron, a quantum of energy greater than required to cause the previous dissociation is emitted, providing impetus and the possibility of chemical work in the molecular systems involved. In action theory, these dissociations of electrons and protons can be considered as quite similar in kind to the change in gravitational distribution of gases such as carbon dioxide in the atmosphere. In the latter case, rather than dissociating protons and electrons from a larger nucleus of oxygen, gas molecules are being dissociated from the much larger material body of the earth. In both cases a more or less transient process is set up in which the coherent systems of particles are driven by impulses from quanta to higher action states. In photoelectron transport in chloroplasts, as electrons dissociate and then re-associate with electron carriers, quanta of lower frequency and longer wavelength appear, potentially being utilised by resonant proteins or similar structures, or simply sustaining the action exchange field of the biological molecules. On withdrawal of the source of the quanta of sunlight, for both cases, the sets of coherent particles (molecules) will soon settle down in lower orbitals of less energy and action as the temperature falls. For the performance of work by phototrophs in ecosystems, some of this incident light will be absorbed by specific pigments, such as chlorophyll or other ancillary pigments, that act as antennae in the cells of photosynthetic organisms (see Zuber, 1987). In all phototrophs, these antennae consist of basic units of polypeptide-pigment complexes arranged in pairs, themselves arranged in larger, highly structured arrays promoting directional energy transfer (Zuber, 1987). It can be anticipated from action theory that correct analysis of the function of these asymmetric physical structures will reveal how energy can be directionally focussed and made resonant with key chemical processes in the reaction centres of chloroplasts. The hypothesis that the highly ordered arrays of pigments known as quantosomes in chloroplasts and in photosynthetic bacteria are concerned with excitation-energy migration has been extant for many years (see Rabinowitch, 1966). Mechanisms of resonance energy migration have been postulated in some theories of the primary photoprocess in photosynthesis. These pigments will be expected to have electrons in orbitals of least action, in their most stable or ground states. According to quantum theory, photons carry momentum as discussed in earlier chapters. Associated with the recoil on absorption of the momentum of photons by pigment molecules, electrons in the pigments are expected to be excited to higher action or quantum states (see the discussion on the Bohr hydrogen atom, in the Glossary/Endnotes). Such processes can be accelerated if the pigment arrays involve amplification of the quantum exchange forces, leading to the generation of larger scale motion or action in macromolecular assemblies in the thylakoid membranes. Electron microscopy sometimes indicates extensive rearrangement in the structure of the membranes of organelles such as chloroplasts and mitochondria, although these may be extensively modified by other forces exerted during fixation and staining processes. As also proposed in action resonance theory, the energy quanta must remain constantly active in the space of the action field between molecules and are actually required to temporarily sustain any elevated action states of the electrons. If sufficiently excited, the dissociated electron will then fall towards the next carrier as a ‘hole’ becomes available, thus constituting an electron current, simultaneously releasing quanta able to activate other processes.

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Electrical current is conventionally regarded as a unidirectional flow of electrons, usually in a metallic wire from the anode to the cathode in an electrical cell. In action theory, we may assume that the rate of change of momentum, accelerating the electron current in one direction, towards the cathode, is exactly matched by the rate of change of momentum of the flow of quanta in the opposite direction. Thus, electrolysis can also be regarded as a process forcefully driven by real energy quanta, as shown in the equation. The magnitude of these energy quanta and their specific rate of impulses or frequency will depend on the difference in the voltages applied to the anode and cathode. A vital difference between the bio-photolysis of water and its electrolysis in an electrical cell is the direct formation of H2 that occurs freely on the cathode surface when a sufficient voltage is applied - this is expressly forbidden in photoautotrophs. In biophotolysis, the protons and electrons produced by light are kept well separated in order that the quanta emitted during transfers involving motion to new quantum states for both the electrons and the protons can do important biological work. 6.2.

Oxidation-reduction potentials and the rH value

As indicated above, primary reactions of great importance in living organisms are the socalled oxidation-reduction or redox reactions. These reactions involve the spontaneous transfer of electrons from one electron-carrying substance to another. The relative strength with which an electron carrier tends to transfer an electron (to reduce) other oxidants is indicated by the electrode reduction potential for a hypothetical half reaction, relative to the hydrogen electrode, designated the electrode reduction potential (Eh, Morris, 1975). When electron carriers with different electron binding strength are brought together, electrons spontaneously flow towards the carriers which can bind them most strongly, releasing quanta which can do work. An alternative measure of the degree of non-equilibrium possible from each of the various oxidation-reduction reactions is given by the rH value, an index for reducing potential which naturally provides an action reference parameter (see Kennedy, 1992, 'Acid Soil and Acid Rain'). In effect, the rH value3 indicates the negative logarithm of the hydrogen gas pressure (in atmospheres) that would equilibrate an oxidation-reduction couple, preventing further reaction. The concept of rH is premised on the fact that all oxidation-reduction couples can be written in such a way that hydrogen gas is formed. Thus, the rH value provides a measure of the capacity of a chemical system to provide electron pressure by dissociation. In action theory, pressure results from the space density of quanta. The concept of rH was introduced early in the 20th century by the 3

rH In the reaction:

= -log(H2)eq ((H2)eq is atm hydrogen gas pressure producing equilibrium). NO2- + H2O NO3- + H2 Keq = {[NO3-](H2)}/{[NO2-][H2O]} Thus -log(H2) = -logKeq - log([NO2-]/[NO3-]) o rH = -logKeq where standard 1-molal concentrations of nitrite and nitrate are present (or any other concentration ratio of 1.0). Then rH = rHo - log([NO2-]/[NO3-]) = rHo - log([reductant]/[oxidant]).

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well-known electrochemist, Mansfield Clark, developer of the Clark oxygen electrode. He proposed it as a means of indicating oxidation-reduction intensity without the need to specify both electrode potential and pH. Clark was at the time a young chemist in the United States Department of Agriculture and was interested in assuring the quality of produce such as milk. Unfortunately, Clark later inexplicably cautioned against the use of rH, perhaps intimidated by the criticism of scientific colleagues, suggesting that it led to distorted redox potentials when compared to electrode reduction potential values (Eh). In retrospect, this was a triumph for the operational or academic approach over common-sense, for unlike the electrode reduction potential, rH provides a direct measure of the actual chemical redox state at an ecosite for each chemical redox system (Kennedy, 1992) and should have been preferred by a realist such as Clark. Electrode reduction potentials are derived from theoretical half reactions that involve a proton (H+) and free electrons. As a result, the estimated Eh values always need to be corrected to actual pH values at ecosites. In fact, they are operationally measured using a standard reference electrode set at pH 0. An opposing point of view, preferring primacy for field or real-world conditions, would logically conclude that it is the reduction potential (Eh) values used by chemists throughout the 20th century rather than the rH values that are distorted. Mansfield Clark’s retraction was a most unfortunate concession to instrumentalism and positivism. Indeed, environmental chemists who regard the ecosystem itself as the most appropriate monitoring site or laboratory are obliged to prefer the real world values for reduction potential of rH. Furthermore, electrode measurements inferring measurements of electron activity are usually very difficult to perform because of interfering electrode processes, even in the case of using highly purified solutions in the laboratory. Because of this practical difficulty, most tabulated oxidation-reduction (Eh) values have actually been calculated from thermodynamic data. The rH value, by contrast, is estimated not by using an electrode (although specific redox sensors that could be directly calibrated for rH values are possible) but from a knowledge of the relative concentrations of the products and reactants. The actual reducing potential of the current concentration ratio of reductants and oxidants for a particular redox reaction can be characterised by writing down a theoretical reaction producing hydrogen gas. Obviously, any ratio of concentrations of reductants and oxidants can be placed in equilibrium by a particular theoretical pressure of hydrogen gas. The negative logarithm of this hydrogen pressure is the rH value for the redox reaction. The greater the hydrogen pressure needed to theoretically achieve equilibrium, the more negative the rH. For comparing different chemical reactions, standard rHo values can be calculated for 1-molal concentrations (i.e. one mole of solute per kg of water) of reductants and oxidants. But the true strength of the rH value is giving a measure of the action exchange forces for chemical reduction that exists in ecosystems. From the equation for rH given in the previous footnote, as the ratio of reductant to oxidant increases the rH value becomes more negative. The hydrogen pressure that the chemical system can theoretically generate at equilibrium thus provides a universal standard for the redox potential allowing comparison with any other redox reaction. One can readily understand that the system producing the higher hydrogen pressure is the stronger reducing system. Indeed, one can estimate the chemical work potential for coupling the two redox systems merely by calculating the work possible in an expansion

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of hydrogen gas from the higher pressure indicated by the more negative rH value to the lower pressure, holding temperature constant. Such a system is preferred in this book on action potentials, since this more closely matches the concept of action presented in Chapter 2. Since the concept of the rH value suggests that a method to measure actual thermodynamic forces for chemical reduction can be found, it would be of great practical value if appropriate sensors could be prepared to allow measurement of the rH value for each chemical redox system in field situations. 6.2.1. Proton gradients and action exchange forces Protons are also released when electrons are transferred from reduced chemical compounds. This applies to all redox processes such as the photolysis of water, as well as in all oxidative metabolic reactions where electrons are dissociated from molecules. Once released, these protons are almost instantaneously bound to the flickering water clusters (Nemethy and Scheraga, 1962) found in cytoplasm. All reactions oxidising reduced carbon molecules4 involve electron transfers as well as the release of protons. Usually, electrons and protons are donated as pairs in reactions involving the enzyme cofactors based on nicotinamide adenine dinucleotides (NAD or NADPH) which accept two electrons; one proton from the substrate is bound to the reduced form of NAD or NADP (NADH or NADPH), with another proton freed to bind to water. In subsequent reactions, where reduced nicotinamide adenine dinucleotide (NADH or NADPH) are used as reducing agents, two protons including the one bound to water are also transferred back to the product organic products. However, the consumption of protons is often delayed, such as when reduced nicotinamide adenine dinucleotide (NADH or NADPH) is oxidised by the electron carriers of the respiratory chain of mitochondrial or microbial membranes. These electron carriers include flavins, quinones and cytochromes, similar to electron flows in photosynthetic electron transport shown in Figure 6.1. Here, intermediate electron carriers such as cytochromes can accept electrons without needing protons, dissociating the two flows of these particles. Most importantly, these protons are spontaneously transported to the opposite side of the lipid membrane to another compartment of lower pH value than that in which they were produced (see Figure 6.2). Further reactions associated with electron transport within the membrane result in additional proton pumping from the interior of the cytoplasm across the lipid membrane. This spontaneous vectorial metabolism (Mitchell, 1965) results in a clear separation of electrons and that of protons, developing a marked gradient of pH values across the membrane. This metabolic asymmetry has important consequences, generating the proton-motive force proposed by the Nobel laureate, Peter Mitchell (1965), to be responsible for the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and inorganic phosphate by ATP synthase (see also Greville, 1969). In fact, this process of bioenergetic phosphorylation can be claimed as one of the most significant in living systems. ATP, called the “energy currency of metabolism” 4

RCH2OH + NAD+ => RCHO + NADH + H+ + NADH + H + Protein-FAD => NAD+ + Protein-FADH2 => Protein-FADH2 + 2cytochrome[haem-Fe3+] => Protein-FAD + 2cytochrome[haem-Fe2+] + 2H.

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(Kornberg and Krebs, 1957), is ubiquitous in living cells, where it provides energy for a huge number of biochemical processes. In a unique sense, ATP is the essential ingredient for the performance of biological work in all living cells.

LOW pH

HIGH pH

Fig. 6.2: Concentrative transfer of protons and ATP synthesis across lipid membranes during electron transport in mitochondria or bacteria. Complex I (NADH dehydrogenase), Complex III (ubiquinone) and Complex IV (cytochromes c, b and a/a3) pump protons to the zone of low pH. The gradient in action resonance exchange forces is proposed to provide energy to ATP synthase for ATP synthesis from ADP and inorganic phosphate (adapted from Kennedy, 1992).

In fact this biological process of ATP formation by photophosphorylation or oxidative phosphorylation was seminal in leading the author to recognise the need for an theory involving real action forces. Certainly, Mitchell’s theory provided the formal thermodynamic basis for phosphorylation and the work of more recent Nobel Laureates, Boyer and Walker, describes the details of function of ATP synthase itself. But while formal thermodynamics can provide a mathematical description of the basis for the proton-motive force, expressing it in terms of the pH gradient and the membrane’s electrical potential, and the details of the action of ATP synthase are illuminating, neither experimental advance provides an explanatory physical mechanism for the power of a proton gradient to do work. This neglected area is the main unsolved problem related to the formation of ATP – what is the specific mechanism that allows a gradient in proton concentration to do work? We do not agree that statistical mechanics can explain this phenomenon or that an operational mathematical equation involving a concentration gradient plus a voltage gradient can provide an explanatory mechanism. Such an equation may describe and predict, but does not explain. How can a greater density of protons on one side of a lipid membrane compared to a much smaller density on the other drive a biochemical work process if protons must be transferred through the membrane one at a time? Greater probability of movement in one direction rather than the other can in no way provide an efficient cause for an isolated proton having the power to do work. On the other hand, a mechanism where protons cooperate and collectively provide an instantaneous force on each proton transferred may have the power to do the work required. It was this dilemma or logical crisis that perhaps more than anything provided the need to develop the theory given in this book. Once purely statistical arguments are considered as logically invalid to properly explain the energetics of ATP synthesis, what

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could the underlying nature of proton gradients be that allows DNA-based systems expressed in chloroplasts, bacteria and mitochondria to synthesise ATP?

Fig. 6.3: ATP synthase is an assembly of polypeptides (proteins) traversing the bilipid membrane of chloroplasts (thylakoid) and mitochondria in eukaryotic organisms and the cytoplasmic membrane in bacteria. The hexagonal α3β3γ complex has been shown to rotate non-randomly with respect to the F0 unit embedded in the membrane. A central pore in F0 accepts protons from the low pH (higher concentration) compartment, which are assumed in action resonance theory to provide the directed momentum and force needed to synthesise ATP, even under conditions a factor 1010 removed from equilibrium. Although the observed directed rotation of the head group has proved surprising to some biochemists, who see it as a rare example of nature using the principle of the wheel, in fact rotation is the most convenient means of natural motion, particularly in dense systems; Einstein included Brownian rotation in his theory (Kennedy, 1981) and Nicod (1923) showed how all translations of matter may be resolved geometrically into two or more rotations. Rotation is obviously central to action resonance theory since all forces are viewed as torques and all action developed is the simple product of torque x time. This implies that the wheel or rolling action is normal in nature and our preference in mathematics for depicting linear systems is an unfortunate abstraction.

The action resonance theory provides a possible solution. Protons can be accelerated during the passage through the ion channel of ATP synthase as a result of the gradient in action exchange forces5 across the membrane generated by differential quantum exchanges between protons. The quanta needed to sustain the dynamic processes of dissociation and binding of protons in water clusters must be far more dense on one side of the membrane than the other. Then the performance of chemical work can result from the transient changes in action state involved when a proton is allowed to make the transition from one compartment to another, discussed in Chapter 4. Quanta essential to 5

(H2O)n + H+
H(H2O)n+ + ΣhνI (H2O)m + H+
H(H2O)m+ + Σhνj ∆E = Σhνi - Σhνj H+ 1 => H+ 2.

Compartment 1 Compartment 2

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sustain the action exchange processes for each field of protons interact during this transition, yielding a net quantum of energy capable of doing work on the ATP synthase itself. One can consider that the associated impulses of these quanta directly provide the force driving the proton through the proton channel of the ATP synthase (see Figure 6.3). 6.2.2. Energy transduction by ATP synthase Chloroplasts, mitochondria and bacteria are said to use the free energy stored in the transmembrane proton gradient to manufacture ATP by the action of an enzyme bridging the membrane, ATP synthase. Studies on ATP synthase have shown it consists of a rotor-like portion (F0), consisting of 9-12 dual polypeptide helices that provide proton channels where they meet a stator polypeptide assembly. The stator protein also spans the membrane, including the characteristic head-like hexameric assembly (F1) that protudes into the interior of the stroma or cytoplasm bearing the catalytic sites on which ATP is synthesised from the dehydration of the reacting ADP and inorganic phosphate (see Figure 6.4). ADP+Pi

ADP+Pi

L O

Proton Flux

ATP

O

1

H 2O

ATP

T

L T

ATP

ADP+Pi

T

ATP

L

2

T O

ATP

L

O

3

Fig. 6.4: Energy transduction in ATP synthase by Boyer’s binding-change mechanism (Stryer, 1988). The three catalytic sites cycle through three conformational states open (O), loose (L) and tight (T)-binding. Proton flux drives the changes in state. Energy from the protonmotive force described in the text is utilised primarily for the dissociation of ATP from its tight association with ATP synthase. In action resonance theory, this dissociation into a molecular field of high ATP concentration is driven by resonant quanta released from the difference in chemical potential of protons across the membrane, then interacting with the ATP synthase. In terms of the action resonance exchange forces involved, this would be analogous to the dissociation of electrons from a nucleus or the elevation of carbon dioxide or water molecules in the atmosphere from the surface of the earth.

Without considering here in detail the mechanism of rotation of the ATP synthase in the membrane (recall the windmills of the Netherlands), the thermodynamic force that generates a torque on this rotating assembly may be assisted by the gradient in electrochemical potential provided by the charge separation existing across the membrane. The protonic action field, exerting impulses providing a torque on the interacting assembly of protons and polypeptides, exists as a result of this gradient. Thus, the asymmetry of exchange forces in the action field is utilised to do biochemical work with an appropriate coupling agent, the ATP synthase. Whether this solution to the problem of ATP synthesis using action exchange forces to exploit a proton gradient will withstand experimental testing remains to be seen.

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6.3.

Biochemical phosphate transfer potential (rP)

A second non-equilibrium action parameter suited to characterising living cells is the rP value, indicating the phosphorylation potential. The rP is indicative of the degree of chemical work potential available, resulting from strong phosphorylation of ADP to form extremely high non-equilibrium concentrations of ATP within healthy living cells. The rP value6 indicates the negative logarithm of the inorganic phosphate concentration in cells that would bring the ATPase reaction (see footnote 6) into equilibrium. For a desirable, strongly negative, rP value to exist within a cell, chemical systems with strongly-reducing rH7 values generating strong pH gradients must be made continuously 6 The concept of rP, introduced by the British biochemist, Dixon (1949), follows from the equation for the equilibrium constant (K’) for the ATPase reaction: ATP + H2O ADP + Pi Such a biochemical reaction if uncoupled to other work processes would simply produce heat, since the enthalpy of the products is less than that of the reactants. However, the overall hydrolysis of ATP in living cells is normally coupled to other action processes. Considering the reaction in isolation for the time being, the equilibrium constant for the reaction (K') can be written: K' = [ADP][Pi]/[ATP] = 105 ; (K' for typical cytoplasmic [Mg2+]=10-2M and pH=7) Thus -log[Pi] = -logK' - log([ATP]/[ADP] We define rP = pK' - log([ATP]/[ADP]) In aerobic cells where ATP is synthesised by mitochondria, the ratio of [ATP]/[ADP] has been observed to be as high as 103. Then, rP = -5 - 3 = -8 for these conditions. 7 Calculation of Keq and rHo values Keq values may be calculated from the thermodynamic relationship: ∆Go = -RTlnKeq = -2.303RTlogKeq logKeq = -∆Go2.303RT = rHo ∆Go is calculated from tables of standard free energies of formation (∆Gof) of the reactants and products: ∆Go = Σ∆Gof (products) - Σ∆Gof (reactants) In an ecosystem, the concentrations of oxidants and reductants will not be 1-molal - nor will their ratio often be 1.0. But the actual rH value is readily calculated when concentrations are known: rH = rHo - log([red(s)]r/[ox(s)]o) The greater the ratio of reductant(s) to oxidant(s), the more negative the rH value. An rH value can then be calculated for any desired set of reductants and oxidants for which a reaction evolving one hydrogen molecule can be written. Comparisons of these values indicate those reactions that can usefully be coupled through electron transport systems containing electron carriers such as cytochromes and quinones; these coupled reactions can provide chemical work potential (-ve ∆G) for ATP synthesis and cell biosynthesis.

∆G = -2.303RT∆rH

(∆rH = rH(oxidising reaction) -rH(reducing reaction))

The usual means of calculating chemical work potential (Gibbs free energy) is by using the redox potentials (Eh in volts) for the two coupled electron transfer reactions (see Morris, J.G. - 'A Biologist's Physical Chemistry'). Then ∆G = -nF∆Eh. The Eh and rH values are mathematically related, but the rH value is recommended for environmental chemistry because it can indicate directly without the need for pH corrections the reducing potential that occurs at a specific ecosite. For reactions that do not involve the production or consumption of protons, the rH value does not change with pH in contrast to redox potentials given in volts. In fact, rH is particularly suited for dealing with reactions that involve the production or consumption of protons, thus changing the pH of an ecosite. Here the effect of pH on rH value is given by the equation: rH = rHo - log([red(s)]r/[ox(s)]o) -∆npH

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available to generate these negative rP values. The transient rP value resulting in cells will determine the current capacity for cell division in growing plant tissues, the power of plant root cells to accumulate nutrient ions such as nitrate and phosphate from the soil solution, and many other ATP-driven processes such as nucleic acid and protein synthesis. The value of the rP parameter is no less applicable to animal cells, where we must include other ATP-driven processes such as the capacity of muscle cells to contract and the transmission of nervous impulses and human thought itself. In some organisms that rely on substrate-level phosphorylation (anaerobic fermenters), the non-equilibrium ATP concentration is maintained by kinase reactions such as PEP kinase, butyrate kinase or acetate kinase. However, in the photoautotrophs such as green plants, chemoautotrophic bacteria using reduced inorganic substances as electron donors with oxygen as a terminal electron acceptor, anaerobic respirers using nitrate and sulphate as terminal electron acceptors and aerobic respirers (Kennedy, 1992), ATP is synthesised by ATP synthase. The activity of this enzyme is thermodynamically driven by proton gradients maintained across membranes by various proton-translocating electron transport reactions. The ability to perform photophosphorylation or oxidative phosphorylation depends on non-equilibrium reducing and oxidising reactions being coupled by electron transport systems. Whether a non-equilibrium coupling is possible and how many ATP molecules may be synthesised by the coupled system can be determined from the respective rH values. A strong rP of -8 would indicate that an impossibly high theoretical concentration of inorganic phosphate (Pi) of 108M would be required to place the ATPase system in an equilibrium state. If such a high concentration was actually realised, ATP could do no biochemical work and no processes such as various biosyntheses or uptake of ions against a concentration gradient would be possible. But the actual inorganic phosphate concentration is normally about 10 mM, a factor of 10 billion (1010) less. As indicated in the equation for rP given in the footnote the larger the ratio [ATP]/[ADP] the more negative the rP value. On the other hand, an rP value of +2 (indicating an equilibrating concentration of inorganic phosphate of 10-2M (also the actual [Pi]), the ratio of [ATP]/[ADP] would be 10-7 rather than 103, 10 billion times less. Here, the biochemical system would be at equilibrium, with no biochemical work using ATP possible. Such a cell would effectively be metabolically dead and no chemical or physical action would be possible. In active living cells, ATP is synthesised steadily and rapidly enough that nonequilibrium concentrations of ATP, ADP and Pi can coexist continuously. Direct ATPase activity is absent and the rate of utilisation of ATP to perform biochemical work is just equal to its rate of production. Under such non-equilibrium thermodynamic conditions, the theoretical chemical work potential per mole (Gibbs free energy)8 for phosphorylation The more alkaline the pH, the more negative the rH value. In reactions where protons are consumed, the opposite is true (∆n is the number of protons produced for each H2 evolved in the reaction; r and o the respective number of reductant and oxidant molecules). 8 ∆G = -2.303RTlog1010 = -23.03RT = -57.1 kJ mol-1 ∆G = -2.303RTlog([Pi]equil/[Pi]actual) = -2.303RT(rP - log[Pi]actual).

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by ATP is –57.1 kJ per mole or 9.5 x 10-13 ergs per molecule, 15.3 times greater than the translational kinetic energy of 6.2 x 10-14 ergs for each ATP molecule. This indicates the thermodynamic work performed by ATP synthase in synthesising a molecule of ATP under these conditions. This value also equals the amount of biochemical work that can be performed by using one molecule of ATP yielding ADP and inorganic phosphate. This means that, under these conditions of the system, the total field energy requirement for each ATP (and water) molecule to generate a torque equivalent to 1.5kT is much greater than that for sustaining ADP and Pi at the same torque or temperature, yielding this quantum of energy when one molecule of ATP is converted to ADP and Pi at at rP value of -8. Note carefully that the rP value is not the negative logarithm of the actual [Pi] but that of a theoretically equilibrating concentration of [Pi] for the ATPase reaction at the prevailing concentration ratio of ATP and ADP. Thus rP, like rH, is a propensity, referring only to a theoretical concentration that does not normally exist. Compared with the actual concentration of this product, the work potential per mole available for actions such as biosyntheses or for transport across membranes against concentration gradients can be calculated from these two values. The work possible in a system with an rP value of -8 can be thought of as the maximum work possible for a 10 billion-fold expansion of a mole of molecules of inorganic phosphate from a concentration of 108M to 10-2M, considered as an ideal gas. Such an expansion can be imagined to be promoted at a catalytic site of any enzyme utilising ATP, considering the equivalent chemical potential of the product of ATP hydrolysis (Pi) as a transition state product, compared to the chemical potential of the product in the bulk solution. In fact, no such expansion occurs but the associated action exchange potential is made available in all the chemical reactions which rely on the huge gap from equilibrium of ATP and water and the hydrolysis products of ADP and inorganic phosphate for their thermodynamic driving potential. This action potential resulting from the far-from-equilibrium ratio of ATP and ADP in living cells is the most important and ubiquitous in ecosystems. It provides the driving force for the majority of the biosynthetic reactions, e.g. those producing sugars, proteins, DNA and RNA, reduction of N2 and so on, as well as the motive force for work processes such as muscle contraction and secretions of hormones. 6.3.1. Boundaries and interfaces Boundaries and interfaces have special significance for the performance of biological work for at these locations there are often gradients in action potential. The membranes in chloroplasts, mitochondria and microbial cells provide excellent examples of sites where sharp gradients in the concentration of active species (such as protons) may occur and where work processes may be more rapid. By comparison, a uniform zone or region even with extremely high concentrations of active species, must be relatively quiescent. In such cases, the microscopic forces balance and the molecular force fields exhibit symmetry, negating action. Apart from gradients generated in membrane-bound systems, macromolecules such as enzymes may also introduce similar asymmetry into molecular fields. These catalysts effectively create field conditions for reactants and products allowing work by the molecular action field on individual molecules approaching the active centre of the

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enzyme to be performed as a result of screening or focusing of the energy field. Equally, work may be done as the result of forming energised enzymic products in the catalytic centre, compared to a need for less field energy when the product is transferred to the action field at large. This may even be decisive in catalysis, providing a significant part of the activation energy required. But this is not the place to discuss the action theory of enzyme catalysis. 6.3.2. Biochemical work and growth Consequently, the rP value, directly indicating the magnitude of the non-equilibrium action potential for work provided by the ATP/ADP system, is of utmost importance as an endogenous factor in living organisms. Other indicators of phosphorylation potential, such as “energy charge” (Atkinson, 1977), are mathematical and lack such a physically logical foundation. For the rP value like the rH value is directly indicative of thermodynamic mechanism and directly indicates the quantum of energy actually available to perform work. The antilogarithm of its value is the ratio of the action in the non-equilibrium and the equilibrium states . 6.4.

Action parameters and the life force

The theme of this and the previous chapter has been the power of impulses from cooperating actons or quanta to generate action on the sun, in the earth’s atmosphere and in green plant cells. An emphasis has been placed on the role of resonance between molecules in amplifying energy-momentum, generating action. The non-equilibrium steady state or the transient equilibrium was recognised as the outcome of changing action potential, varying as the intensity of radiation varies from dawn to evening and from one season to the next. The action parameters rH and rP mentioned above will become progressively more negative in photosynthetic cells as the intensity of the radiation storm increases, and the coupling agents respond. Through metabolism, molecular systems on earth will also respond by continuous readjustment in the position of equilibrium of the processes as a result of the expression of least action. The position of equilibrium varies because it represents the position of balancing of the forces, and since the solar force at any point on earth varies from one instant to the next, the position of balance of these forces varies from one instant to the next. In Chapters 5 and 6 we have discussed two major processes on earth that illustrate this phenomenon. These are the meteorological dynamics of the earth’s atmosphere with its associated hydrological cycle and the process of photosynthesis in the cells of green plants and some bacteria. In the atmosphere, the daily and seasonal cycles can be seen as imposing either gradually increasing or decreasing forces on molecules and molecular systems of the air. Each day, as the intensity of solar radiation rises and the earth’s surface warms, the exchange forces of action resonance will cumulatively rise, originating at low altitude and diffusing upwards. The action exchange forces first cause greenhouse and then other gases to disperse, expanding both vertically (while cooling) and laterally, seeking the current position of equilibrium and action that would allow balancing of these intermolecular forces with gravitational forces acting downwards. In fact, balance can never be achieved. At the moment the intensity of solar radiation passes its maximum as

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the position of the sun passes the meridian of longitude, the action exchange forces emitted from the surface of the earth will still increase for some time, as the emission of heat converted from light reaches its maximum. Only when this emission from the earth’s surface has commenced to decline, some time later, will the action resonance forces in the atmosphere decline. However, when this decline occurs, the expansion of the atmosphere will be reversed and the air will now commence to fall towards the surface once more, reaching its minimum at some point in the early morning near sunrise. The same cycle is repeated day after day, with either an increasing or a decreasing maximum of action resonance, with the extent of the daily lift of the atmosphere reflecting this. Each day from the winter solstice, the maximum radiation and action resonance will increase and from a day soon after the solstice the degree of atmospheric lift will reach its minimum and the night fall its minimum. Thereafter, the maximum lift and action each day will increase, reaching a maximum soon after the summer solstice. Photosynthesis within plant cells pits solar radiation and the action resonance exchange forces it causes within the molecules of green cells against the resonant forces binding the electrons of pigments in their orbitals. The impulses of photons of specific resonant frequencies are capable of lifting these electrons clear of their binding nuclei to the point at which they dissociate and then re-associate in the screened zones or shadows of neighbouring nuclei, emitting energy as they fall into new orbitals. In principle, these processes do not differ from those mentioned above for the uplift or fall of whole molecules in the atmosphere. This forceful flow of electrons by elevation from one nucleus to the next is linked to chemical changes involving protons resulting in their forced pumping from one side of a biomembrane to another. Subsequently, carbon dioxide is fixed into organic molecules and macromolecules, using the reducing potential and phosphorylation potentials generated in the energetic phase of photosynthesis. The sizes of the quanta concerned in the action exchange forces in photosynthesis are sufficient to cause chemical rearrangements and the synthesis of new, reduced compounds of high energy content, unlike the rearrangements of the meteorological cycle which mainly involve spatial rearrangements of the existing molecules in air. But while there is a difference in the scale and the degree of chemical change in both these action processes, the nature of the underlying action exchange forces involved is the same. In one case we are concerned at the scale of more or less coherent bodies of associated molecules in air whose action is governed by the exchange forces exerted between stable molecules interacting with gravitational forces; in the other we are concerned with exchange forces exerted between atoms in molecules with the exchange forces generated by catalytic macromolecules in living cells. In a real sense, each of these different kinds of processes contributes to the forces which drive life, but the same kind of force is exerted in all living and non-living matter. In the next chapter we shall examine how the action exchange forces of life systems differ from those exerted within inanimate matter such as earth and rocks, water and oil, fire and air.

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THE GENOTYPE-ENVIRONMENT INTERACTION

Electron micrograph of lupin nodule showing symbiosis between plant and bacteria. The genotype x environment can result in complex associations between different species of organisms, sometimes very intimate indeed, as shown in this electron micrograph (ca. x2000) of a section of a lupin (Lupinus luteus) nodule cell prepared by the author, each cell bounded by cell walls (CW), containing thousands of Bradyrhizobium lupini bacteria (B) only about 3 µm in length in plant cells about 30-40 µm across (containing nuclei (N), mitochondria near the air spaces (AS) and vacuoles (V)). These genetically distinct organisms support one another in a symbiotic association, in which the plants provide photosynthate as organic acids such as succinate and malate to the bacteria and the N2-fixing bacteria provide ammonia in exchange to the plant cell. Considering that most of the world’s legume plants are nodulated and that about 0.5% of the fresh weight of the plant may be bacteria, such rhizobial cells may be the most widely occurring genus of bacteria on earth, probably totalling many millions of tonnes of cells. Yet, as this chapter affirms, even for prey-predator relationships, the action theory suggests that mutually beneficial symbiosis may be a much more useful way to characterise the overall biological diversity of ecosystems rather than fierce competition. Such a conclusion has profound implications for the theory of evolution.

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“The process (of evolution of species) must have been directed by an orderly innovating principle, the action of which could only have been released by the random effects of molecular agitations and photons coming from outside, and the operation of which can only be sustained by a favourable environment”. Michael Polanyi quoted by E.W. Tomlin (1977) in the Encyclopedia of Ignorance, R. Duncan and M. Weston-Smith, eds., Pergamon Press, Oxford UK.

“You expressed quite correctly my views where you said I had intentionally left the question of the Origin of Life uncanvassed as being altogether ultra vires in the present state of knowledge”. Charles Darwin quoted in Evolution from Molecules to Men edited by D.S. Bendall, Cambridge University Press, 1983, p. 178.

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Chapter 7

THE

GENOTYPE

x

ENVIRONMENT

INTERACTION Action processes define microbes, plants and animals Life processes - carbon, nitrogen and mineral nutrition Symbiotic interactions Chance and necessity – selfish genes forced to be altruistic Order from chaos Productivity in natural and agricultural ecosystems A cautionary note The origin of life 7.1.

Action processes define microbes, plants and animals

Living organisms are classified and defined by their physical form and how they reproduce, but also by what they do. We recognise that their capacity for action in ecosystems depends on their physical form and resultant capabilities. As a result of its adaptation to the ecosystem, we can usually conclude that each species performs a different identifiable role. This is usually regarded as being driven by self-interest and mainly contributing to the survival of each species, but also on occasion, as argued in this chapter, for the common good in ecosystems. How are these very convenient outcomes achieved, and is our ability to identify such roles evidence for a master design in ecosystems? The specific modes of action of each species are of prime interest, for these define their role in a living community. What decides the modes of action in the life of each species? Indeed, what is the essence of life itself? One remarkable response to this question was that of Schrödinger (1944), in his short but fascinating book, What is Life?, first read by the author some 40 years ago. His answer was that a characteristic feature of living organisms is their capacity “to feed on negative entropy”. He might equally as well have said “to feed on free energy”. We saw in the discussion on the second law in Chapter 4 that this amounts to a process where the amount of radiant energy contained in a system or its surroundings is spontaneously increased, although at action states of higher potential energy where fluctuations involve quanta of lower characteristic frequencies. It is true that this capacity to consume free energy is a key feature of living organisms, but as Karl Popper (1976) commented, this characteristic holds equally well for any steam engine, which we certainly do not consider to be living. In any case, the exact meaning of the thermodynamic concept of entropy remained a mystery for most, let alone negative entropy. In Chapters 3 and 4 we showed how entropy as a function of action has a positive role in life systems, since ecosystems must have an entropy content well above that at absolute zero to function at all. Many of the key functions of life systems have been shown in earlier chapters to directly involve increasing entropy and action and the notion of inevitably increasing entropy, considered always as increasing disorder, is

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grossly misleading. Living organisms must reach an optimum range of entropy content to function effectively and they and the ecosystems in which they function must remain in this range to be considered sustainable. Nevertheless, sources of negative entropy or free energy are also essential because it is the very process of converting free energy into entropy that is integral to life. Fortunately, this paradox regarding entropy can easily be clarified by the application of action resonance theory. Obviously, the entropy of life systems cannot increase without limit because the information stored in molecules that is essential for life would be lost. However, such unrestricted increase in entropy is not normally possible on earth because of the limited rate of supply of energy to the biosphere and its inevitable subsequent reemission to space. Under these constraints, only a certain quantity of energy will be resident in the biosphere, sustaining an amount of action characteristic of the temperature. Still, we can recognise the results of unrestricted increase of energy in local catastrophes such as wildfire, thermonuclear explosions or other events on a cosmological scale. Schrödinger’s use of the verb to feed is rather apt and, using the action thermodynamics outlined in Chapters 3 and 4, the meaning of negative entropy or free energy in life should be more obvious. Molecular or matter-energy systems on which living organisms feed, when rearranging in order to reduce stress or chaos on a microscopic scale, have a large capacity to make energy from the action field available as quanta: this energy provides the streams of impulses or actons needed to cause the action, movement and entropy we associate with life. As we emphasised in Chapters 5 and 6, sunlight has the primary role in initiating and sustaining this action on earth. By temporarily causing chaotic conditions of higher free energy before relaxing to states of higher entropy, sunlight can somewhat enigmatically be considered as a pure stream of negative entropy. 7.1.1. DNA as a source of information in ecosystems Perhaps more importantly, Schrödinger’s book also discussed the concept of “the hereditary code-script”. There is no doubt that he considered this to be an equally essential feature of life – one that clearly excludes the steam engine as a living organism. It is remarkable that his book was written well before the three-dimensional helical structure of deoxyribonucleic acid or DNA (Figure 7.1) had been revealed from the x-ray crystallographic data of Rosalind Franklin and M. Wilkins by F.H.C. Crick and J.D. Watson at Cambridge University in 1953. This was even before it was certain that DNA specified hereditary characters, by the use of a code involving the sequence of the chemical bases, adenine (A), guanine (G), cytosine (C), and thymine (T) to generate information, which is translated in RNA to uracil (U), cystosine (C ), adenine (A) and guanine (G) coding for particular amino acids (Figure 7.2). Importantly for the development of Watson and Crick’s theoretical model DNA, E. Chargaff of Columbia University had shown that there were equal amounts of adenine and thymine and of guanine and cytosine in living cells. The triplet base code that provides a highly reliable means of selecting from the score or so different amino acids to be used in protein biosynthesis was deciphered experimentally by Nirenberg (1963) and his associates in the early 1960s. Together with the “stream of negative entropy” that preserves living organisms from disintegration, this hereditary code transmitting the capacity for specific

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modes of action from one generation to the next should be considered as an equally important part of Schrödinger’s definition of the uniqueness of living organisms. Schrödinger’s prescription that life needs both a stream of negative entropy and a code-script acting in complementary roles emerges with even more clarity when interpreted in terms of action exchange forces. The informational content of DNA is completely reliant on energy flow in order to be expressed. DNA at or near the absolute zero of temperature has little or no influence on its surroundings since no forces can be exerted to cause changes in action states. A temperature at least 273oK warmer is required for its normal function. Conversely, DNA will only express nonsense rather than information if the optimum temperature range is exceeded and too much action exchange occurs. DNA usually responds physically to too high a temperature by denaturation, in which the double-stranded helix (Figure 7.1) becomes unravelled, so great are the exchange forces between the complementary bases when there is too great an energy content. However, as long as the genotype x environment interaction can be expressed within the correct temperature range, the hereditary code as a source of information can act. It would appear that the simple prescription by Shannon (1949) for expressing entropy as the negative logarithmic function of the information content of a message proves inadequate for biological systems.

Fig. 7.1: Molecular models of the double helix of deoxyribonucleic acid (DNA). The stick model on the left (prepared by N.K. Matheson) shows the white parallel H-bonding of nucleic acid bases in the interior with the sugar-phosphate helices on which the bases are suspended; the alternate space-filling model of DNA photographed on the right approximates to

the van der Waals volumes occupied by the mobile electrons and nucleons of the H, C, N, O and P atoms making up its polyymeric structure. The two models shown typify the emptiness of the molecular structure as sensed by radiant energy and the solidness sensed by interaction with other molecules. Both descriptions are needed to describe the properties of DNA.

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A medium for transmission of the message is also essential, as the Canadian critic Marshall McLuhan sought to point out with his statement that for television, the medium is the message. However, provided it has the opportunity to operate within its correct environmental range, DNA can directly impose the order that we recognise as the specific modes of action for each species, physically and chemically guiding the stream of negative entropy as it does work. In action theory, the code establishes a forceful relationship and interaction between quantum effects, inheritance and evolution. The information contained in the code determines that specific sequences of amino acids will be forcefully selected in the biosynthesis of gene products, rather than amino acids simply being selected randomly. That is, information restricts the range of choices and randomness, leading to a more purposeful result. By this means the concept of the gene, originally formulated from a study published in 1866 on the inheritance of phenotypic characters in garden peas (such as shape and colour) by the Augustinian monk, Gregor Mendel (see Peters, 1959), was able to be incorporated into modern science as the determinant for the mechanism of natural selection. 1st (5’) U=A

C≡ ≡G

A=T

G≡ ≡C

2nd

U=A

Phenylalanine Phe Leucine Leu Leu Leu Leu Leu Isoleucine Ileu Ileu Methionine Valine Val Val Val

C≡ ≡G Serine Ser Ser Ser Proline Pro Pro Pro Threonine Thr Thr Thr Alanine Ala Ala Ala

A=T Tyrosine Tyr Stop Stop Histidine His Glutamine Gln Asparagine Asn Lysine Lys Aspartate Asp Glutamate Glu

G≡ ≡C Cysteine Cys Stop Tryptophan Arginine Arg Arg Arg Serine Ser Arg Arg Glycine Gly Gly Gly

3rd (3’) U=A C≡ ≡G A=T G≡ ≡C U=A C≡ ≡G A=T G≡ ≡C U=A C≡ ≡G A=T G≡ ≡C U=A C≡ ≡G A=T G≡ ≡C

Fig. 7.2: The genetic triplet code in RNA and DNA for protein synthesis by specifying amino acid sequences (modified from Patterson, 1978). A sequence of 18 bases in RNA of AUGGGUGAUCCCUUUUAA will transcribe or synthesise a short tetra-peptide made up of four amino acids as Gly-Asp-Pro-Phe whereas most proteins have 100-1000 amino acids or more and genes specifying them at least 306 - 3006 bases long. This would correspond to translation of information stored in DNA as TACCCACTAGGGAAAATT. Bases uracil (letter U), cytosine (C ), adenine (A) and guanine (G) occurring in RNA provide 61 codons selecting 21 amino acids (eg. UUU tr. Phe, GAA tr. Glu) and three stop codons. The complementary bases in DNA (A, G, thymine T, C) are shown second, with the number of hydrogen bonds possible indicated. In DNA, G≡C and A=T bonds have three and two hydrogen bonds respectively. Action resonance theory predicts that analysis will show this complementary bonding results from screening effects and that selection of amino acids will employ similar means. Note that redundancy occurs where the third letter does not affect the amino acid selected (e.g. UC, Serine; CU, Leucine; CC, Proline; CG, Arginine; AC, Threonine; GU, Valine; GC, Alanine; GG, Glycine). AUG is part of the initiation signal for protein synthesis as well as coding for internal methionines.

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Mendel’s great achievement was to recognise that the inheritance of these characters could be understood if characters were inherited in normal cells as duplicates, with one dominant gene (A) and the other recessive (a), which segregated in germ cells and recombined in progeny. Thus, four kinds of combinations were possible (AA, Aa, aA and aa). The pollen or egg cell of the peas carried only one form (A or a) but segregation could result in a 3:1 ratio since all individuals carrying A would express the dominant character. The results of plant and animal breeding ever since have confirmed Mendel’s interpretation, although more complex characters may not be inherited in this simple way. The active role of genes as sources of information and non-randomness is even more obvious when we recognise the role of action exchange forces in transcribing and translating the message that genes contain. In one sense, the individual bits of information carried by the code in DNA do not represent any new principle of chemistry. It was pointed out in Chapter 2 that all molecules carry some information, although asymmetrical ones carry more. All molecules consisting of dense particles that are able to redistribute the impulses from energy in the action field are informative. Asymmetric molecules will redistribute action exchange forces in a non-random fashion. The more complex the molecule the greater will be this effect on the action field. But DNA has a special property in that its hereditary function stores information as three-dimensional “software” that can be remembered in a coherent fashion from one generation to the next. 7.1.2. Genes specify coupling agents But what are the essential features that the code-script of DNA specifies about life? Part of the answer, a key theme of Action in Ecosystems, is that genes made of DNA provide information that specify the synthesis of cell-specific coupling agents that guide the generation of action by matter-energy. The coupling agents, acting as the biological mechanisms (Kennedy, 1984) by which sources of negative entropy can benefit organisms, are essential “hardware” in all living species. Every cell must contain a complementary set of coupling agents which directs the dynamic flows and rearrangements of molecules in the ongoing action known as metabolism. This process provides the subject matter of the discipline we know as biochemistry. However, this discipline is commonly presented as a catalogue of two-dimensional maps of connected metabolic pathways illustrating inter-conversions of molecules (see the Krebs tricarboxylic acid (TCA) cycle in Figure 7.3). These maps represent the static chemical structures of biochemical intermediates and indicate the locations for catalytic role of the bio-polymers or proteins known as enzymes, that can speed up the flows of molecules through the metabolic pathways, facilitating the conversion of negative entropy into entropy or action. Every step of the TCA cycle requires the operation of a specific coupling agent or enzyme, synthesised as the product of a specific gene. The Krebs TCA cycle performs a dual role in metabolism. First, it oxidises pyruvate to three molecules of carbon dioxide (CO2) and, once the five equivalents of reducing potential (10H) released in the cycle have been passed on to oxygen, forming water. It also carries out a biosynthetic role, since two of its intermediates, 2-oxoglutarate and oxaloacetate, are important precursors for the synthesis of the amino acids, glutamate and aspartate respectively.

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Fig. 7.3: The Krebs tricarboxylic (citric acid) acid cycle needs coupling agents known as enzymes to catalyse all the reactions shown. Pyruvate, the end-product of the glycolytic pathway from glucose, is converted to acetyl-CoA and then completely oxidised in the TCA cycle, requiring two protons and two water molecules and yielding two more carbon dioxide (CO2) molecules per turn of the cycle plus 10[H] (= 10 electrons + 10H+) as reductant from each pyruvate molecule. This reductant is then passed to oxygen (see Chapter 6, Fig. 6.2) via an electron tramsport system associated with membranes, forming water and 14 ATP molecules from ADP + orthophosphate (Pi). The 4-aminobutyrate/succinic semialdehyde bypasses also shown provide alternative metabolic routes used in specialised tissues such as the brain of mammals or in legume nodules (Kennedy, 1992). Succinic semialdehyde is perhaps the strongest organic reductant known in metabolism with a highly negative rH value easily capable of reducing hard-to-reduce electron carriers such as ferredoxin needed in biological nitrogen fixation. Realising the cyclic nature of such metabolism was Sir Hans Krebs’ greatest achievement (although his first attempt to publish this idea was rejected), but we now recognise that all metabolism must have a cyclical nature when it is considered as part of the normal function of ecosystems. Nature recycles!

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These coupling agents in cells known as enzymes both catalyse the rates of biochemical processes and also direct their paths (Fersht, 1977). As the chief agents directing biological work in living organisms, their role in sustaining ecosystems is palpable. Their primary function as coupling agents in living cells is to respond to specific impulses from their substrates in the action exchange field and to generate new impulses or forces, directly fashioning benefits for each organism and for ecosystems. The operation of these agents depends on environmental conditions (e.g. temperature, light intensity) and the presence of many other essential factors such as the cofactors for enzymes – the vitamins. Within limits, the function of the coupling agent will be sufficiently variable to provide a necessary degree of constant internal conditions or homeostasis in living organisms, so that the transformations they direct will continue unabated if necessary despite altered environmental or external conditions. In the case of enzymes, these direct products of genes, the regulation of the coupling agents is particularly well developed. For example, a surfeit of substrates tends to increase the rate of reactions; conversely, this result may be compensated by feed-back inhibition from products as they tend to build up, acting to dampen the rate of the reaction. Overall, these regulatory controls can provide the homeostasis needed, such as that of the constant pH values in the sap of plants or the blood stream of animals (Kennedy, 1992). We have already emphasised the role of the activity of protons and pH value in life systems, from nuclear fusion on the sun to the synthesis of ATP in cells. In this book we wish to draw attention to a more dynamic concept of biological chemistry - enlivened by the real action of molecules directed by the immediate exchange forces of the action field described in Chapters 2 and 3. Instead of linear sequences or cyclic sets of molecules joined by arrows we must think of clustered sets of molecules exhibiting Brownian rotation and translation, directed by forceful impulses in action space, oscillating between the catalytic macromolecules known as enzymes. This action is far from completely random because biological molecules are characteristically asymmetric in structure, one half of a set of mirror images, which have the property of rotating the plane of polarised light. Such directional interactions with light quanta suggest that action exchange forces from quanta at all wavelengths will also act asymmetrically and hence exert non-random effects on the motion of molecules. We saw in Chapter 5 that the asymmetrical construction of the Crookes radiometer confers a specific direction to the motion of the vanes, even though the radiation first falling on them is randomly directed. This conclusion infers a fruitful field of investigation with respect to spatially directed or vectorial binding of metabolites by enzymes and in the chaperoning and location of macromolecules in cells. Each chemical metabolite such as ATP may participate simultaneously in molecular flows as intermediates in several processes, driven by dispersive fields that decide the trajectory for any particular molecule. There is an element of chance involved, but the dice are heavily loaded in terms of a restricted range of possible temporary destinations. Any molecule may escape from a locality of high chemical potential either by active diffusion to a zone of lower concentration, or more directly, by conversion into a different chemical product. Because chemical reactions release energy from the action field as a result of different needs for sustaining energy by reactants and products, a series of controlled quantum explosions then continues to drive the life process. We now have a vision of metabolism very

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different from the printed maps of static sets of objects that we currently use as descriptive aides-mémoires. The coupling agents operating in cells define a unique set of action processes characteristic of each particular organism. The choice of the adjective “coupling” agent here is quite deliberate, because the role of the gene products specified by DNA is to couple the action exchange forces caused by all the molecules present, including their own fields, to the performance of biological work. These coupling agents regulate and speed up the rates of thermodynamically spontaneous flows and processes. The genetic composition of each organism specifies which coupling agents will be present and the potential rates of the processes they catalyse. But the actual rate of these processes will in many cases be determined by interaction with the environment, since both the level of genetic expression and the actual activity of the coupling agents are regulated by local conditions such as chemical composition and temperature. The rich fabric of metabolism possible allows living cells to generate a huge diversity of metabolic results. Some at first sight appear as energetically uphill. However, every uphill process must involve another spontaneous downhill process that provides the energy required to lift and sustain the other metabolic system to a higher level, just as we showed in Chapter 5 how sunlight can elevate the atmosphere on daily and seasonal cycles. As long as there is a sustaining energy flow through the system the variation in the equilibrium point can be maintained. Thus, the growth of an organism such as a tree can be thought of as a DNA-regulated system seeking a receding point of equilibrium and the maximum point of growth represents one where all the forces causing growth have been exerted to the greatest extent possible. No further growth is then possible since the dispersive forces between molecules are now in balance with other forces such as gravity. The capacity to grow in a given environment is specified by the genotype and the range of gene products that the organism produces. Then the actual growth achieved is a matter of the instantaneous balance of action exchange forces that sustain the growing organism and the back-forces of the environment such as gravity, winds, the impacts of other organisms and so on. These action processes define the life of organisms much more aptly than detailed descriptions of genes or DNA sequences, their products or the metabolic pathways that are generated. There may exist a plurality of means, or redundancy, for achieving needed results. Alternative sets of catalytic proteins or different organisms may catalyse the same overall biochemical processes. This plurality leads to speculation that the need or opportunity for particular actions to be fulfilled by organisms in ecosystems will actually favour the appearance of the appropriate coupling agents. There is a trace of Lamarckism in this, but only in the sense that the fulfilment of particular needs (d’avoir besoin) is favoured in evolution. This result in no sense suggests the inheritance of acquired characteristics but does imply a mechanism for natural selection of characteristics that are thermodynamically favourable. Thus, natural selection must operate in the world as an actual guided result from the balancing of action exchange forces, in stark contrast to the abstract principle as an achievement of blind chance. Action exchange forces will always be expected to automatically select less stressful or chaotic arrangements of matter and energy in space in complete accordance with our new understanding of the second law of thermodynamics outlined in Chapter 4.

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7.1.3. Basic statements regarding the genotype x environment interaction So we can now extend Schrödinger’s programme for defining life in terms of the quantum theory, summarising the extra insight that the action resonance theory brings to our understanding of the use of information in life systems as follows: •

The balance between internal and external action exchange forces directs the growth of each living organism from the first moment of its conception as a genetic individual in a process of morphogenetic development known as the genotype x environment interaction. In living organisms specifically-coupled sources of action exchange forces, resulting from the impulses of quanta exchanged between molecules, accelerate molecules to new physical and chemical action states of least action and energy under the prevailing environmental conditions. The range of environmental conditions in which the genotype x environment interaction can be expressed are rather stringent. Inanimate materials merely respond to the current environmental thermodynamic forces as a result of more or less random action exchange processes. The uniqueness of living organisms, on the other hand, is that the process of arrangement of their materials occurs interactively with the environment as the result of a programmed sequence of action states clearly delineated in time. This programme is complete at the moment of genetic conception or haploid cell fusion yielding a new individual and the continuously developing phenotype is the product of this interaction. The programmed sequence of events is uniquely controlled by the genes present in the organism through coupling agents and any particular step of the process is contingent on the success of the prior steps. Each step involves a regulated process of biosynthesis of coupling agents specified by the hereditary code of DNA, required for each internal and external interaction. The internal forces generated by organisms, which tend to equilibrate with external environmental forces, are specifically and sequentially generated by the genotype. The fully developed organism then must represent an assembly of coherent molecules, approximately in bio-thermodynamic equilibrium with its surrounding environment and exhibiting the dual properties of minimum energy and least action described in Chapter 3.

•

Interaction of genotypes with environmental action exchange forces also dictates the development of new genotypes, as part of the evolutionary process leading to organisms or new species with different phenotypes. These phylogenetic action exchange forces dictate the generation of diversity in these species, in filling all available niches and in providing redundancy of evolutionary solutions. Coupling agents (proteins, organs, organisms, etc.) are proposed to possess overlapping roles in carrying out life processes in ecosystems. As pointed out by Schrödinger, fluctuations in quantum states of sufficient magnitude (e.g. ultraviolet radiation) cause mutations. This may be regarded as a random process, in that quanta of sufficient energy rarely occur at the temperature of living systems. Nevertheless, an average frequency of mutation in DNA may always be

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measured. These local fluctuations in action states caused by random processes are normally adequate to allow sufficient rates of gene mutation to allow natural selection to maintain a sufficient rate of adaptation. However, the hypothesis is presented here based on action resonance theory, that the genotype x environment interaction provides a mechanism for accelerated evolution of genotypes in times when environmental change is rapid. Where a genotype is no longer well adapted to its local environment during rapid change (e.g. of temperature, changes in order organisms such as prey or predators, etc.), marked dissonance between the environmental action exchange forces and least action states for molecules may result. This would then be expected to raise the bio-thermodynamic selection pressure as a result of the greater forces generated, leading to accelerated evolution. Therefore, the action resonance theory seems to provide an interactive wave-guide for the mutual evolution of all organisms occurring within each physico-chemical environment. •

The action exchange forces of the [genotype]n x environment interaction will also lead to the generation of a hierarchy of diverse life forms in which a large base of simpler organisms or coupling agents will also help sustain the activity of fewer but more highly developed life forms capable of coupling more complex processes, each level in the resultant hierarchy acting in community to achieve its ends. Such mutual interactions will be characterised by cooperative solutions to the function of cycles in ecosystems, acting to establish a dynamic equilibrium in which the capacity to do work is shared. The new understanding of the second law of thermodynamics made possible by the action resonance theory in Chapters 3 and 4 means that higher biological order from initially chaotic conditions is a natural outcome of evolution. This order is predicted as action and entropy are optimised by action exchange forces generated by energy inputs, according to the principles of momentum conservation, least action and minimum energy.

These basic statements derived from the action resonance theory will be logically tested in the following discussions. Experimental testing of these statements is also possible, providing rigorous tests of the action theory and its predictions and a more scientifically rigorous study of the theory of evolution of species by natural selection. based on action exchange forces and the principle of least action that they produce. 7.2.

Life processes - carbon, nitrogen and mineral nutrition

One of the most striking features of the metabolic systems supporting life is the existence of environmental chemical cycles. In the cases of carbon, nitrogen and sulfur, the most abundant elements participating in life systems, each of these atoms exists in molecules in a reversible sequence of more oxidised or more reduced chemical states (see Kennedy, 1992 for more details). These transformations are carried out under genetic control by microorganisms in soil and aquatic systems. The substrates for one organism are the

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products of others so that overall, a complete cycle of transformations occurs. For systems more or less in a steady state, the actual concentrations of the intermediates may not change much, but the total turnover of chemical intermediates over a period of weeks or a year is many times the actual quantity of each present at any one time. Thus carbon atoms oscillate between highly oxidised carbon dioxide (CO2) and fully reduced methane (CH4), nitrogen between oxidised nitrate (NO3-) or dinitrogen (N2) and reduced ammonia (NH3) and sulfur between oxidised sulfate (SO42-) and reduced hydrogen sulfide (H2S). Apart from their inorganic forms, these elements are also incorporated into bio-organic materials in living organisms where they exist for a time before being returned to the ecosystem stock as inorganic waste products. The fact that the cycles constantly recur was referred to in Chapter 4, where the point was made that the total molecular entropy on earth is barely changing with time, belying the common opinion about increasing disorder as the universe runs down, at least locally. If the molecular entropy on the earth’s surface could be shown to change significantly with time, then we would have an excellent indicator of the lack of sustainability of current systems and their outputs. In all these cycles the characteristic we know as oxidation number varies by eight, providing the opportunity to transfer eight electrons and protons associated with converting reduced forms of molecules containing carbon, nitrogen or sulfur atoms and water, leading to the generation of more oxidised products. In the reversal of these processes, oxidised forms of molecules containing these atoms are then capable of accepting eight electrons, regenerating the reduced forms of the atoms and water. This paradoxical situation is thermodynamically possible because oxidations of reduced chemicals are coupled to the utilisation of atmospheric oxygen (O2), which avidly reacts with excess electrons and protons to produce water. On the other hand, reductions of oxidised nitrogen and sulphur are linked to the oxidation of strongly reduced carbon compounds produced by photosynthesis. Note the essential role of sunlight in sustaining both these processes, producing both the reduced carbon substrates needed for reduction of oxidised materials and the oxygen needed for re-oxidation. This emphasises the fact that life on earth could not be long sustained without the impacts from the intense daily illuminations of the sun falling on its landscapes. Without oxygen being produced so prolifically on earth in photosynthesis, the diversity of life forms possible on this planet would have been extremely restricted. These balanced cycles all seem wonderfully if fortuitously organised. This may be less surprising when we observe the achievement of balanced outcomes in one organism, evolved for the benefit of a single organism. Somehow it seems less expected that similar coordination will be observed as cyclical chemistry of whole ecosystems. But from the point of view of action biothermodynamics, this is merely the same evolutionary solution to the same problem. The stresses of action exchange forces are not limited to individual cells but are expressed throughout ecosystems transcending such boundaries. The opportunity to respond to these stresses so as to relieve them can be responded to in any genome able to sense the stress. Usually, this response is quite opportunistic for the species responding.

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7.3.

Symbiotic interactions

A strong theme of this book is the concept of cooperative activity. In fact, action resonance theory presents forceful recognition that no individual species of organism can be considered as a self-existent entity, completely independent of its environment. The continuous impulsive exchanges of energy between the individuals of each species and the environment guarantees this outcome. If completely removed from its environment to a zone of complete vacuum, bereft not only of matter but also energy including the zero point energy, the organism would instantly disintegrate in an explosive reaction because of the imbalance of action exchange forces. In fact, if energy and matter are considered, action resonance theory recognizes that in reality “nature abhors a vacuum” and that there is no such place anywhere nearby devoid of both. Every organism must always be considered as interactive with its environment. Its existence would not be intelligible otherwise, since it was evolved to adapt itself to its environment. Thus, the concept of organisms occupying niches must be dominant theme. Natural selection will ensure that each species will find or fashion its own niche. The idea of evolutionary extinction, where one species must directly compete with another in a fight to the death, is not tenable since there is practically an infinite supply of potentially unique niches available providing refuge from conflict. Extinctions may occur, but these are more likely the result of catastrophic events or too rapid changes in the local environment that wipe out many species simultaneously. In nearly all cases, a species will simply evolve into something else if it is severely threatened, barring these catastrophic events. The inevitable result of this will be evolutionary adaptation not only to the local physical and chemical environment but also to the local biological environment. As a consequence, mutualism or symbiosis ‘at a distance’ is likely to be a feature of ecosystems because the occupant of one niche can provide benefits to others or derive benefits from others. If a mutual benefit involving economy in the use of resources is possible, action resonance will favour its selection. Given time to adapt, nature will waste no resource whatsoever. We can see this operating in the apparent evolution of the different species of microbes participating in the nitrogen cycle of ammonification, nitrification, denitrification and nitrogen fixation. In some cases, more intimate symbiotic associations may occur, where both species jointly occupy the same niche or are physically intertwined. Sapp (1994) has described why there was considerable reluctance to accept an important role for symbiosis in evolution, where concepts such as the ‘survival of the fittest’ tended to emphasise the competitive aspects at the expense of the cooperative activities. Recent genetic studies on molecular evolution now leave little doubt symbiosis provided the means by which eukaryotic organisms gained rapid access to the complex metabolic capabilities of other prokaryotes (Douglas, 1994). Two different kinds of direct successful symbioses between plants and bacteria will be discussed below. However, the general scope for recognising symbiosis as acting to give effective, mutually beneficial, cooperation between species in ecosystems is emphasised in this chapter. Symbiosis is a term denoting the living together of dissimilar organisms. This may extend from commensalism or simple sharing of space and substrates, to mutualism

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in which both host and guest clearly benefit from the association, and even to parasitism. Here, symbiosis as mutualism has the preferred emphasis. The neglect or refusal to accept the general significance of such interactive mutualism may have contributed to mismanagement of agricultural ecosystems in recent times. This is true in cases such as the overuse of agrochemicals to control pests where the mutual benefits such as utilising information on prey-predator relationships as part of a programme of integrated pest management might have been better exploited. 7.3.1. Chloroplasts and mitochondria as symbiotic organelles in plant cells Chloroplasts were discussed in Chapter 6 as the intercellular sites of harvesting the impulses from sunlight. Their main chemical products are oxygen, ATP, reduced electron carriers (such as NADPH), sugars and amino acids; chloroplasts are found only in green plants. Mitochondria are superficially similar to chloroplasts, but they are quite different in function and these organelles are found in all animal and plant cells, concerned with the oxidation of reduced carbon compounds such as sugars and oils consuming oxygen (see Figure 7.3). They release carbon dioxide to the environment and produce ATP by the process known as oxidative phosphorylation. This is similar in principle to the production of ATP in chloroplasts by photophosphorylation. More recently, it was recognised (Margulis, 1993) that both organelles were probably once the cells of independent prokaryotic microorganisms, captured in the cells of eukaryotic higher plants as these evolved. The plastids of plants seem to have been derived at a primitive stage of the evolution of eukaryotes from photosynthetic cyanobacteria while mitochondria appear to owe their origin to purple bacteria. Whatever the conditions that led to their initial capture, currently these organelles carry out essential roles in green plants and divide whenever the plant cells divide. The fact that both organelles carry self-replicating DNA coding for some of the proteins that go towards making up their structure and function is now considered as evidence for their prokaryotic origin. While the chloroplast and mitochondrial genomes are incomplete and would not allow either organelle to survive independently of the plant genome, this DNA still plays an essential and unique role in the life of plants. An interesting consequence of DNA being contained and replicating in these organelles is that inheritance of this DNA is through the maternal line, since the ova of plants carry both organelles in their cytoplasm. This linkage of genes can have practical consequences in plant breeding or genetic engineering. 7.3.2. Symbiotic nitrogen fixation in legumes The enzyme nitrogenase The author of this book has spent most of his career studying aspects of the process of symbiotic nitrogen fixation. This process is an essential part of the environmental nitrogen cycle, including the fixation of atmospheric nitrogen (N2) as ammonia. Biological nitrogen fixation involves the catalysis of a remarkable chemical reduction by an enzyme called nitrogenase1. This macromolecular biological catalyst overcomes the great stability of dinitrogen to reduction at ambient temperature by using the energy made 1

Nitrogenase reaction: N2 + 8Ferredoxinred + 8H+ + 16ATPMg2- + 18H2O => 2NH4+ + 2OH- + H2 + 8Ferredoxinox + 16ADPMg- + 16H2PO4-.

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available from the conversion of two molecules of ATP and water to ADP and inorganic phosphate for each electron transferred (Kennedy et al., 1968). Chemists have traditionally regarded dinitrogen as so stable as to be almost inert and the great Baron Justus von Liebig, the 19th century father of agricultural chemistry in Germany (as Sir Humphry Davy was in Britain) even dismissed the possibility of its biological fixation. After a long period of dispute during the middle of the 19th century, his countrymen, Hellreigel and Wilfarth, put beyond doubt by carefully controlled experiments that legumes inoculated with appropriate bacteria of the genus Rhizobium could fix atmospheric dinitrogen (Nutman, 1998). It was also recognised during this same period that a broad range of free-living nitrogen-fixing bacteria could grow as saprophytes on decaying organic matter or associated with the roots of plants (Tchan, 1988). By contrast, industrial nitrogen fixation in the Haber-Bosch process discovered in a Europe deprived of sources of mineral nitrogen during the early part of the 20th century by war requires very severe reaction conditions of high temperatures, several hundreds of atmospheres pressure of dinitrogen and hydrogen gases and the presence of industrial metal catalysts to form ammonia. The contrast between these two systems, both forming ammonia, provides a good example of the difference between an industrial solution to a chemical problem that uses ‘brute force’ and a biological solution using the path of least action instead. Industrial catalysts for nitrogen fixation based on iron compounds tend to be short-lived and of limited efficiency. By contrast, nitrogenase2 is a marvel of threedimensional molecular architecture (Figure 7.4), incorporating cofactors of iron, molybdenum and inorganic sulphur linked to a complex poly-amino acid structure (Kim and Rees, 1992; Giorgiadis et al., 1992). The full story of the role of ATP in the reduction of dinitrogen by nitrogenase remains to be told. Its hydrolysis is able to increase the rH value for reduction of dinitrogen (N2) by reduced ferredoxin. But the power of evolution in generating such a remarkable catalyst when needed to complete the nitrogen cycle can only be admired. Even more remarkable is the fact that every amino acid molecule of the 500 or so making up the chain is coded for by the triplet base code in DNA. Hundreds of nucleic acid bases, strung together like pearls on a spiralling string, guide the protein synthesis system to unfailingly choose the next amino acid in the sequence. The macromolecular protein can then spontaneously select its correct morphology by spontaneous folding as a result of interaction with its environment (Kennedy, 2000), embracing its metal clusters as it does so to become a functional enzyme.

2

In the late 1960s, the author had the privilege to spend 18 memorable months as a Fulbright fellow in the laboratory of Len Mortenson at Purdue University working in a research team on the purification of nitrogenase into the MoFeS and FeS components from Clostridium. The slogan in this busy laboratory – dominated by red cylinders of hydrogen vigorously bubbling the buffers used for the anaerobic gel filtration columns (that would probably be banned nowadays by risk management personnel) – was “crystals by Christmas”. This spurred our hope to be able to understand the molecular structure of nitrogenase soon, using x-ray crystallography. Alas, our slogan went unrewarded and around 20 festive seasons would pass before crystals of adequate quality could be prepared from Azotobacter vinelandii in another laboratory, leading to the image shown in Figure 7.4.

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Fig. 7.4. Nitrogenase (x10,000,000). This multi-subunit brown-coloured enzyme has four ATP molecules bound as two pairs on either side on each of the terminal FeS-protein molecules known as nitrogenase reductase; each bound ATP is separated by half its length and oriented towards a single 4Fe4S cluster, adjacent to the P (FeS) cluster and the FeMoco cluster, where the nitrogenase substrate, NŁN, is bound and converted to ammonia. By some unknown means, the hydrolysis of ATP is able to project electrons from 4Fe4S to P and then to FeMoco, so that together with protons, they can reduce NŁN to 2NH3. Action resonance theory suggests forceful roles for quanta from ATP hydrolysis by anisotropic acceleration of electrons through these centres, and/or in dissociation of the FeS protein to extract the next electron from ferredoxin. The FeS protein, coded by the gene nifH,, dissociates once for every electron used, then associating with ferredoxin to receive an electron and binding ATP molecules in each of the eight cycles needed to produce ammonia. Dr D.C. Rees (University of California) and Dr D. Dawson (John Innes Centre, UK) are both thanked for this image, based on x-ray crystallographic analysis of the purified enzyme from Azotobacter, transmitted kindly by Dr Ray Dixon (John Innes Centre, UK).

Just how this and many other enzymes of similar complexity were coded for in the first place still defies imagination. A large number of both non-symbiotic and symbiotic bacteria are able to carry out the nitrogenase reaction, expressing this enzyme only under microaerobic conditions of low oxygen concentration under nitrogen-limited growth conditions. Nitrogenase is an extremely oxygen-sensitive enzyme. Symbiosis and the role of molecular dialogues A most striking feature of symbiotic nitrogen fixation in legumes is the remarkable biological cooperation that exists between the two completely different plant and microbial species that are concerned. In fact, there are many examples of such cooperation, by no means limited to biological nitrogen fixation. But this is an excellent

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example to illustrate how acting together, two separate organisms each with its own complete genotype involving many thousands of genes, are able to achieve much more than either could separately. In the process of symbiotic nitrogen fixation in legumes the capacity of the plant to fix carbon dioxide from air, producing photosynthate capable of generating reduction and phosphorylation potentials (rH and rP) while releasing oxygen, is complemented by the ability of bacteria from the genus Rhizobium to produce ammonia from nitrogen gas in air by the activity of nitrogenase. Together, these two species of organisms provide a system capable of reducing dinitrogen to ammonia using hydrogen atoms and electrons derived from water without adding to the greenhouse effect by producing carbon dioxide, in contrast to industrial nitrogen fixation. The molecular dialogue between plant and bacteria involved in the development of the legume symbiosis (Denarié et al., 1992; Perret et al., 2000, see Figure 7.5) highlights the cooperative nature of the process of development. Initially, the plant excretes signalling chemicals known as flavonoids into the rhizosphere where a certain number of Rhizobium bacteria respond genetically by initiating the production of specific lipo-chitopolysaccharide nod factors. These nod factors in turn induce the legume root to initiate the meristem for a nodular structure in the root, so that infection and colonisation of the nodule by the rhizobia can occur. The response of the nod genes in the bacteria and the nod factors they produce introduces the element of specificity into the symbiosis, ensuring that an effective N2-fixing symbiosis results containing all the coupling agents needed for the symbiosis. Only certain strains of Rhizobium are able to enter into successful symbiosis with particular species of legumes (Denarié et al., 1996; Long, 1996). This molecular dialogue regulates the expression of genes in both bacteria and the plant that allows the orderly development of the legume nodule to proceed. The chemicals involved act as hormones switching on genes that produce coupling agents as products leading to a cascade of events culminating in the formation of an effective nodule (see the frontispiece to this chapter). This is a concerted action process of extensive plant cell division followed by colonisation by Rhizobium bacteria (Figure 7.5). One can readily imagine that action exchange forces are involved in all these processes for the initiation of molecular motion. For example, cell division involves forceful but purposeful mass transport of many cell elements including proteins, cell organelles such as mitochondria, the dividing chromosomes in mitosis, and their transport to their new locations. Each of these components must find their place, by minimising action exchange energy, in this dynamic system. We can anticipate that a full understanding of the structure and function of these cell components will include knowledge regarding the mechanism by which they can move to find their place, as Aristotle would say, in interaction with other components such as microtubules.

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Fig. 7.5: Symbiotic colonisation of legume roots by Rhizobium; establishment of root-nodule primordia. Rhizobia (rz) present in the plant rhizosphere adhere to the root-hair (rh) surface. B. Nod-factors induce root-hair curling as a result of differential growth and permit bacterial entry at the centre of infection (ci) where the nucleus (n), which precedes C., growth of the developing infection thread (dit). D. Infection thread ramifies (rit) near the dividing cortical cells of the nodule primordia; abbreviations: epidermis (ep), cortex (c), endodermis (ed). E. N2-fixing bacteroids (b) released from the infection thread (it) into nodule cells surrounded by a peribacteroid membrane (pb), forming a symbiosome in which bacteroids may accumulate energy reserves as poly-β-hydroxybutyrate (phb; abbreviations: digestive vacuole (d), nucleus (n). This orderly process occurs with sophisticated genetic control in which a genotypel x environment x genotype interaction is expressed. Reproduced from Perret et al., Mol. Microb. Rev. 64, 180-201 (2000), with permission from the American Society for Microbiology.

So in legume symbiosis, an orderly sequence of events occurs spontaneously as a result of the genotype x environment x genotype interaction triangle. Some of these events (described by several authors in Spaink et al., 1998) include: • • • • •

Binding of rhizobial cells by plant root surface Plant root response by synthesising nodule primordia from induced meristems, perhaps favoured by polyploid nuclei in root cells (Nutman, 1998) Root hair infection and development of infection thread or crack entry of rhizobia Nodule development and colonisation of nodule cells by rhizobial cells Synthesis of nodulins – gene products usually enzymes specific to N2-fixing symbiosis including leghaemoglobin for oxygen transport to rhizobial cells, enzymes of carbon metabolism such as PEP carboxylase, plant glutamine synthetase,

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• • •

asparagine synthetase, ureide metabolism for ammonia assimilation - in root nodule cells Expression of nif genes in nodule bacteria setting up nitrogenase activity and differentiation of rhizobia as bacteroids expressing nitrogenase Repression of ammonium uptake mechanism in bacteroids so that ammonia formed from nitrogenase is excreted into the nodule plant cell cytoplasm Full establishment of the metabolic exchange of reduced carbon compounds from photosynthesis with nitrogenous products from nodule metabolism

The capacity of the gene products from two different species to coordinate their function so successfully, producing the practically seamless functioning organ on the roots of legumes (see the frontispiece to this chapter) is a remarkable example of concerted evolution and of the effectiveness of symbiosis. The highly cooperative general metabolism of legume nodules is shown in Figure 7.6. Here we have flows of carbon and nitrogen between plant host cells and microbial cells (bacteroids), also with seamless operation of the overall metabolic system.

Fig. 7.6: Symbiotic metabolism in the principal compartments of the central tissue of legume root nodules. In an infected cell, the metabolic compartments are in mitochondria (M), amyloplasts (A), the symbiosomes (S), the bacteroids (B) and the cytosol in which the pools of substrates and products are enclosed in dashed boxes. Neighbouring cells are connected via plasmodesmata (P) with greater thickness of the cell wall bordering a gas-filled intercellular space. Major flows of C-substrates, originating from host photosynthesis in the leaves of the legume plan, indicate use by mitochondria to produce cytosolic ATP, processing in amyloplasts, use by bacteroids to support nitrogenase activity and use in assimilation of NH3 into aminoacids and amides. These assimilates then pass out of infected cells into the xylem stream of the plant. Other features include the transport of oxygen via leghaemoglobin (LB) to bacteroids from intercellular spaces, the formation of the polymer poly-ȕ-hydroxybutyrate from acetate in bacteroids and the recovery for metabolism of electrons from H2 produced by nitrogenase activity using an uptake hydrogenase (Hup). For simplicity of presentation, the metabolic compartments of the uninfected nodule cells have been omitted. The role of gas-filled intercellular spaces in the central nodule tissue is indicated (reproduced from Kennedy and Cocking (1997) by kind permission of Dr. Fraser Bergersen, Australian National University, Canberra).

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However, the intimate cooperative metabolic activity that one recognises in legume symbiosis also occurs in the general operation of the carbon, nitrogen, sulphur cycles, although requiring a broad range of different organisms without such direct connections. Indeed, in considering the remarkable cooperative activities of one organism with another one realises the paradox associated with the notion of defining the function of leguminous root nodules. One may consider function as a verb drawing attention to the mechanism of how nodules operate, described in detail elsewhere (Spaink et al., 1998). Alternatively, one may consider the noun function to indicate the characteristic action or even the teleological purpose that N2-fixing nodules of growing legumes play in raising the nitrogen status of soils to the benefit of other species in these ecosystems (Kennedy and Cocking, 1997). This obvious need of ecosystems for fixed nitrogen is met by the Rhizobium-legume symbiosis, as part of completing the cyclic processes involved in the metabolism of nitrogen. Ultimately, the need for nitrogen is thermodynamic, driven by high carbon to nitrogen ratios in soil organic matter. 7.3.3. Completing the nitrogen cycle Consider a planet with earth-like life in some faraway galaxy, where there was no process of biological nitrogen fixation but where the other biological processes such as photosynthesis had evolved. What would need to happen and how could the web of life be sustained? Provided all the other phases of the nitrogen cycle still occurred, one must assume that on this planet there is a more or less inexhaustible supply of reduced nitrogen or ammonia, so that nitrogen fixation would not be needed. Presumably, purely chemical processes that occurred while the planet was being formed must have laid down a huge store of reduced nitrogen such as urea, readily converted to ammonia. Ammonia itself would be unlikely to provide a suitable reserve, since it is toxic, but it could be inactivated and stored by being bound to clay. If so, the process of nitrification could still occur and nitrate could be made available as a product, providing this as a substrate for plant growth. Importantly, there would still be the acidifying phase of the nitrogen cycle by consuming oxygen gas and releasing two protons to the environment for every ammonia molecule oxidised (Kennedy, 1992). Following the growth of nitrifying organisms producing nitrate from ammonia, the process of denitrification would occur, in which nitrate would serve as a terminal electron acceptor. As a result of the consumption of reduced photosynthate such as sugars or fats, nitrate could be converted to nitrous oxide and then dinitrogen, neutralising just one of the two protons produced in the prior process of nitrification. Gradually, the store of ammonia would be reduced in size, but its sheer magnitude might allow life to continue for a period. However, there could be serious problems as a result of the gradual acidification of the environment because now, only one of the protons produced in utilising each ammonia would be neutralised. Life could only continue as long as the soil remained alkaline. So such as system is inherently unsustainable. Eventually, the store of ammonia would become depleted, or the degree of local acidification would be such that aluminium toxicity for soil below pH 4 would threaten plant life (Kennedy, 1992). By

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now, nearly all the available nitrogen would have been transferred to the atmosphere as nitrogen gas. To rescue ecosystems from the lack of nitrogen and to correct their widespread acidification, it would now be necessary to invent the process of nitrogen fixation. If intelligent beings had already evolved, or arrived in space vessels from elsewhere, the process could even be a synthetic one, but this would need to be carefully managed. To prevent a greenhouse effect, the generation of hydrogen would need to be directly from water rather than by reaction of steam with reduced carbon compounds. This would presumably require that this truly intelligent life-form had decided to use solar energy to form the gases, hydrogen and oxygen, directly from water by electrolysis (see Chapter 6). Otherwise, as is actually the case with the Haber-Bosch process invented by the less intelligent Homo sapiens, an equivalent amount of carbon dioxide would be evolved in generating the hydrogen needed (Kennedy and Cocking, 1997), adding to a growing greenhouse problem. Hydrogen for the Haber-Bosch process is generated from hydrocarbons reacted with steam, with carbon dioxide as a major by-product of up to 5% of the total generated from consuming fossil fuels. In the absence of intelligent life at this stage of the planet’s evolution, a natural, biological solution to the problem would be needed. We can assume that the N2-fixing system evolved by the process of natural selection in response to the ecosystem’s need would involve generation of reducing potential by photosynthesis using water to provide reductant, so that no carbon dioxide production would be needed to produce ammonia. One can only wonder at the power of evolution and natural selection to generate such intelligent solutions. For such symbiosis does not involve a single mutation but the generation of a complex set of new genes, many of which appear to have no logical basis other than their role in the fully functional system. It is therefore impossible that they could all evolve at once without a selective advantage for the intermediate stages in the evolutionary process (Quispel, 1998). The borderline between symbiosis with obvious mutual benefits and parasitism, where only one partner in the association benefits, is not always clear. Possibly, parasitism offers an intermediate stage of selective advantage. This is an unsolved problem, but we also know that bacteria can acquire complete sets of genes for particular purposes. For example, many of the genes coding for symbiotic N2 fixation are carried on transferable plasmids. These transfers may even occur across species boundaries and we can only speculate about the limits to the possibilities for such rapid natural genetic engineering. The existence of a thermodynamic force favouring such outcomes may be decisive in achieving these dramatic evolutionary solutions. 7.4.

Chance and quantum necessity – selfish genes forced to be altruistic

One of the sharpest philosophical differences of opinion in science hovers over questions related to chance or necessity in nature. Is the existence of the universe in any sense meaningful, or is it just the outcome of a completely random juxtaposition of independent material objects acting quite blindly without purpose? Many scientists have questioned whether there is any evidence in nature of such order, or if there exist any signs of a grand plan? Peter Medawar, the British Nobel laureate claimed from a logical positivist viewpoint that a scientist could only take a negative attitude to such questions. If science

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can’t experimentally test it, it doesn’t exist. In fact, Karl Popper had already refuted the rational basis of such positivism early in the 20th century, when he noted the inability of science to establish anything with such certainty. Yet others have just as earnestly taken the obvious relation between structure and function of complex organs such as the human eye or hand as clear and specific proof of some kind of divine purpose in nature. Since action resonance theory now actually proposes a mechanism for arranging the universe that can be tested, it may well be that Medawar’s grounds for dismissing nature’s grand plan are not valid in any case. In biology, the interface between genetics, environment and evolution seems to produce the most strongly held differences of opinion. For example, in Richard Dawkin’s 1989 book, The Selfish Gene, this author elevated genetic mechanism and the gene to a dominant role, suggesting that the purpose most clearly recognisable in biology is the gene’s ‘selfish’ quest for survival, this devaluing any non-material sense of purpose. However, partly as a result of the negative response of many readers to the rather bleak message of The Selfish Gene, in Unweaving the Rainbow Dawkins (1998) has become more aware that satisfying the self-interest of particular genes also requires cooperation between many genes comprising the whole gene pool of the species. While his viewpoint was one focussing on natural selection favouring the survival of particular genes, he now recognises that no gene could survive independently of others. In this chapter, we have gone much further with the theme of cooperation, pointing out how the genotype x environment interaction for one species may involve symbiotic cooperation with other species, since the expression of its genes also forms part of the environment of the first species. Also, the survival of no gene is guaranteed, given the ease with which natural selection will reject it if a better gene can be generated; all genes are naturally called on to seek excellence in the sense of doing better and to be absolutely self-sacrificing should they be exposed to competition with a superior gene generated in just one individual for the same or similar purpose. It would seem that it is not the survival of the gene itself but the excellence with which the biological task can be performed that is the higher purpose that evolution seeks. Action exchange forces even offer the means by which cooperative excellence can be achieved, through the forceful quest for economy or parsimony in energy use and least action. Such a period of ultimate economy may not always be obvious, for all changes must occur as a result of trial and error. Selecting superior results step by step from the natural rate of variation involves a constant risk that retrograde developments will also occur in individual genomes. But each gene is forcefully enjoined to be altruistic and must submit to superior judgement of a larger grouping at each and every step on the long and winding road of evolution. The debate about chance or design has exercised the most able minds, but seemingly with no clear victory for either camp. The debate could also be said to provide the clearest cases of the reductionist versus the holist viewpoints. Is the whole merely the sum of the parts, or does it add up to more? In fact, in this book an emphasis has been placed on examining whole systems and a strong case has been developed that action resonance needs the whole system for exchange forces to act effectively. But it should also be understood that the whole is often less than the sum of the parts - at least with respect to the need for sustaining energy.

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Earlier, Richard Dawkins (1986) had published The Blind Watchmaker, where he examined the role of blind chance in evolution. In fact, in this book Dawkins willingly recognised that more than blind chance was required. For Dawkins noted that there were far too many possibilities and insufficient time for blind chance to have generated living organisms. He invokes Darwinian natural selection so that organs of amazing complexity, such as the patterned peacock’s tail, or even the human mind, could be generated in a cumulative fashion, improving the odds for success in the time available. The disassembly and re-assembly of molecules are both performed under strictly contingent conditions where there can be no such thing as true statistical independence. What exists before always provides the historical matrix for what will be and all rearrangements must be made under the direction of quantum exchange forces. Perhaps statistical independence is more of a mathematical construct of the human mind (man acting in God’s image) than a reflection of the real world. True, the random selection of objects in one region of space and their completely independent transfer to other regions would generate nonsense, or highly improbable arrangements that might not appear guided by natural forces. But is chance ever blind? And what is the source of cooperative and symbiotic activity discussed above in legume symbiosis? Certainly not blind chance, but directed forces! The action resonance theory clearly proposes purposive interaction in nature rather than blind chance. Furthermore, it provides a very simple physical mechanism to achieve this. This physical mechanism involves the resonant impulses of quanta, providing forceful wave guides for the trajectories of all material particles. Every molecule must continuously run the gauntlet of the action field, but in the end, molecules will arrange themselves so as to minimise the need for energy to sustain them in the system where they occur in a state of least action. The fact that the impulses of sunlight drive the synthesis of strongly reduced compounds from electrons abstracted from water, simultaneously providing the energy as quanta needed to sustain them, allows complex organisms to develop. The Nobel laureate, Ilya Prigogine, can then quite legitimately claim (1980) that these sequentially evolved, self-organising dissipative structures utilise the forces developed by irreversible processes and non-equilibrium to function. But we prefer to draw attention to their organising role as flexible but deterministic coupling agents, spontaneously linking the potential of action exchange forces to productive work. Such exchange forces operate at every stage in the expression of DNA as gene products, using constant feed-back mechanisms to maximise the efficiency of productive work and of completing particular tasks. But deterministic biological mechanism does not completely eliminate a role for randomness or for chance. Particularly in systems near equilibrium there is ample opportunity for meandering motions with no sustained direction of flow, because the action exchange forces have become more balanced and the impulses of quanta from all directions are more or less equivalent. Chance encounters will then dictate rearrangements of position in the system, which for the most part involve rotational motions resulting from the torques generated by impulsive quanta. We might conclude that so variable are the parameters involved, that a particular situation and arrangement in space is always a unique moment in time, a transient state never to be repeated. On the other hand, because of the curved responses mentioned above, recurrences favouring

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repetitions of particular arrangements of matter will be expected to be a feature of the action resonance field. For example, daily and seasonal positioning of places on the earth with relation to the sun, or of the tidal influences exerted between the earth and the moon will be repeated and will form part of the natural rhythms of the environment to which each living organism is subjected. These recurrences are interesting because they automatically generate oscillations in thermodynamic conditions, drastically shifting the current position of equilibrium, such as when sunlight appears in the daily cycle. The action resonance forces that result are bound to dictate non-random flows in these fluctuating natural systems because of their inherent properties. In these conditions, gradients in the force fields will be produced and the systems will attempt to readjust so as to reduce the intensity of gradients in action resonance forces by generating flows of matter. The uncertainty principle of quantum mechanics disallows attempts to define simultaneously both the position and the momentum of individual particles of such low inertia as an electron. But the practical certainty is absolute that molecular systems such as those on the surface of the earth will spontaneously change temperature daily under the influence of sunlight, or that the atmosphere will heat and spontaneously rise in the earth’s gravitational field. In reality, quantum uncertainty becomes indistinguishable from the fuzziness inherent in the distribution of impulses in the action field. This is merely a product of the relative significance of the effect of individual impulses (which provide our only means of detecting an electron) on its path of motion. Just as Albert Einstein believed all his life in determinism – expressed in his famous statement expressed typically in religious terms that “the Lord does not throw dice” – we assert that every change in the trajectories of the electrons of DNA molecules will result only from the impulses given by the actons of quanta. Certainly, we are denied the practical possibility of predicting the future motions of individual particles, since this would require complete knowledge of all aspects of the structural and relational orientations of all matter and all future energetic impulses, no matter how distantly they are generated. But we can still be satisfied with the knowledge that all changes in the trajectories of particles are absolutely determined by impulses on electrons and nucleons. Furthermore, we may even be happier with the willful property of our human minds that allows us to make prudent judgements internally, calmly selecting among the possible alternatives, and then choosing when to act externally. This cooperative power of mind over matter is true, at least for the range of actions that involve relatively small changes in inertia, freeing us from the spectre of merely being impelled by surrounding forces in any direction completely against our will. Another of Karl Popper’s observations was his remark that it was only a step from the amoeba to Einstein. This may seem somewhat disrespectful of the genius who has recently been judged Time magazine’s Man of the 20th Century, although it could be remarked that the 20th century still had one year to run3 when the award was made. But 3

Time magazine, like the media everywhere (except under a well-informed government edict in Cuba), in conflict with the facts, decided that the 20th century should be over on January 1, 2000, an event objectively occurring a year later. For why should the lack of a zero in the set of Roman numerals require that either the 1st century or the 20th century only have 99 years? Indeed, who when told that they could live for a century in either epoch would be satisfied with one year less? This triumph of falsehood shows the power of media propaganda today and the lamentable acceptance of relativism instead of seeking objective truth (but perhaps more an impatient desire for a good party sooner rather than later).

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such lack of objectivity by the media aside, Popper was referring to the method of conjecture and refutation that both the amoeba and Einstein would use to solve problems. Obviously, the amoeba’s approach to acquiring information or knowledge is much more primitive and less ambitious, but it is still required to make choices to obtain enough food and has learnt to employ chemotaxis (by evolution of its genetic apparatus) to do this. Plants have obviously employed similar strategies to develop the means to acquire sunlight, to attract pollinating bees to their flowers or even to skilfully trap insects using analogues of hammers and sticky surfaces. Einstein retains the abilities of the amoeba and some of those of green plants but clearly has access to much more highly evolved and better means to acquire and use knowledge. From Popper’s perspective, the whole of evolution can be regarded as a continuous explanatory quest for superior knowledge of our environment, using a rational process of self-improvement by testing better hypotheses with reality. This is a far more noble purpose for evolution than the purely materialistic selfishness of genes. According to action theory, even apparently random events are real, objective, responses that are never statistically independent. One event stimulates another. And as suggested elsewhere in this book, the very nature of randomness does not preclude absolutely predictable outcomes in a matrix with the property of asymmetry. Properly considered with the benefit of action theory, the statement that there is nothing more certain than a random process seems apt – unless there is actually no net process occurring at all. Particularly where the process involves small step-by-step readjustments in action state as a result of thermodynamic gradients or initial chaotic conditions, the forces generating the response and outcomes are irresistible. That is the very basis of the overwhelming significance of thermodynamics. This suggests that the problem solving methods used by amoebas, Einstein and all other organisms never involves blind chance, but have a rational basis involving real physical interactions through directed impulses. So, based on action resonance theory, we claim that both the survival of genes or their natural selection owes nothing to blind chance. 7.5.

Order from chaos

7.5.1. Genes directing action in morphogenesis Molecular genetics and biotechnology is one of the most impressive areas of modern science. The ability to relate sequences of bases of DNA in chromosomes as genes to the synthesis of specific proteins and in turn to relate these to specific functions or malfunctions in organisms has provided very powerful means of problem solving. The fact that DNA can be modified, spliced in large sections and even cloned into cells of different species has resulted in a huge range of potential applications of this technology. The modern world is well aware of the potential for applications of biotechnology in all professional areas from medicine to agriculture. In fact, the possibilities for genetic manipulation have even become a matter of significant public dispute in the areas of human biology and genetically-modified foods. Strangely, this is often being achieved without a clear understanding of the mode of action of particular gene products. As in the past with many of the other sciences such as

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medicine and engineering, empirical approaches are often adequate for generating practical solutions. For molecular genetics and its associated biotechnology, this is at once a strength but also a potential Achilles heel for the new technology, in case there are unpredicted outcomes of the technology. Indeed, this is the main basis for caution in areas such as genetically modified crops. Without a fuller understanding of how genes and genetic products act, the possibility of catastrophes must be considered to exist, however unlikely these may appear to be. As discussed earlier in this chapter, genes specify coupling agents as gene products. But the modes of action of these gene products are often by no means clear. For example, the problems of plant and animal morphogenesis are far from solved. Despite some promising efforts made by some individuals, the relationship between the expression of gene products such as specific enzymes and plant hormones is far from understood, although much information is currently being obtained about gene expression in particular plant tissues. The appearance of certain proteins and other small molecules directing the expression of genes and enzymes is being accurately and graphically mapped with development, often using impressive and colourful genetic markers, and there will soon be a huge dossier of information regarding these phenomena. But the directing mechanisms by which plant cells, particular organs and the flowers of plants take on their particular shapes and dimensions remain completely obscure. Unfortunately, the early promise of mathematical approaches to morphogenesis such as those of Alan Turing (1952) has not been realised. Turing laid the basis for a linkage between the new science of molecular genetics, then in its infancy, and morphogenesis. He outlined the essential features of the problem, relating them to the mechanical state of developing tissues describing the positions, masses, velocities and elastic properties of plant cells and the chemical state involving composition, diffusibility. He proposed to take into account changes in position and velocity of cells as given by Newton’s laws of motion, the stresses, including osmotic pressures, chemical reactions and diffusion. He introduced the notion of non-diffusible morphogens for genes and other diffusible morphogens as gene products (e.g. hormones). He was able to show using ring-shaped and spherical mathematical models and the University of Manchester’s new computer that certain well-known physical laws were adequate to account for many of the known facts regarding the growing plant embryo. The need for a continual supply of free energy to maintain these wave patterns for growth was shown. He even introduced some of the concepts related to development of catastrophe theory of the 1980s, such as metabolic oscillations, stationary and travelling chemical waves. This was a promising beginning, although Turing was modest about the extent of his success remarking that the principles which had been discussed “should be of some help in interpreting real biological forms”. Many others have attempted to build on Turing’s approach, or to develop new methods. But this promising beginning of almost half a century ago has hardly progressed. It is true that biologists such as D’Arcy Thompson (1942) of an even earlier epoch had developed a strong appreciation of the probable role of forces such as surface tension and minimising surface energy in the growth and form of organisms and the capacity of mathematical approaches to describe many biological body and sketelal forms. So we now have a situation where the very bulk of descriptive data is increasing without limit, particularly as the techniques of molecular biology are more widely

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applied. But lacking a suitable physical model to handle all this data, a considerable back-log can be expected. The frontispiece at the commencement of Chapter 4 showed some examples of the effects of surface effects on the deposition patterns developed on a microscope slide when a solution of asymmetric macromolecules and small molecules found in living cells is stressed. The most extraordinary patterns emerge in relieving these action exchange stresses, indicating that cellular structures can be spontaneously formed even in the absence of genes. The genotype ensures that such spontaneous processes can be directed so that structures characteristic of the morphology of each species are formed. 7.5.2. Evolutionary action With the advent of action resonance theory, a more deterministic viewpoint between the evolution of genotypes and environmental change could now be justifiable. As discussed earlier, Schrödinger identified the essential role of the quantum theory in this linkage of genes, environment and evolution when he further recognised the essential role of quanta in generating mutations in the genetic code-script. Thus, in one small book he laid down an extraordinary blue-print for the development of the science of molecular genetics that is just reaching its zenith in the biotechnology of today. In fact, action theory extends natural selection from the realm of the evolution of sets of genes to the developments involved in the very trajectories of molecules and the chemical reactions themselves. In action resonance theory, one can readily recognise that even the mechanism of generating genetic variation as a result of quanta causing mutations may be partly controlled by the environment. It may do this by increasing the frequency of mutation as a result of stresses in the environment. While we may consider that the rate of mutation is in some way controlled at a fairly constant rate by the internal chemistry or physics of DNA, like radioactive decay of unstable nuclei, when comparing different ages this is not necessarily so. Since intermolecular forces can easily be amplified in action resonance theory, particularly by collisions of massive objects, or even in active chemical processes such as wildfires, we should not exclude such crises from a role in biological evolution. It seems that our laboratory-based approach to science and the careful control of experimental conditions causes us to routinely dismiss these intermittent catastrophic states from our thinking, appealing instead to some steady-state rate of natural radiation to determine the rate of mutation. However, the reality is that such crises occur frequently in nature. Molecular geneticists even use ballistic projectiles as one means of introducing new genes into the functional chromosomes of other organisms such as plants and animals. So in addition to its direct role in mutation, we propose that action resonance can amplify the forces available in collisions and in other crises, so altering the action state of genetic material that accelerated evolution occurs. This prediction can be subjected to experimental testing, using the methods of molecular genetics with microbes, containing the most easily manipulable genetic material. In higher plants and animals, the development of each organism commences with the process of embryogenesis in which a single fertilised cell as a result of protracted divisions differentiates into separate tissues with separate functions. No-one supposes that embryogenesis proceeds by random or chance processes. On the contrary, it is a

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process clearly controlled by the genotype x environment interaction. As discussed above, the exchange forces of action resonance can be invoked to explain the orderly nature of this process of development. Yet the evolutionary development of new species is often regarded as a chance process. The dilemma posed by suggesting different mechanisms for individual morphogenesis and species morphogenesis from one generation to the next is a logical problem. However, we can escape this difficulty (Tomlin, 1977) if the origin of species is regarded simply as a gradual passing over of one species to another. Then the forces of morphogenesis of the individual can be regarded as the simultaneous cause of the evolution of species and the development of the phylogenetic tree, making use of the variation in genes from mutation. In that case, the genotype x environment interaction serves to explain both individual development and evolution, providing a unified mechanism of causation. To test this theory, we must also expect to find the causes of evolution in the genotype x environment interaction. There should be an obvious correlation between the origin of new species or the disappearance of old species and changes in the environment. From this viewpoint, species that appear to have become extinct may actually survive in modern day species ņ consistent with the supposed evolution of dinosaurs into birds. Even species appearing in the phylogenetic tree as an evolutionary dead-end nevetheless play a role in the overall evolution of species by their activity and contribution to the global genotype x environment interaction. Their very disappearance, if unable to adapt rapidly enough, provides the opportunity for new species to emerge, just as gas may flow spontaneously from one zone in space to another when these are connected as in the GayLussac experiment. Recognising the genotype x environment interaction as the driving force for evolution through action resonance would also explain the problem of diversity in nature. Darwinian selection allows the development of diversity but does not explain its occurrence, particularly when it is considered that the harshest environments often contain greater diversity. The action resonance theory, by contrast, actually requires diversity as part of the satisfaction of the principles of momentum conservation, least energy and least action. It can also explain how evolution leads to so-called higher forms of life. The processes of adaptation and natural selection of genotypes with advantages for survival do not necessarily lead to higher forms. Bacteria may be as well adapted to their environment as humans are. But, if the development of higher forms is seen as part of the forceful dynamic equilibrium generated by action exchange forces, then higher forms seem inevitable, just as the Boltzmann distribution for conformation of molecules is inevitable. Obviously, higher organisms will then be sustained by the action exchange forces of the genotype x environment interaction. 7.6.

Productivity in natural and agricultural ecosystems

The genotype x environment interaction has been illustrated in this chapter as a realistic, forceful encounter between an organism and the environment that gives it sustenance. Every organism develops from its earliest germinal material within the environment and its form and function is responsive to it. Prior evolutionary action has given it the genes

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required for a particular set of responses to the environment, expressed in the form of coupling agents for particular functions. These functions will allow each organism to grow and develop, to search its environment for nutritional materials and to carry out the biochemical and physiological processes necessary to ensure it continues all its life processes. Measuring the productivity of natural and agricultural ecosystems can be a perplexing task. Where a single output is desired or a general outcome is required, this may be measured. However, it is clearer by the year that no single measure of productivity is capable of giving a sufficient answer. The various externalities accompanying any productive activity, including negative environmental impacts but also various benefits in ecosystems suggest that a matrix function would be more appropriate to express what is being achieved. A problem in this kind of analysis can be unknown factors. For example, a major international ‘brainstorming” workshop held in the mid-1970s identified a set of research imperatives (Brown et al., 1975) that might contribute to agricultural crop production, to help meet the challenge of providing sufficient food for the increasing human population. This included a proposal to reduce the extent of photorespiration in C3-plants by plant breeding. As a result of later research in biotechnology, the proposal to genetically engineer one of the most common enzymes and proteins on earth, ribulose-bisphosphate carboxylase (Rubisco) in order to enhance the ratio of its carboxylase activity versus its oxygenase activity emerged. In C3-plants using the Calvin cycle to fix atmospheric carbon dioxide, Rubisco can either fix carbon dioxide, making two molecules of 3phosphoglycerate or fix oxygen from the atmosphere or chloroplasts in a reaction producing 3-phosphoglycollic acid as well. There is no obvious reason for the oxygenase activity and an extensive metabolic rescue process known as the photorespiratory cycle must be undertaken. This appears to be an energetically costly and pointless process. The author of this book suggested (Kennedy, 1989; Kennedy, 1992) that the oxygenase activity could be of importance in controlling the pH value of the chloroplast stroma, in producing acid to neutralise the alkalinity produced when nitrite is reduced to ammonia for amino acid production in chloroplasts. Two hydroxyl (OH-) radicals are produced for each nitrite reduced in the chloroplast stroma. In C4 plants, which lack photorespiration, the processes of nitrite assimilation and Rubisco activity occcur in different chloroplasts and it was further suggested that the evolutionary pressure for the development of C4 plants provided a solution to this problem caused by inorganic nitrogen nutrition. Several attempts to obtain research funding from Australia’s premier granting agency to test this hypothesis were not forthcoming. Perhaps this was because many plant physiologists have regarded the dual activity of Rubisco as nature’s mistake, and the agency preferred to fund research to rectify this mistake. In the interim, several research projects in Australia and overseas have sought to engineer the gene coding for Rubisco, substituting amino acids in the active centre in order to modify the ratio of carboxylase to oxygenase activity. These projects have all reported abject failures. No improvement in the ratio could be achieved, let alone an improved productivity from the C3 plants involved from energy saving using the genetically-modified Rubisco. The alkaline reaction hypothesis remains untested.

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A problem for researchers in describing and explaining functions of plants and other organisms is that they may not have a unique objective. It is a feature of action resonance theory that a solution to one evolutionary problem is likely to be complementary to other problems. Because life is an overall process of accomplishment from the complex genotype x environment interaction and because the selective mechanisms involved in achieving least-action, least-energy solutions may be optimised for several results simultaneously, we should not be too surprised if the two meanings of the word, function, are expressed ņ namely function as mechanism and function as role. If so, teleological outcomes are probable. Regarding energy needs, it is usual to consider the total energy as related to the enthalpy and entropy and to relate each to biochemical mechanisms. Action resonance theory presented here extends the potential role for energy in ecosystems. While the capacity to generate favourable high energy rH and rP values is clearly important, energy is required as quanta covering a broad range of frequencies, all of which are essential in sustaining living systems. The resonant quanta providing the turgor pressure in plant cells, allowing the plant to stand erect, are clearly just as important as the quanta allowing photosynthesis or protein or starch synthesis to proceed for storage purposes in the seed. We need to consider Haldane’s concept of the overall living process and to see the role of energy flux and the gradual dissipation of high frequency quanta to longer wavelength quanta. All these quanta may have a specific role to play in cell processes. Since all molecular motion is dependent on resonant energy and its associated impulses or actons, we cannot omit any of these stages of dissipation because the transport of chromosomes in mitosis may require resonant quanta of a particular wavelength. Equally, the folding of newly synthesized proteins may be achieved by quanta made available by particular oscillations or reactions. So the oxygenase activity of Rubisco and the resultant photorespiration might also assist C3 plants to generate specific quanta needed for cell processes, such as cell division and the function of microtubules. Such speculative suggestions need experimental testing, We should also expect to find some degree of harmony between the processes of an organism and those of the surrounding environment. Mutual advantage has rewards for both organisms, which can be selected simultaneously through the mechanism of action resonance fields. This possibility should be a warning for plant breeders. In the area of the breeding of legumes as new crops, it can happen that selection for agronomic traits is performed using inorganic nitrogen nutrition with chemical fertiliser, rather than with rhizobia for nodulation. Because the genotype x environment x genotype interaction now involves two organisms, action resonance theory would predict that the breeding process should be conducted in an interactive mode, varying the genotypes of both the legume plant as well as the Rhizobium bacterium. The host plant genetic control of the efficiency of symbiotic nitrogen fixation has been rather neglected. The late Alan Gibson discussed research work performed in this area (1988), drawing attention to early research of Nutman (1968, 1984) indicating the potential for good results in this area and subsequent work by a few score of researchers. Significant genotype x environment interactions were observed in the case of the tropical legume Spanish clover (Pinchbeck et al., 1980) and mean heterosis indicated that F1 crosses fixed an average of 78% more nitrogen than inbred parents. All these results indicate that significant advantages could be gained by

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evolving legumes cooperatively with their microsymbiont. However, the desirable outcome of actually heeding this suggestion has often been absent in legume breeding programmes. The use of suitably adapted soil or rhizosphere microbes as biofertiliser inoculants, capable of speeding up the mobilisation rate of soil nutrients such as phosphorus or even of fixing nitrogen from air when grown cooperatively with cereals such as rice or wheat or other gramineous crops such as sugarcane and maize, seems to have both environmental as well as a socio-economic advantages (Kennedy and Cocking, 1997; Kennedy et al., 2001, in preparation). In all these cases, due consideration to the implications of the two basic statements in this chapter on development, evolution and the action resonance theory for the genotype x environment interaction is essential. 7.7.

A cautionary note

The fact that no genotype can be expressed except as an energetic exchange interaction with the environment to which it is adapted must now be recognised. Not only does this deterministic interaction define the limits of growth and productivity for a given genotype, but it also provides the ultimate limits to the range of sustainable possibilities in evolution. Many characteristics of organisms involve multiple alleles of many genes. Thus, the range of sustainable proposals for biotechnology using genetic engineering that can easily be achieved is limited. Although Richard Dawkins has ameliorated his promotion of the primacy of the ‘selfish gene’, at least modifying it to that of the ‘selfish cooperator’ (Dawkins, 1998), he still prefers to depict the whole organism as derivative and somehow subservient to the survival of the genes themselves. This viewpoint overlooks the fact that selection can only operate by gauging the success of the genotype x environment interaction and thus the fitness of the organism’s phenotype, rather than being exerted specifically on separate genes. Obviously, a mutation in a particular gene that allows the whole individual to perform better has a greater chance of being selected than a mutation that reduces an individual’s fitness. So that individual genes simply must do what they are told. If they do not perform their task well, they will soon be eliminated by not being selected as a result of the relative inefficiency of their carriers. The particular role of each gene is meaningless unless expressed as an interaction with the DNA of many other genes of each individual. Therefore, it seems illogical for Dawkins to persist in his rejection of the individual organism as the functional means of Darwinian evolution. Only the performance of the individual can be used to test the hypothesis that one form of DNA as a gene is better than another. The advent of the action resonance theory, which strengthens the idea of the living genotype as a wholly interactive process rather than as the object of a linear sequence of bases of DNA, should raise serious doubts about the primacy of the selfish gene as a viable concept. Nevertheless, Dawkins should be congratulated for his positive achievements, such as dispensing with the concept of ‘blind chance’ as having a role in evolution, by his ardent promotion of the advantages of natural selection, in The Blind Watchmaker. The discussion he has fostered also allows us to see more clearly a critical difference between the natural selection of superior genotypes during evolution and the

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use of genetic engineering. Those who seek to obtain rapid advances by these artificial means of gene modification have a responsibility to recognise they are bypassing the normal phenotypic selection mode for superior genotypes. This anomaly poses a two-fold risk. Firstly, natural selection of superior mutants provides better insurance against lethal or damaging consequences in the future. The generation and testing of new genotypes in highly-regulated environments may fail to provide the degree of selection against negative developments that natural selection of phenotypes in variable environments would. Possibly, new tools being developed in genomics allowing the extent of up- or down-regulation of thousands of other genes at once to be monitored when mutations are made in particular genes can help minimise this risk. Secondly, the extent of the effects of variation in genes is almost infinite, because of their multiplicity and research could become a very costly process if alterations of genes are carried out one by one just to see what happens. Consequently, there is an urgent need for predictive models indicating the probable results of multiple gene variations. Even knowledge of the complete gene sequence of organisms does not help much, since the genetic code is not digital, merely selecting a linear branching sequence, or certainly not a three-dimensional blue-print. Instead, the tri-base scheme provides a powerful analogue field potential for a process using the multi-dimensional extension of Cartesian geometry, directly generating an intermolecular quantum state language with the most comprehensive grammar and punctuation. The action resonance theory can now provide a feasible method for analysing this space-time language and for sounding out its predictions. Therefore, an investment in the development of such predictive tools from the theory would be expected to lead to large cost savings in projects such as the study of the human genome. This is equally true for all the molecular proposals of biotechnology. 7.8.

The origin of life

In this book we have deliberately left out any discussion of the efficient cause of the origin of life, considering that Darwin’s statement given at the beginning of this chapter may still be valid. However, if action resonance theory is valid, action resonance exchange forces would clearly play a role in such an event. Since Louis Pasteur4 ruled 4

It is of interest that Louis Pasteur, although acknowledged as the founder of microbiology and immunology as modern disciplines, never considered it necessary in his work to use pure microbial cultures. Despite his insistence in his dispute with German chemists regarding the competing hypotheses that fermentation was biological rather than purely chemical in nature, he preferred to allow the environmental conditions to select the microbes that would be present. In his applied research from 1854 at the Faculté des Sciences at Lille, seeking to correct problems arising in local beer and wine-making, the young chemist concentrated on providing good environmental conditions using natural inoculants, inventing pasteurisation by heating fermentations of wine or beer to about 600 C for a few minutes to reduce the numbers of pathogenic microorganisms. In fact, he never worked with pure cultures of yeasts or bacteria, an attitude he maintained even later when with public subscriptions in gratitude for his immunological work on human diseases he was able to establish the Institut Pasteur in 1888 near Montparnasse in Paris (Jean-Paul Aubert, Institut Pasteur 1994, personal communication). We can now recognise that Pasteur was relying on thermodynamic control of microbial populations and due recognition of the power of the genotype x environment interaction. Ironically, it was left to a German microbiologist, Robert Koch, to define the precise method of

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out the spontaneous generation of life from organic materials in his famous experiment using ‘goose-necked’ flasks at the Institut Pasteur, chosen to prevent the settling of microbe-carrying dust particles into his growth media, this question has remained as one inviting speculation embedded in the distant past, without definitive answers emerging. Charles Darwin’s admonition quoted at the beginning of this Chapter remains as relevant as ever, since we are seemingly still far from obtaining this knowledge. This is not from want of examination of the question of life’s origin, with the likelihood that life even began on earth now seemingly doubtful (see Davies, 1998). However, the argument that life will emerge if we are patient enough to “throw the dice” enough times, simply as a result of the ‘laws of chance’, can definitely be rejected. A clear conclusion of action resonance theory, from the principle of conservation of momentum in the forceful interaction between energy and matter (see Chapter 2), is that the passage of time cannot ever allow thermodynamically improbable events to occur. Therefore, we could conclude that life was initiated as a result of a spontaneous juxtaposition of matter and energy, directed by a dynamic template provided by the universe itself, as a naturally programmed event. Quite possibly, the probability of this event was 1.0. Dawkins has rightly emphasised that there has not been enough time for life to have emerged by blind chance, given the huge range of unproductive possibilities available. Further, he has shown that natural selection provides a mechanism to shorten the time required. The deeper understanding of the simplicity of natural selection now available with the action resonance theory emphasises how unimportant a role blind chance has played in the development of life systems. Furthermore, a new possibility emerges that simple forms of life have always existed from the moment that conditions suitable for its sustenance were reached, as part of the process of condensation of energy as matter and further cooling to extract more energy that physicists propose followed the Big Bang (Davies, 1998). If the necessary molecules were formed spontaneously as part of its creative role simply as a result of action exchange forces, all that would be required to initiate life would be the necessary physical and chemical conditions and a short time for diffusion and assembly. Nature, allowing the genotype x environment interaction to be so expressed, would then spontaneously nurture life.

proving the causal relationship between microbe and any process, such as disease, in the experimental protocol known as Koch’s postulates. Louis Pasteur’s career is a fine example of the point of view that there is no true distinction between basic and applied research because one should always interact with and support the other. It may be possible to isolate aspects of a problem for basic study, but in the interests of efficiency and eventual application, this should usually be conducted as part of a collaborative research programme.

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THE ACTION RESONANCE THEORY

The Vitruvian canon of human proportions. Drawn around 1490, Leonardo da Vinci’s fascinating design (held in the Accademia of Venice) is based on a geometric prescription given by the Roman architect Vitruvius and provides a fine example of the symmetry (or asymmetry) found in nature. In action resonance theory, all such symmetry is a natural outcome of the balancing of forces as part of the interactive action field of matter and energy. The drawing is remarkable in containing sixteen alternate poses for the human figure, each representing a different action state in the gravity field. This and other drawings by da Vinci (see Gibbs-Smith and Rees, 1978) also exemplify the spirit of processes in action, such as those in which he depicts turbulence developing in impeded water flow. Reproduced with permission of the Accademia of Venice.

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“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory, in which it lives on as a special case.” Albert Einstein, Über die Spezielle und die Allgemeine Relatavitätstheorie Braunschweig: Viewig, 1917.

“…. God alone is the author of all the motions of the world in so far as they exist and in so far as they are straight, but that it is the various dispositions of matter that render the motions irregular and curved. …. the theologians teach us that God is also the author of all our actions, in so far as they exist and in so far as they have goodness, but that it is the various dispositions of our wills than can render them evil.” René Descartes, quoted from Descartes (1664): The World, Stephen Gaukroger, ed., Cambridge Texts in the History of Philosophy, p. 30, Cambridge University Press, ISBN 0-521-63646-9, 1998.

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Chapter 8

THE ACTION RESONANCE THEORY The action revision A metaphysical research programme

8.1.

The action revision

The reader, having persisted this far, will surely have perceived some of the unique features of action, its relationship to energy and its significance in evolving ecosystems. A few, like the author, may even have become excited by the potential role of action and the means proposed of linking together the fabric of science in a way never previously thought possible. Perhaps some readers will already have applied action theory, at least qualitatively, to examine and solve problems of their own. This would be most pleasing, since encouraging the use of the action theory by others was the author’s sole objective in writing this book. It is unlikely, however, that many readers will have seen as broad a range of potential applications of the action theory as the author and his colleagues. We commenced its development by various interactions with many colleagues beginning 20 years ago and have now had ample time to examine its ramifications. The integrating consequences of action theory were realised by the author years before the writing of this book was commenced in late 1997, but always seemed much too ambitious to pursue. However, it is not necessary here to include a detailed discussion of all these aspects and consequences. Indeed, most were deliberately omitted from this book, partly to provide a challenge to the reader to explore now or later; there is no area of science and technology that would not, in our opinion, benefit from revision in terms of action theory. This universal approach was deliberately born of a Cartesian experience of the author, around the late 1970s. This was Descartes’ recommended method (Descartes, 1637) of consciously doubting received scientific dogma before re-admitting only those elements considered as clear, logical and essential. It is for that reason that some concepts frequently used by contemporary scientists and prominent in nearly all physical and chemical texts are not even mentioned here. For example, little or no use is made of the familiar and useful concepts of charge and voltage in action theory. Nor is it necessary or desirable to do so in future. The main thrust of my argument has been to emphasise the role of external action exchange forces in generating the coherence of molecules, molecular systems and even whole ecosystems rather than to rely on central attractive forces, such as the hypothesis of opposite charges. The idea of equal and opposite charge enables one to model their binding force as though the two charged species were isolated objects in the universe, but considering any object in isolation is contrary to the basic statements of the action theory. It will, of course, remain necessary to recognise a specific periodic interaction between electrons and protons sustaining their coupling via

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exchange of quanta ņ an interaction not possible between electrons and neutrons. But with action theory, understanding and explaining their bonding and the mechanism of interaction by energy quanta now seems more open to investigation than ever. This can certainly be achieved without the notion of attractive opposite charges, which has been a convenient assumption since the 19th century, but not a real explanation at all. Even magnetic forces in action theory can now become a realistic problem of dynamic geometry, specifically involving the factors of orientation, screening and synchronicity of electronic orbitals and spin. This sets the magnitude of the dispersive action exchange forces somewhere between zero (attraction) and some maximum value (repulsion) depending on these factors. As for the multifarious sub-nuclear particles from quarks to neutrinos proposed by atomic physicists to have at least transient existence – should they ever become interested in joining the action revision to better comprehend their nature, Feynman (1967) in his theory of world-lines and exchange forces has already provided the basis for this task. This would best be physicists’ responsibility and is far beyond the scope of this book. But it can at least be pointed out that one must begin by inverting the direction of the strong interactions, recognising that actons transfer momentum and force from the rest of the universe, thus cementing the nucleons together by exerting pressure from outside. The problem now becomes how to explain what sustains the structure of nucleons and the nucleus, holding them apart, preventing their collapse and disintegration into energy as occurs in fusion on the sun, rather than of what holds them together. All the families of sub-nuclear particles found in accelerators may then be considered as the special creations of the environmental conditions in which they are detected. Couplings can be understood as dynamic balancing or temporary equilibrium of internal and external forces exerted on material particles by actons, which are themselves self-caged, condensed actons. This conjecture has the potential to simplify the overall problem of the nature of matter and energy enormously, by potentially reducing the fundamental number of elements required in the universe to just one – the acton. It has been inferred earlier in the book that even the concept of gravity as a central attractive force may need an action revision, for the sake of a consistent theory. We do not resile from this undertaking and will tackle it later in this chapter and elsewhere in future. But the basic statements of action theory outlined in section 2.2. apply just as well to the generation of gravitational fields by planets as to van der Waals’ forces generated by molecules. Given the extremely large values of the action states involved, gravitational quanta would involve almost infinitesimally small variations in energy states. These could logically involve uncoupled actons or quanta approaching infinite wavelength or zero frequency, corresponding to radiative emissions or reflections from bodies at or very near the absolute zero of temperature, and in fact comprising the zero point energy. Unlike the electromagnetic forces of electrons and protons, these interactions would also allow resonances between neutrons as well as electrons and protons, allowing all matter to participate in gravitational interactions. But these ultralow-frequency radiative emissions would necessarily sustain the space between material bodies in stable orbits with streams of energy-momentum carried on actons of extreme impulsive intensity but generally leading to no net acceleration to different action states because of the existing overall balance of forces. Even in the long term in the vicinity of

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the earth angular momentum and action are conserved at this scale, except in regions of major energy fluctuations. The reason for the acceleration of a falling apple may then be explained, just as for condensing raindrops, as an anomalous result of the sudden withdrawal of its sustaining potential energy. This is real resonant energy, derived partly from sunlight, holding up the apple as an integral part of the apple tree. The weight of the tree itself is sustained by resonant energy in the soil and the earth beneath it. In biochemical terms, we can remark that abscissic acid production in the stalk of the apple has weakened the inter-molecular bonding of the adhesive cells as part of the process of ripening, eventually causing a break or abscission in physical structure. The real potential energy formerly enjoyed by the apple and sustaining it in its place in the universe was immediately transferred to the branch of the tree, becoming slightly less burdened and rising in the gravitational field appropriate to the change in the weight of its fruit. Obviously, the rate of acceleration of the apple as it fell towards the earth can provide an exact measure of the imbalance between the flux of momentum carried on actons from above the apple and the flux of momentum carried on actons emanating from beneath the apple. Because of the screening provided by the matter of the whole earth implied in the statements of the action resonance theory, this imbalance naturally results in a negative dispersive force, appearing to be attraction. So this net force of actons from the outer part of the universe accelerates the matter of the apple towards the centre of the earth (and, ever so slightly, vice versa for motion of the earth towards the centre of the apple). For the sake of simplifying the problem we can ignore the impulses of the energy arising from the universal field of potential energy, as Newton did and that western scientists have implicitly agreed to do ever since. Instead, in the Newtonian theory we focus on the small differences in the gravitational field with direction (i.e. up versus down). Or, as Einstein sought to do in his theories or relativity in the first decades of the 20th century, we can recognise the probable reality of the huge ocean of radiating energy sustaining the universe implied by E = mc2. We may then reasonably conclude that the difference between the rate of impulses from actons directed from above and directed from beneath the apple with its severed stalk is equivalent to an acceleration or rate of change of velocity of 980.7 cm per second per second1, at the surface of the earth. As an approximation, the acceleration remains constant since the difference in intensity of 1 This would be a net normal impulse equivalent to a 980.7 g.cm sec-1 for each gram of the matter in the apple, or the impulse from an excess of actons equivalent to 2.940 x 1013 ergs or 2,940 kJ of energy per second. If carried on quanta transmitted at the speed of light, this integrated impulse would be generated from a hemisphere extending out to 3 x 1010 cm for each second, their direction corrected for the angle of incidence. This difference would be about 107 times greater than the intensity of the impulse given by the quanta of sunlight on the earth. While this concept regarding unseen or dark energy seems extraordinary at first, it may be feasible in reality, since the difference represents only one part in 107 of the total energy implied for each gram of matter of 9 x 1020 ergs, from Einstein’s relationship E = mc2. If the primary impulses or actons, rather than their cooperative expression as quanta, could be exerted even faster than the speed of light, the required differential in impulse would be amplified by the appropriate factor. The resultant net acceleration at any distance r from the centre of the earth can easily be established from the observed value of the earth’s characteristic celerity (see Glossary/Endnotes, since this indicates the centrifugal acceleration that is required to balance the centripetal acceleration, generated by screening, towards the earth’s centre of mass: Celerity a3ϖ2 = Ca Acceleration rω2 = C/r2.

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actons from above and below remains constant as long as we are considering objects located near the radius of the earth subject to the same degree of screening by the earth’s matter. Apparently, each gram of the dense point masses of the constituent particles of the spacious apple is equally accessible to impulses from actons over the relevant period of time. Until the abscissic acid did its bond-weakening work, these up and down forces were in balance, as long as no wind blew or no bird alighted on the branch. Such a difference in the rate of impulses from actons on matter from the different directions, once a situation of non-equilibrium is temporarily generated, must then indicate a necessary property of the dynamic geometry of space and time in the universal interaction between matter and energy. We now have a rational explanation for gravity, as the relative absence of sustaining force from the down direction, but only for anomalous cases such as apples felled by abscissic acid and falling raindrops formed by convective cooling of humid air whose location is space no longer sustainable. These material objects must fall - until such time that there is equilibrium between the up and down forces, re-established by interaction on the ground. All these consequences of action theory arise from the basic statement in Chapter 2 that action exchange forces result from superficial impulses of energy quanta composed of the individual impulses of actons exerted on the internal and external surfaces of molecules. This proposal was based on the findings of Einstein regarding Brownian particles (1917). But his important finding is extended here to propose that all force fields have the same basis. Since molecules sense all impulses as equivalent, they need not distinguish between their sources, but will merely respond to the total integral of the impulses, to conserve momentum. Future developments will show if such a radical departure from the notion of unchanging central force fields controlling the motion of accelerating particles and bodies opens the door to remarkable new means of locomotion. It is predicted here that it will. In action resonance theory, individual or collective motions of molecules result entirely from the local action of impulses and the emphasis moves from the passive idea of the inertia inherent in bodies to the active idea of impetus constantly generating new states of action. Both the inertia of matter and the structural integrity of any system are continually being sustained by local impulses. This prediction of action theory should simplify the problem of achieving acceleration and transport to any desired destination. These are all cases where one might reasonably conclude that the action resonance theory is merely another physical point of view, and nothing new. This is true, as this book has sought to demonstrate. However, there are so many strong departures from current scientific opinion in the action theory here outlined, such as that regarding the source of inertia, that a new set of solutions and insights, possibly with radically different effects, are expected from testing and applying the action theory. 8.1.1. Action resonance, quantum theory and life In the 19th century, science advanced on broad fronts. Classical physics and chemistry were formulated. But its most enduring products that are dealt with in this book included equilibrium thermodynamics, a highly appropriate development in the industrial age of steam and simple heat engines. In biology, Darwin’s much heralded theory of evolution

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based on natural selection by the principle of fitness for a particular environment, and the more quietly accepted but related theory of inherited traits or genes, advanced by Mendel, were outstanding developments. Science in the 20th century has been dominated by three main new developments. These include the related theories of special and general relativity, advanced by Albert Einstein in the first two decades of this century and drawing attention to the significance of the limits imposed by the maximum speed possible for the transmission of light. It has been hinted here more than once that the more difficult predictions of these theories may become more easily understood and emerge naturally in action theory. Einstein provides numerous clues for achieving this project in his other papers, where he discusses the forceful interaction between energy and matter and the role of impulses in moving molecules. Making use of these clues and the insights provided by action theory is an important future project. The reluctance of some physicists such as Percy Bridgman (see Bridgman, 1983), himself a Nobel laureate, to accept that special and general relativity corresponded to physical reality, leading to his strong promotion of these theories and all scientific theories as merely operational, can be understood. However, the strangeness of mass increasing to infinity as velocity approaches the speed of light, of length contracting at the same rate and space being curved may now be explained in terms of simple reality as action. Like charge, action is relativistically invariant with the change in velocity of matter. Indeed, if action resonance theory has such a wide range of applications in the world of everyday objects as this book claims, it would be surprising if it had no relevance for the theory of relativity. Conversely a prediction is made here by the author, based on the significance of action resonance in generating dispersive intermolecular forces, that both special and general relativity have significance for life systems and consciousness itself. We hope to explore this area in future. There is also the brilliant theory of quantum mechanics, initiated by Max Planck and Albert Einstein and extended mathematically to predict energy levels in molecules and molecular spectra by Nils Bohr, Erwin Schrödinger, Werner Heisenberg and many others. A reconciliation is needed between action theory and various aspects of quantum theory including the fundamental quantum-mechanical commutating relation2 of Heisenberg (Born et al., 1926), involving the multiplication together of matrices giving physical dimensions of action. Schrödinger’s (1926) wave equation, related to Heisenberg’s matrix mechanics, would also benefit from this revision, yielding a more realistic model relevant to molecular structure. Both of these approaches employed Planck’s quantum of action as the natural unit. There is an opportunity for a better understanding of the uncertainty principle using action resonance theory for analysis of the scattering of light and electrons from slits. The wave character and interference patterns involved become physically explicable when action resonance traversing the slit is considered to provide the basis of the statistical scattering. The narrower the slit the greater the exchange force generated and the greater the scattering. This analysis can now provide confirmation of the scattered but still deterministic nature of this quantum phenomenon, of such importance to an individual electron. The fuzziness introduced has no power to turn the tide of events of human affairs. The clear and rational philosophical insights of Karl 2

pq – qp = h/2πi.

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Popper (1982), in terms of the propensity interpretation of the wave equation for the electron, may provide welcome guidance in this project. As a ‘rough and ready’ start, a rudimentary action revision for the model of the Bohr hydrogen atom is provided in the Glossary/Endnotes. The most recent development of the 20th century, molecular genetics – its programme initiated by Schrödinger by his book What Is Life? completed in Dublin in 1944 – has been extended by J.D. Watson, F.H.C. Crick, A. Kornberg, J. Monod and even more actively recently by many others. So well have the techniques of this disciplinary area been worked out that the mapping of the complete chromosomal base sequences for a microbe, for a plant or even for the entire human genome, has been undertaken and will probably be concluded as you are reading this book. The significance of action resonance theory for interpreting the information and protein structures predicted by these sequences, many millions of bases long, was dealt with more explicitly in Chapter 7 as the genotype x environment interaction. No apology is made for directing attention to the very earliest substantial findings in these areas, for it is here at the heart of the matter that reconciliation should most readily be achieved. The rest will follow. It is to be hoped that this enterprise will prove successful soon, because a crisis has been developing, perhaps unnoticed in these days of contracting research funding, for biology in general and molecular biology in particular. Despite the rapid early advances made, mainly in the first half of the 20th century, it has proved too difficult to solve mathematically the complete wave equations for even the simplest macromolecule in living organisms, or even for ATP. As a result, both physics and chemistry are currently contributing relatively little to the advances now being made in agriculture and medicine. More and more scientists are now needed to work in areas of remediation of environmental and human health, repairing damage resulting from the mis-applications of 20th century technology. Empirical methods are increasingly being used to solve problems - such as those related to structure and function of enzymes, other macromolecules and the design of medicines and agrochemicals. For example, if we look at macromolecules as independent objects, like widely separated gas molecules, we will fail to predict accurately their properties such as how a newly synthesised protein will fold in its actual physical and chemical environment in the cell. These empirical methods will also prove completely inadequate to handle the huge numbers of possible choices to be made of what to do next, since they work only on a case-by-case basis and provide few general principles. Interpreting the DNA code-script in the complete genome of even a simple plant like Arabidopsis thaliana will present so many possibilities that valuable funds are bound to be wasted. For the human genome, where the vast majority of the DNA codes are for unknown products with unknown function, it may take a century or more to unravel, by an army of researchers. Perhaps we can say that Schrödinger’s blueprint to obtain knowledge about what life is, prescient though it was, by now has run out of steam. But his vision can be re-stoked. Action theory, with its emphasis on providing realistic physical models as dynamic three-dimensional maps of the force fields needed to sustain these structures in their local environments, may now provide the answers, once suitable computer models generating these dynamic maps can be prepared.

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8.1.2. A role for action biothermodynamics An extended role of thermodynamics has continued to intrigue some scientists. Although molecular genetics and biotechnology currently holds sway as the discipline widely considered as most useful to science and humanity, there have been a few savants like Ilya Prigogine and the Katchalsky brothers, who recognised that thermodynamics still poses the most fundamental questions in science. It is the only discipline that can define the range and the limits of what can be achieved. No degree of excellence in genetic engineering can develop a biological result for which there is no spontaneous propensity, favoured by the underlying thermodynamic forces. The fact that many molecular biologists are now completely ignorant of the nature of these forces, proceeding largely on the basis of trial and error, emphasises how much more efficiently we could proceed with better knowledge. The action resonance theory could be called the ‘poor-man’s theory’ of fields and of non-equilibrium thermodynamics. It is deliberately designed to operate with as few working concepts as possible. It makes only a small number of basic statements using no principle other than the conservation of momentum in its physical model of energy interacting with matter. All other rules of physical, chemical and biological behavior can be considered as derivative, results constrained by the local dynamic geometry of matter. It can build on all of the developments of the 19th century in thermodynamics, quantum theory and even relativity, readily subsuming them. Thermodynamics can now be seen as the statistical outcome of many individual cases of particle dynamics, based on the principle of conservation of momentum transmitted via impulses from quanta. This is a poor-man’s theory not least because it actually proposes nothing new. By adopting a common-sense approach to the postulates of previous theories, it merely seeks the common elements of truth in each. Sometimes it finds that ideas that were criticised and even scathingly rejected by previous generations may in principle be reinstated in the action resonance theory and reconciled with their successors, with better explanation. The first premise involved in the development of action theory was that some common basic elements, essential for progress, had been long overlooked. Another important premise used was the test of simplicity. A universal theory of any practical value would need to be simpler than any current theories rather than more difficult. If so, the universal theory could surprisingly be discovered by anyone, without the exercise of genius or rare intelligence, or requiring the use of complex mathematics. Rather, it would always have been available to anyone of normal intelligence, its key assumptions already being used now and then from the time of the academies of the ancient Greeks or even much earlier. This implies a key tenet for action theory that understanding the world lies easily within ordinary human understanding, as the late Karl Popper would have preferred, simply by the rational exercise of common-sense. So we propose that action theory has simply lain there mainly obscured, a golden nugget or multifaceted diamond periodically partly emerging to view but then quickly being resubmerged in the dust. Still, it would be accessible even by a simpleton stumbling across it, curious and interested enough to bend down to examine it when it shone, to pocket it; and, later, patient and persistent enough to use it to refract and re-focus his sources of knowledge. Most importantly, one needed to be perverse enough to look in the wrong

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direction in order to catch its brilliance, better eyes askance or downcast, casually stubbing a boot cap or toe from time to time into the surface soil. Certainly no theory to be found from searching in the heavens nor in today’s splendid ivory towers of academia, nor in the latest current top-echelon scientific journals. Excellent as these might be as sources of new knowledge and learned erudition, they could never conceal this philosopher’s stone so well as the dust of the winding road. Although this book merely sketches an outline of the action resonance theory, enough has been said to illustrate how the theory may also attempt to pass the third essential test, that of universality. Karl Popper pointed out that the most remarkable advances in science occurred when a new theory could accommodate the predictions of the old – such as Einstein’s general theory of relativity accommodates those of Newton’s theory of gravitation – and then should make new predictions covering new phenomena like the rate of precession of the orbital perihelion of the planet mercury. Finding out if the action resonance theory has this quality of universality should now be the task at hand, but one happily much too large for any individual or group to undertake. The evolution of all physical, chemical and biological systems on earth can be considered as dynamic processes of natural selection, using the same basic principles of conservation of momentum and energy and minimisation of action exchange forces. Quantum theory should no longer be considered a specialised area of study for a small number of elite scientists. All action is clearly quantised because of the impulsive unity of the acton and now quantum theory must be concerned with all changes, no matter the scale involved. The problems raised by special and general relativity regarding mass, length and time are a product of mathematical approaches based on Euclidean geometry and ideas of absolute linear time. Finding common-sense solutions to these problems is now possible. This will require acceptance that all action is local action derived from quantised exchange forces, and that time itself may be quantised and based on relative angular motion, relative to signals as exchange forces originating elsewhere in many different epochs. Means now exist to re-evaluate the physical meaning of the Schrödinger equation and matrix mechanics as action resonance mechanics. The promise in action resonance theory is that simpler methods to model the structure of macromolecules and their interaction and catalysis itself may now soon be found to complete Schrödinger’s vision expressed in What is Life? Furthermore, there are prospects that the genotype x environment interaction will now be amenable to study in the same way as simpler systems are with action resonance theory. We now have at least the beginning of a means of approaching such problems as embryological development in plants and animals and of estimating the limits of food and fibre production on earth with available resources. Even more intriguing theoretical problems of natural, psychological and social sciences may be amenable to study, but we will leave these possibilities to the reader’s imagination.

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8.1.3. Action resonance is not vitalism The dynamic and continuous juxtaposition of energy with matter in living cells essential to action resonance theory may suggest the vitalist ideas of the past, long discarded by scientists. This suggestion could not be more wrong! Action exchange forces are proposed to be real physical impulsive forces, present in all molecular systems both living and dead. But the non-living usually has more chaotic dispersal of these action exchange forces, less capable of concerted and purposeful activity. This explanation for the vitality of organisms (temporarily captured in ATP) provides a universal force, only contained for a time within each organism but continually flowing across its boundaries and being exchanged with the surrounding environment and other organisms. This is the same force that generates the weather, or storms in the ocean and on the sun. It even sustains the entire universe. Early in the 20th century when the quantum theory was being born, J.S. Haldane, FRS, (1921) strongly criticised the idea of ‘vital force’ or ‘vital principle’ as a non-physical factor guiding the processes occurring in living organisms as worthless to science as it suggested no experimental programme. Even Hans Driesch’s later refinement of vitalism in Leipzig using the old Greek idea of entelechy, based on his studies of the blastula of the sea urchin – a term for the organising principle still referred to today in the literature – did not rescue vitalism from Haldane’s criticism. Incidentally, Haldane rejected vitalism partly on the grounds that it contravened the first law of thermodynamics since guidance of living organisms implied a creation or destruction of energy. But more importantly, the hypothesis provided no testable predictions, suggesting only that the organisation of a living organism cannot be understood by the aid of physics and chemistry alone. However, it is of interest that Haldane also did not accept that the dualistic theory of living organisms simply as physico-chemical mechanisms, as advanced by Descartes in De Homine almost three centuries earlier, was an adequate replacement for vitalism. Indeed, he was at pains to show that the mechanistic aspect of this theory was also inadequate to explain life. The main strengths of the mechanistic theory arose from the fact that all physiological activity in organisms was apparently correlated with physical or chemical causes. Also, the mechanistic theories were capable of being experimentally tested. But Haldane considered that living organisms did possess more than merely physical and chemical mechanisms, energy and matter. He recognised that the continuity of function of living cytoplasm through time and the ongoing exchange between organism and environment was a function of the activity of the organism as a whole. Many scientists today would agree that this continuity of activity in the cytoplasm of all living organisms has existed ever since the first living cell was formed. According to the Darwinian theory of evolution, for more than four billion years life has been transmitted from one cell to the next through all the generations like a fire that has never gone out. So in deciding what it means to be living it was most important for Haldane not to separate the study of living matter or structure from its activity. The biological structure itself should always be conceived as simultaneously active – the very essence of being

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alive! The statement by Schrödinger that life feeds on negative entropy from the sun would seem scarcely different, from Haldane’s view. This focus by Haldane on the life process itself rather than just the physical or chemical mechanisms that could be measured separately has coincidences with action resonance theory. As mentioned earlier, action theory is above all a biological theory, designed to deal with living organisms in their interaction with their environment and to explain elements of their operation and organisation not readily accounted for by traditional physics and chemistry. Although action existed before cellular life, there is a sense in which the power to cause changes in action states or quantum states by the fluctuations in the flow of energy was from the beginning a sign of the propensity for life. This sense foreshadowed and even directed the origin of life itself, in primitive selfreplicating processes, acquiring knowledge by providing memory and allowing recreation of particular action states that relieved chaotic conditions causing excessive local action exchange forces. We may consider that life began somewhere with the right mix of chemicals in water at the right temperature, producing a cytoplasm with some means of storing its blue-print or code-script for repetition. Wave-like changes in action state of this cytoplasm as a result of periodic fluctuations in energy flow with each sunrise and sunset may have provided essential preconditions for life. This ebb and flow would give a basic repetitive mechanism selecting from alternative chemical candidates for storing information that coded for the production of simple coupling agents. The language of the genetic code is not arbitrary but is itself a result of natural selection. The best matching of bases and amino acids would be selected naturally by energy fluctuations and action resonance, using the principles of least-stress and least action based on the conservation of momentum. Less successful or unstable essays could be sorted and eliminated by the cooler conditions at night while this forcing principle would be more relaxed. However, this rudimentary account merely serves to show how ignorant we are about the origin of life. The only appropriate response is a sense of absolute wonder at this event and the unique conditions that must pertain in the particular epoch and locality where life began. We can state though, with the benefit of the action resonance theory, that these special conditions involved forces derived from a global interaction with the complete environment that the universe provides. We can therefore imagine that the universe itself provided the forceful counter-template on which life is based. Whether one considers that the particular juxtaposition of the universe’s matter and energy involved was determined as a result of mere chance or as an expression of the mind of God must be a matter of personal belief. Science alone is not fit to decide between these two viewpoints. Nevertheless, in a physically real sense the genotype x environment interaction has existed most intimately from the first moments of life. We may justifiably conclude that the propensity for life is a natural expression of the interaction between matter and energy that existed from the moment that the universe began. Action theory and changes in action state emphasise dynamic process rather than the physical and chemical mechanisms of ecosystems. The latter are merely the Brownian scaffold on which the dynamic life processes take place. The focus shifts from being to becoming in action theory and the organising linkages of processes spontaneously set up between energy and matter in the development and evolution of these systems. A living

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organism is no longer merely a set of physical and chemical mechanisms that responds to certain physical or chemical stimuli but a dynamic process of continuous and indefinite duration. Physiologists like Haldane could monitor various properties of organisms such as oxygen production or consumption, carbon dioxide production and pH values. But, as he recognised, these values are nothing more than indicators or correlates of the physiology of the organisms interacting with their environment. Organisms are not selfexistent objects and such measures do not provide integrated knowledge associated with each species of plant or animal. For this reason, the increasing use of video bringing us television programmes like the BBC’s Life on Earth has real value that static text or tables of statistics can never convey. We need more action models of organisms as processes in given environments rather than as material objects, i.e. less structure and more function, if we are ever to fully understand their needs. 8.1.4. Electromagnetism and gravitation The neglect in this book of many of the familiar physical concepts of electromagnetism and gravity does not mean that these concepts are now invalid. It is merely a proposal that action resonance theory can readily accommodate all the important outcomes of Faraday’s and Maxwell’s theories of electromagnetism – although no serious attempt will be made to demonstrate this here. In other words, it is claimed that rational primary dimensions of mass, radial separation or range and frequency should also suffice for the properties of a suitable physical theory of electromagnetism. For this revision, it would be desirable that all exponents for these dimensions should be integers, rather than the fractional exponents for mass and length characteristic of charge and voltage3. The derivative factors of linear momentum or impulse, rate of change of momentum or force, and the rotational equivalents of angular momentum or action and energy or torque, should provide an adequate action theory of electromagnetic fields without the need for abstract factors with fractional exponents. Obviously, a similar restriction should be placed on the factors used in describing gravity, radioactivity and nuclear interactions. In the action resonance theory, inertia as a force tending to continue motion of a body in a straight line is replaced by continued curved motion as the net result of the integration of all previous and current impulses on the body - an outcome that we may refer to as its impetus. A body with great inertia is one exchanging more energy and therefore most resistant to changes in its current state of motion, that is hardly ever in a straight line. Only if all other matter and energy in the universe were suddenly removed to infinity could a body continue in a straight line. Straight line motion of particles or massive bodies in real systems would require continuously fluctuating changes in energy state whereas the natural state of motion for an equilibrium system is curved, at constant total energy and action, as concluded by Einstein in his theory of general relativity. This recalls that Galileo favored impetus or kinetic energy over the inherent inertia of bodies, when studying their motion under gravity. Newton, of course, later appealed to the idea of linear inertia as an essential property of bodies, installing it in his first law of 3

Charge has fractional physical dimensions of m1/2r3/2ω and voltage of m1/2 r1/2ω.. We can observe that the product of charge and voltage generates energy (mr2ω2), indicating that each property is a complementary aspect of the system’s energy, rescuing them both from the fate of an obscure and irrational physical meaning (see Endnotes for discussion of dimensional analysis).

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gravitation as an essential feature of their motion. He then introduced the simplified idea of gravitation as a central force of attraction4 to describe the elliptical motion of bodies in orbit around a central body. So the straight line motion caused by inertia is curved by the force of central attraction. This ‘saves the appearances’ by replacing the abstract quality of straight line motion with the elliptical relative motion actually observed in a gravitational system at equilibrium. A similar approach is taken by physicists to motion under Coulomb electrical forces where bodies are assigned opposite charges (traditionally, positive or plus and negative or minus). Note that in action resonance theory, the “pluses and minuses” of protons and electrons must have some real physical meaning related to the rate of exchange of actons between like and unlike charges. Thus attraction or coherence results from a lower mutual rate of exchange of momentum from a particular direction and repulsion from a higher rate of momentum exchange from others. In contrast to the concept of the absolute attraction or repulsion of independent positive and negative charges assumed by the Coulomb law, the dynamic balancing of mutual action resonance exchange forces within chemical species and with the matter of the rest of the universe is substituted. Attraction or repulsion is then the net outcome of interaction between chemical species from positive impulses, with the actual trajectories of the material species involved determined by the balance between these consistently positive dispersive forces. Thus, the acceleration of a falling apple as an irreversible, non-equilibrium process results from the absence of dispersive force from the direction of the centre of mass of the earth acting from the moment when the apple breaks its bond to the tree. Rather than being the presence of an attractive force, gravitation becomes the absence of a repulsive force, but having exactly the same effect as an attractive force with action at a distance. Plainly, the action is immediate, seeming to occur with infinite velocity, since it always represents the instantaneous balance of impulses reacting on the matter of the apple. Similarly, electrical polarisation of molecules by redistribution of electrons, charge and voltage can still exist in action resonance theory, but does so as the derivative of action exchange 4 It should be noted that Isaac Newton, other than as a mathematical formalism, never insisted that the force of gravity was essentially attractive. On the contrary, he was most unhappy with the idea of a force having instantaneous ‘action at a distance’ for which no mechanism could be advanced. He usually avoided defining the nature of gravity. In the Scholium generale at the end of the Principia Mathematica he commented ‘So far I have explained the phenomena … by the force of gravity, but I have not yet ascertained the cause of gravity itself … and I do not arbitrarily invent hypotheses’. In the second edition of the Principia (1713), regarding gravitational attraction he said, ‘I here use the word attraction in general for any endeavor whatever, made by bodies to approach each other, whether that endeavor arise from the action of the bodies themselves, as tending to each other or agitating each other by spirits emitted; or whether it arises from the action of the ether or of the air, or of any medium whatever, whether corporeal or incorporeal, in any manner impelling bodies placed therein towards each other’. Elsewhere he stated ‘What I call attraction may be perform’d by impulse, or by some other means unknown to me’. Thus, it seems that Newton’s view might well have allowed gravitational attraction as the net outcome of mutual repulsions between two bodies being less than repulsions of each by the rest of the universe. Indeed, elsewhere he had considered the idea of a greater external pressure from the ether, pushing the earth towards the sun. However, Newton usually preferred to abstain from passing judgement on the mechanism of gravity and was clearly less dogmatic than many of his protagonists of later times. The author of this book considers that Newton would have accepted that the impulses of the action resonance theory could be the efficient cause of gravitation, regarding his theories of inertia and of gravitation as a useful instrument that enabled him to calculate orbits as though only two bodies were present.

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forces rather than as the primary cause. In a truly universal theory, differences between interpretations may often be reconciled as semantic when these are considered as different points of view of the same physical reality. In the action resonance theory, every impulse from a universal environment contributes to the current action and trajectory of motion of matter and there is no inherent resistance to the expression of new impulses, other than the current expression of the time-integral of all other impulses. The current state of motion of any object is therefore the result of all other impulses since time began. The extreme minuteness of the impulse from each acton is of no consequence, since it is the sum of many such impulses of equal moment that determines the path, expressed as the balance from all directions. The sole justification for these restrictions on the range of physical properties is the quest for a more global simplicity. It is reasoned that the best theories must above all be simple. No simplicity can be expected if the terms of reference for a new theory must include all the scientific properties currently considered valid. After all, the probability that modern science in all its fields has been extending everywhere on lines of equal validity must be extremely low indeed. Even cursory examinations of the scientific literature at the end of the eighteenth and nineteenth century serve to emphasise that many promising trails being earnestly followed by their proponents at any given time will not survive. However, there is a natural reluctance to reject useful approaches. Even more, to suggest worthwhile benefits justifying the large readjustment in thinking proposed in the action resonance theory may seem improbable. But how else than by a fundamental revision or paradigm shift can a genuinely significant change in our knowledge base be found? It should also be recognised that adopting action resonance theory does not necessarily require rejection of the current approaches to problem solving, since the new theory may provide the rational, complementary, basis by which these can be improved and extended. Above all, it should be understood that the strongest reasons for proposing the action resonance theory are biological. It was from considering the function of living cells that the action theory had its genesis and in comparing and contrasting biological observations and phenomena with physical and chemical theory. There are so many examples of the operation of asymmetric forces in biology that some means has to be found to explain them. Action theory, by proposing that the molecules themselves generate these asymmetric fields solves the problem. The rational principle involved in reaching this conclusion was that living systems above all would have long ago thoroughly examined the true basis of forces in ecosystems as they evolved and would have the best opportunity and the most efficient means of exploiting them. The conclusion that this leads to is that life, despite the many promising scientific beginnings made in the 20th century foreshadowed by Schrödinger, cannot now be better explained other than by a revision of the quantum theory itself. The contingent relationship between the statistical probability of electronic orbitals, caused by the impulsive nature of quanta as resonant energy and the resultant shapes of atoms and molecules that define regions of space impenetrable to other molecules (but not to quanta), must be understood. In molecular systems, the nexus between force and statistics, spontaneity and the propensity for action in the exchange between free energy

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and entropy must be made clear. In a physically real sense, action theory states that there is nothing more certain than a truly random process, seeking the position of equilibrium and least action by the tiny steps (petit pas) of the impulses of individual quanta. Despite the uncertainty inherent in the quantum of action as a product of indeterminate position and linear momentum, as a change in action the outcome is always exactly integral. We may now understand that Planck's quantum of action defines the least change possible with perfect exactness. Any uncertainty results from the inherent imperfection of any fixed system of coordinates when dealing with such minute particles as an electron with its correspondingly minute inertia. As a consequence, we may yet agree with the consistently held opinion throughout life of Albert Einstein that “The Lord does not throw dice”. And quantum theory did not necessarily imply blind chance at the microscopic level of electrons when it proposed the uncertainty principle. Perhaps we will recognise that we inhabit a saner and safer universe if we can agree that this uncertainty resides in our mental construct of the origin of a coordinate system, rather than as some flaw in the necessary outcome of the most minute impulses possible. In quantum theory, there has been debate regarding the meaning of Schrödinger’s wave function with reference to the spatial distribution of electrons. Are the electrons really not localised but smeared out, as some infer, or does the wave function indicate the probability of finding electrons in particular positions, indicating the average distribution of the orbitals for many atoms? Or does it indicate the propensity for electronic orbitals to occupy particular positions in future, as Popper has suggested? If we truly understood the fine structure of the electron and the other sub-atomic particles providing the reflective process for quanta, we might be able to dispense with the uncertainty principle, despite the current fondness for its implications of indeterminacy. Action resonance theory offers the possibility of obtaining a realistic outcome in which the position of electrons and nucleons is exact and deterministic, as Einstein posited. But it may still be impossible to predict its trajectory because of the problems of predicting where the next impulse affecting the electronic action will come from. In fact the simplicity of action theory may lead to astonishing results. All forces can now be recognised as manifestations of the same force, but exerted on different scales characterised by the radial separation and the transit times of the trajectories of quanta. Action resonance as stated in Chapter 2 readily links all these scales, achieved by the simple mechanism of directing resonant forces in a matrix defined by the geometrical distribution of matter in space and time, the speed of light and the local intensity of quanta. Each scale is characterised by more or less coherent or clustered sets of matter moving in concert – nuclei, atoms and molecules or supermolecules (icebergs and rocks), living cells, organisms, communities of organisms, cyclones and ocean currents, whole ecosystems, planets and satellites, planetary systems, galaxies and so on. All impulses from the energy exchanges between and within these clusters either generate or reduce the action of the cluster. Coherent bodies or particles simply follow the curved spatial contours precisely mapped out for them by the current net effects of the minute forces of the action field. Every body plays its part in establishing the potentials of the action field, by its own emissions and reflections of quanta. Every reflection provides a screen for the other members of a cluster, but increases the rate of dispersive interaction within the group. In such a system, as Einstein also held, space must surely be curved.

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There is no intention or need in advancing the theory of action resonance to challenge the validity or to seek displacement of any of the currently accepted scientific theories. Action resonance is anticipated to play a complementary role to that of most current theories, providing a means of linking one specialty to another and of improving our understanding of each and of nature in general. However, it is anticipated that in some cases where specialisation is unnecessary there will be large economies in the use of resources and of time, both for teaching and for research. A generally applied physical model should allow more efficiency in problem solving and more active participation by a broader range of people in major problem areas, possibly giving solutions to research problems that would otherwise remain intractable. 8.1.5. Honing Ockham’s razor One or two of my colleagues have objected when confronted with the introduction of quanta or actons into the mechanism of molecular collision, compared to the apparently simpler Newtonian model involving conservation of momentum in collisions by hard spheres. They have done this on the grounds of a suggested violation of Ockham’s razor, by which one would logically prefer the model with the fewest assumptions. However, Ockham’s famous dictum - pluralites non est ponenda sine necessitate – can best be translated from Latin as “multiplicity ought not to be posited without necessity” (Webering, 1953). The English Franciscan and logician born in Surrey around 1280, who was known in his time as Venerabilis Inceptor, taught that matter had its own essence apart from form. He added that there was no real distinction to be made between matter’s essence and its existence, for which we might now substitute its action since this expresses its existence in quantum theory. On these grounds, there seems little doubt that Ockham would have preferred the single kind of exchange force proposed by action resonance theory with its broad range of physical scales from microcosm to macrocosm rather than the current multiplicity of nuclear strong, nuclear weak, electromagnetic, centrifugal, inertial and gravitational forces. Confirmation that a singular basis of force can explain all the current forces and that one scale of operation merely provides the coherence of matter for the exercise of the action of the next scale is another challenge posed by action resonance theory. 8.2.

A metaphysical research programme

8.2.1. The null hypothesis and scientific theories While discussing the growth of knowledge Karl Popper (1972) proposed that any new theory, to have value, should satisfy three requirements. The first was that the new theory should proceed from some simple, new, powerful, unifying idea about some relation between hitherto unconnected things (such as apples or raindrops and planets) or facts (such as inertial and gravitational mass) or new ‘theoretical entities’ (such as fields and particles). An important ingredient of the idea of simplicity can be logically analysed. This is the idea of testability, leading to the second requirement that the new theory should be independently testable. The new theory must, apart from explaining all that it was designed to explain, have testable consequences, preferably of a new kind. It must

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lead to the prediction of phenomena that so far have not been observed. This second requirement ensures that the new theory will be fruitful as an instrument of exploration, even if it is refuted by the new tests. The third requirement for a good theory is that it should actually pass some new, and severe, tests. The difference between this requirement and the earlier ones is that the first two formally decide whether the theory should be accepted as a serious candidate for the rigorous empirical tests implied in the third requirement. Popper did not even require that the third requirement succeed, since even good theories can be wrong, but could still aid the growth of objective knowledge, even if only by ruling out some idea. To what extent does the action resonance theory satisfy these three requirements? Since the theory as proposed has novel characteristics with a broad range of unifying consequences, it may have merit regarding the first requirement. Indeed, Popper’s first requirement might even have been part of the blueprint for the theory’s development, although that was certainly not intentionally the case. The author was already thoroughly indoctrinated with Fisher’s “Null Hypothesis” as part of his study of the biometric analysis of the variance of experimental data long before he had heard of Karl Popper. The action resonance theory can also predict phenomena not so far observed or examined in detail and it should therefore be independently testable. Indeed, numerous untested predictions from the theory in thermodynamics, the elevation of greenhouse gases in the gravitational field and others have been outlined in this book. Although action theory is designed for describing and explaining complex systems it is also consciously guided by strong common-sense notions. It is plainly a far less demanding theory overall, considering its full range of applications, thus meeting the criterion of being simple. Will it meet Popper’s third requirement? That is not for the author alone to judge, but it can be remarked that application of the theory does allow many predictions, usually as solutions to practical problems. Some of these are made in this book. In many cases, there is previous knowledge and much collected data, often not rigorously examined before now, that can also be used to test the action theory. The author has already found the theory to be remarkably consistent with previous observations, at least qualitatively, that a strong measure of confidence regarding its durability already exists. In other cases, the action resonance model provides a physical explanation where none currently exists. Readers of this book are also invited to perform such tests to their own satisfaction. But the most severe testing will surely result from predictions requiring new data, to avoid any charges of engineering self-fulfilling prophecies. It is admitted, however, that this phase will only be concluded when others have performed the tests, perhaps long after this book has been published. Furthermore, some of the most severe tests will only be possible in years to come when further development of the theory has taken place, enabling the theory to predict more effects more precisely. Because the success of action theory therefore depends on a programme of research to which many can contribute perhaps it may be regarded as a metaphysical research programme, in Karl Popper’s terms, rather than as a free-standing testable scientific theory. Popper at times considered that the Darwinian theory of evolution was such a research programme rather than a simple testable theory. Perhaps, as the range of application of a theory and closer to the truth of its central tenets, the more difficult it will become to imagine a single simple test to disprove it. There is no limit to the range of

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topics that may be examined using the action theory, because it is so fundamental in its approach. Yet, its range of application appears to us to be broader even than the theory of biological evolution since it is just as applicable to chemical and physical evolution. The tests of fitness and natural selection using the principle of least action can be extended to include the evolution of all energy and matter in the universe, subsuming physics and chemistry as well as biology. It should be obvious to the reader that the author of this book has strong sympathy for Popper’s viewpoint that science progresses by trial and error, using hypotheses that can be tested against factual data and rejected (falsified) if these are not in agreement with the facts. Not everyone agrees with this approach (see Chalmers, 1976 for a broad-ranging discussion), partly through ignorance but also as ‘a matter of principle’, albeit misguided. The basis for this sympathy is not only philosophical but also logical, since it may now even be possible to validate Popper’s recommended method as the most honest approach to scientific truth. Action resonance exchange forces offer an efficient mechanism for this process of gradually establishing the truth by a process of reiteration, so that a key aspect of natural evolution becomes the advance of conscious objective knowledge of the universe, also generating the substantial content of Karl Popper’s world 3. At the University of Sydney the well-respected psychologist-philosopher Bill O’Neil (O’Neil, 1972) was a prominent academic when the author of Action in Ecosystems joined the university staff. His erudite seminars and relaxed, down-to-earth, discussions in the University Club afterwards made their impact on a young lecturer and Bill O’Neil is likely to have agreed with Popper that rationalist explanations seeking positions of unassailable truth are to be rejected. He discussed rational theories involving explanation as well as description and contrasted the attitudes of the rationalist versus the empiricist. The empiricist regards the situation as adequately explained when it is implied by some supportable general premises. The empiricist merely asks that the premises be testable. The rationalist seeking explanations usually goes much further and asks that the premises be necessary, self-evident, indubitable or in some other way unshakeable. Certainly, action theory is proposed as rational rather than empirical, although it does not anticipate that a set of unshakeable solutions will soon emerge leaving no role for the pursuit of excellence. To do better than before is the hallmark of excellence and that would always be the main aim of a continuing action revision. However, O’Neil made the following remark in a concluding statement in his book Fact and Theory: An Aspect of the Philosophy of Science, in discussing several famous case studies in science - the motion of the blood; the motions and spacing of the planets; the periodic table of the elements; inheritance and the gene theory. “What makes the rationalist’s case plausible is that the most impressive explanations are those in which some of the bases of explanation are of great generality and are so abstract that they can be seen to have reference to the particular events to be explained only after long chains of inference are unfolded. Scientific laws have these features, physical laws having the possibility of greater generality than biological laws, and biological laws than psychological laws, and so on”. He pointed out that inferential chains do not necessarily run from physics to biology, from biology to psychology and so on, even though especially strong ones do take this direction. “Further, laws alone are not enough for the deduction of particular events. Other and more specific considerations need to be taken

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in conjunction with them.” O’Neil’s conclusion regarding the looping hierarchy of rational explanation, not necessarily always proceeding from the reductionist bases of the principles of physics, could form an apt prescription for the programme of the action revision proposed here. The action resonance theory provides an example of just such a rationalist approach that is both abstract but fundamentally realistic in explanation and completely general in its application. It goes much further than simply to provide an operational model, or a useful instrument, and seeks what Popper would have described as a solution based on realism (although its bases contain many conjectural elements that must be refined by testing). Could it even be that, justified by the extreme breadth of phenomena that can be used to test the theory, the action resonance theory can provide a more secure basis for the validity of the concept of objective knowledge than has been available hitherto? 8.2.2. Being and becoming It was mentioned near the beginning of this book that action is an ancient property, considered even by the ancient Greeks. Indeed, Aristotle gave action a very strong role, contrasting the active sense of action with the associative or passive sense of passion. This dichotomy is rather consistent with the current view, corresponding to the contrast between dissociation as energy is added to a system and association of its constituents as quanta are withdrawn. Furthermore, Aristotle’s physical concepts of matter were focussed on the active science of becoming or of the change resulting when objects were located out of their natural place. He had a sense of the notion of eventual equilibrium in nature, shown when he proposed strict limits to change in saying “A consideration of the other kinds of movement also make it plain that there is some point to which earth and fire move naturally. For in general that which is moved changes from something into something, the starting point and the goal being different in form, and always it is a finite change. ……. thus, too, fire and earth move not to infinity but to opposite points; and since the opposition in place is between above and below, these will be the limits to their movement. There must therefore be some end to locomotion: it cannot continue to infinity” (Aristotle, 3rd century BC). We can contrast Aristotle’s dynamic, organic, view of nature with that of Plato’s – as the revered teacher of Aristotle and the philosopher actually preferred by the Renaissance men from the time of Galileo and Newton. Plato was more concerned with being rather than becoming and with the continuous reality of the world of ideas rather than that of processes of change in inorganic or organic materials that interested Aristotle. Thus we may consider these two giants of ancient Greek philosophy as exponents of the two notions of equilibrium and of non-equilibrium respectively. Non-equilibrium implies the spontaneity of consequent change, based on the unfamiliar notion proposed in this book that chaos and entropy are not to be equated although this has been routine for the past century and a half. In action theory, chaos is the stressed, energy-laden, non-equilibrium state of relative uniformity from which an orderly evolution to more diverse states is bound to occur, rather than a subsequent high-entropy equilibrium state. Perhaps it is no accident that Aristotle was a keen biologist interested in growth and development, who saw the conditions for change and evolution all around him but who was also well aware that there were limits to change. He was thus fully cognisant of spontaneity but also the

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role of equilibrium and natural place in ecosystems. As Prigogine sought to express in his philosophical books (Prigogine, 1980; Prigogine and Stengers, 1984), the second law of thermodynamics as traditionally understood seems inadequate to explain the remarkable order that arises in biology out of chaos. Prigogine proposed a new organising principle based on the phenomena of irreversibility and non-equilibrium. The action resonance theory extends his proposal but provides more clarity about what this means since it includes a simple physical mechanism and, by the re-interpretation made to the second law in section 4.1 in Chapter 4, enables order to arise naturally from chaos. Scientists have usually explained the apparent increase in order and free energy that arises in the physical structure of organisms, such as the synthesis of sugar and fat from carbon dioxide, as being paid for in one system by a greater increase in entropy in another system. The dumping of heat as a by-product into a colder system elsewhere, can thus be used to save the appearances of the second law. This implies that life is a just a ‘spinoff’ from processes that overall are dissipative. In this book we have pointed out that the very process by which the hot radiation from the sun associated with the emission of quanta of low entropy is converted into colder, higher entropy, radiation, by which matter can be sustained at higher potential energy at ambient temperature is also essential for the process of life. Even the high entropy quanta associated with the translational motion of molecules have an essential if transient role to play. However, we must now understand life as an action process of an ecosystem’s field of matter-energy, rather than as a list of lifeless material structures that merely provide a scaffold for the various action processes. The action revision offers the prospect of restoring common-sense to real world processes. It substitutes an efficient causal mechanism based on no more than conservation of momentum, by locally minimising action exchange forces and overall action in the distribution of energy, as a universal organising principle. This replaces abstract, less comprehensible, scientific laws of thermodynamics or any mysterious teleological principle devoid of testable mechanism. It is a widely held logical fallacy that finding a rational explanatory mechanism for any natural process, such as natural selection for the evolution of species, allows one to dismiss the need for God. Thus, science is considered to be able to answer a theological question. But this is surely not a legitimate use of science for why should a rational God, in particular, only exist as long as we humans lack rational explanations? Science, justifiably, should only be used to ask questions relevant to the search for truth regarding all aspects of the natural interaction of matter and energy, including that in life systems. It is possible that the findings of science, by informing us more and more about that which is not true may have implications for philosophy and theology as well as morality. But scientists who do not favour the idea of a deity for personal reasons should be careful not to allow this to affect their attitude to the conduct of serious tests of a hypothesis proposing a degree of teleology in nature. In terms of simultaneously fulfilling the needs of many individual biological organisms, all carrying DNA evolved at the same time in the same environment under the selective action of local exchange forces, the overall result of such mutual evolution may be indistinguishable from teleological viewpoints of final cause. Evolution, as a result of action resonance theory, can now be regarded not merely as a numbers game with the explicit aim of maximising the rate of occurrence of genes as inanimate sequences of DNA but instead as the selection through the genotype x

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environment interaction of those genes that respond best to the needs of the individual interacting with the complete environment. In this case, teleology may justly re-emerge simply from the application of the principle of economy. Why continue to reject a principle, that we now claim this book has shown may have a simple physical basis, just to preserve the notion of the independent evolution of individual organisms? This simple basis follows because the action exchange forces generated by individuals are not self-sufficient but result from an interaction throughout a system in a contingent fashion, both in space and time. Those who adhere to strict Darwinian competitive selection as completely blind to any common purpose (other than accidentally, from selfishness) now run the risk of being accused of instrumentalism and of adopting an operational approach that is unscientific because it does not provide a set of hypotheses testing its validity. It would be an even worse kind of instrumentalism if it has continued to be used as an approach persisting partly as a useful dogmatic rule or stick with which to beat others for non-scientific reasons. In action theory, the best and most enduring solution to the forceful stress experienced by one organism in its niche because of adaptation may even be the same solution as that minimising the stress on all. So a challenge is made that the action resonance theory, in contrast to Darwinian instrumentalism, can provide testable hypotheses by which the search for truth in nature can be advanced. We can all recognise that the benefits flowing from symbiosis resulting from the forceful process of natural selection, sustaining individuals through the cooperative actions of their own coupling agents, can simultaneously contribute to the good of all. Some are quite fond of the holistic though somewhat mysterious statement that (presumably as a result of synergies), the whole may be greater than the sum of the parts. This is clearly a true statement about the nature of the possibilities, but there is also validity in the counterclaim, based on the cooperative means of action exchange revealed in this book, that systems function because, in terms of matter and energy, the whole is less than the sum of the separated parts. There are many economies that result from cooperation, not least in the amount of energy required to sustain given levels of action by matter. There is therefore a strong consonance between the action of Aristotle’s biological theories and the action resonance theory. Action resonance theory exists today as a reconciling theory because of the author’s perception of what is really needed to explain biology. It would be true to say that it was invented because of the failure of statistics alone to explain developmental biology and the function of ecosystems. The action resonance theory of fields and of random forces is fully consistent with statistics but these exchange forces generated by resonant impulses between material particles provide the security of an elastic environmental wave guide by which particles may find their optimum place. Particles are far from blind since they are embedded in a dynamic web of sensation from innumerable impulses each second from all over the universe. In fact, such a successive stream of forceful sensation is all we know, as pointed out in the 18th century by the Scottish philosopher, David Hume, for the benefit of the only living species that knows it knows. If the external organising principle of action resonance is accepted by experiment to be true, any idea that nature and evolution operate by blind chance, as was proposed by Nobel laureate, Jacques Monod (1972), can

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summarily be rejected forever. The role of chance is real but it merely selects between a huge range of potential solutions to the local problem of minimising stress in systems of molecules. There is a multiplicity of solutions needing approximately the same energy to the problem of how to arrange matter to minimise the rate of action exchange. Thus, novelty, variety and diversity can never be wanting in nature because of the role of chance in selecting alternative routes of least action for development. As a consequence, in action theory chance and necessity are not mutually exclusive alternatives indicating either indeterministic or deterministic universes but denote two creative, fluctuating, aspects of the same reality. 8.2.3. Gaia and action fields Some readers of this book may have already drawn conclusions about the possible significance of action theory with respect to the Gaia hypothesis proposed by James Lovelock in 1969 and advanced in two other books (Lovelock, 1979; 1988). Gaia (from the Mycenaean goddess of the earth) implies that the biological earth is a self-regulating entity with the capacity to keep itself healthy by controlling the earth’s temperature and the composition of the oceans, the atmosphere and the soil. If humanity makes the earth unhealthy for itself, Gaia will respond by evolving some newer species than man that can help the earth to achieve a new, more comfortable, environment. The nutrient cycles for carbon, nitrogen and sulphur discussed in Chapter 7 that involve all the earth’s plant and animal species are thermodynamically self-regulating processes controlled by action resonance. These automatically seek outcomes of minimum energy by optimising action and entropy for a given energy content. The reversal in action theory of force fields from operating inside molecules to acting as stabilising exchange forces between them, thus providing controls of the extent of development, also has overtones of Gaia. Of course, Le Chatelier’s well known chemical principle - that any system subjected to stress adjusts its position of equilibrium so as to overcome the stress - is entirely consistent with the idea of Gaia. Action resonance theory gives the physical explanation for Le Chatelier’s principle as an automatic consequence of distributing energy to provide least action for the current temperature. Indeed, action resonance theory removes any sense of mystery about these outcomes in ecosystems. There are, however, limits to the speed with which signals and impulses can be transmitted between different parts of ecosystems. Action resonance even provides an analogous efficient mechanism to Rupert Sheldrake’s (1982) morphic fields, which may determine the shape of a plant, the development of root nodules on legumes and the colourful patterns developed in beauteous flowers, although only over a short distance. But these action exchange fields are dominated by interactions with the local environment because of the limitation of the speed of transmission of impulses to natural speeds such as that of sound or diffusion of heat in soil, water and air. There is a role for rapid transmission through space at the speed of light of the tidal influences of the sun or the moon - these can have profound influences on the life cycles of plants and animals. But even these fields will take time to exert their effects in ecosystems on earth because they must be sequentially transmitted as disturbances or waves through molecular fields and they never act instantaneously.

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What is practically instantaneous in action theory is the immediacy of the response of molecules and molecular systems to the most current impulses, even though these may have originated as energy emitted separately in very distant past epochs. Thus the latest impulse affecting the inertial state of the body of any organism may have been emitted from a distance 4.34 light-years earlier from Alpha Centauri or the Andromeda galaxy. But it is important for astrologers and others to recognise that the total magnitude of impulses from Alpha Centauri falling at every locality on earth would be extremely minute indeed, given the vanishingly small dimensions of this source as a proportion of the total field viewed (i.e. the solid angle subtended) from any organism! Far more important is the impact on human minds of highly amplified, focussed, images of Alpha Centauri, by helping us to better understand our immense universe, as part of Karl Popper’s world 3. These connections of action theory to Gaia need to be drawn with care. Unlike Gaia, action resonance theory does not propose that any major conceptual change occurred when organic life appeared on earth, such as a reversal of the outcome of increasing disorder and entropy predicted by the second law of thermodynamics as time progresses. It is true, however, that the greater asymmetry and information that life generates was a major change. As explained in this book, diversity and complexity of arrangements of different basic building blocks is the natural outcome of the second law. With energy added, the action and entropy of living systems is greater than that of the raw materials from which they are generated. Life is an optimised action process and increasing action is increasing entropy. Even the human mind is a dynamic arrangement of matter in motion producing unexplained optimised action states of a remarkably cool plasma of energy interacting with matter. The mathematical idea that dictates a second law where maximum order is continuously replaced by increasing disorder as a linear process is plainly wrong. The thermodynamic order we associate with advanced intelligent life must be an ideal zone or sequence of quantum states - the crest of a wave or a bellshaped function in a four-dimensional reality characterised by optimally sustained, or fluctuating action - with other zones of increasing disorder surrounding it from too little energy on one side to too much on the other. As pointed out more than three-quarters of a century ago by the Oxford physiologist, J.S. Haldane (1921; the father of J.B.S. Haldane), we can never hope to understand consciousness from physical or chemical experiments unless we also understand that they only produce limited sense data, providing a very incomplete viewpoint of the consciousness of the whole living organism. It appears that despite all the best efforts since of very many talented individuals in the 20th century, this viewpoint of Haldane remains as valid as ever. Max Bennett (1997) of Sydney University very recently acknowledged this continuing difficulty for neuroscience, recognising that it may currently be limited to explaining “the neural correlates5 of consciousness, leaving the difficult problem of what consciousness is untouched”. At least “the concepts and techniques which neuroscience now has available offer the opportunity to identify and explore those parts of the brain which generate the different contents of consciousness .….. importantly, it will give us the means of ameliorating those distortions of 5

For example, by measuring electric potentials of nerve cells, imaging of the brain by magnetic resonance, etc.

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consciousness which arise in psychotic conditions responsible for much mental suffering in the world.” This may seem a limited reward to those neuroscientists who have so earnestly sought more ultimate meaning from their research on the idea of consciousness. Could it be that the four-dimensional sense of continuity between organisms and their environment given by action resonance theory and its essential role in providing more meaning to the term living organism is the missing ingredient in the current research? If so, there is even less hope that the essentially linear integrated circuits of modern digital computers and microprocessors could ever be meaningful mimics of human consciousness. Or even of the rudimentary “consciousness” of a living green plant, well adapted and fully resonant (in a wholly analogue sense) with its own environment. Perhaps claiming this for action theory would be to claim too much for a scientific theory at any stage of its development, but let’s wait and see. 8.2.4. The flow of energy and the sustainability of ecosystems At the instant life appeared on earth and beforehand, the propensity for all kinds of living processes already existed. Obviously, the material coupling agents needed did not yet. However, the rates of processes such as oxygen formation were soon speeded by many orders of magnitude once the genes synthesising the appropriate coupling agents were in place and ecosystems were formed. The populations of organisms exploiting the huge comparative advantages now available to these early photoautotrophs would have been extremely prolific, since all nutrients needed were available. This would no doubt have led to a very rapid increase in oxygen concentrations in the atmosphere, although we cannot say how much oxygen was formed from non-biogenic sources such as the photolysis of water when UV-absorbing ozone was less prominent in the upper atmosphere. As discussed in Chapter 6, action resonance theory particularly emphasises the role of the flow of energy through the earth’s ecosystems as the driving force for all chemical processes. Indeed, this flow provides the impulses needed to generate all the action on earth. Even in the pre-biotic period, the same regularities regarding chemical activity would have been observed. However, without doubt the appearance of life would have generated huge changes and has continued to sustain these changes. Without the steady though fluctuating energy flux from the sun to the earth’s surface a return to oneway processes would soon occur, oxygen would be consumed and acidification would result. Sustainability is a concept much discussed in recent times. Definitions abound, but accepted conclusions about its true meaning and value are few. Action resonance theory may provide the answer to the meaning of sustainability and could help to define the cases where it is achievable or even desirable. Because the theory can reveal how to achieve the greatest economy of action for a given energy input. There is little doubt that the most inefficient and wasteful processes may be sustained indefinitely as long as sufficient resources are made available. But a more judicious selection of the action to be achieved and its relationship to other processes could give much more productivity from the same level of the energy flow, as a result of action resonance. We may be able to agree that the concept of sustainability has value where it enables us to define the following helpful criteria:

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•

Which processes are beneficial in ecosystems and their desired results

•

The most efficient means, in terms of the true current and eventual costs, of achieving these results

We are more aware now than ever of the finite nature of the resources of this planet and the need to avoid irreparable damage to them. The extent to which action theory will prove useful in improving our understanding of the needs for sustainability remains to be seen. Using action theory, sustainability can be defined as the capacity to continue a dynamic, ordered, coupling between energy flow through an ecosystem and the attainment of a level of action that protects the diversity of genetic information responsible for the action. Both the source and the operation of the coupling must be protected, requiring a self-monitoring system. Sustainable agriculture must also be economically viable. It would not be the first time that a promising beginning eventually languished for lack of champions. The universal theory of action that beckons, using the content of this book and the key findings of many others as its basis, should prove beneficial to a broad spectrum of human knowledge. It is anticipated that these benefits will range from questions related to the most practical applications in industry, transport, agriculture, the physical and social environment even to the meaning of life and human existence. This book closes with both an invitation and a challenge. Readers are invited to participate fully in the action revision and to contribute to its future development, for there is much to do and new frontiers now possible to explore. Its very nature invites cooperative action where everyone can contribute in their own unique way, by paying particular attention to developing their own skills for mutual benefits to all, allowing the energy available to resonate longer and more efficiently. Common-sense, personal integrity and recognition of mutual benefits from cooperative action are consistently applied criteria recommended for use by all the participants at this action round table.

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ENDNOTES & GLOSSARY Action A thermodynamic property of matter, with the physical dimensions of angular momentum. The action state designates the quantum state of a system and the higher the quantum number, the higher the action. It is a property related to the everyday notion of action, which indicates doing something, corresponding to a change in the action state.

Adiabatic lapse rate of atmospheric temperature with altitude No generally accepted mechanistic theory of the fall in temperature of the atmosphere with altitude exists. Indeed, the effect is so well known that it is taken for granted. In general terms, the decrease in kinetic energy with height is demanded to maintain equilibrium of energy distribution in 3-dimensional space. As a result, because molecules higher in the atmosphere have greater potential energy, they must have less kinetic energy. Otherwise molecules higher in the atmosphere would have a greater capacity to do work. This general principle is responsible for the fact that temperature falls about 10oC for each kilometre of altitude in the atmosphere, at least in the zone close to the earth’s surface containing the bulk of the atmosphere. In principle, the total energy of particles sustained in free orbit around a central body is a variable, dependent on the radiant energy density. This is obvious in the treatment of the Bohr hydrogen atom (see below). However, in making the transition from an orbit of higher potential energy to a lower one, energy reappears partly as kinetic energy and partly by the emission of radiant energy as quanta. Molecules in the earth’s atmosphere are not in free orbit moving at orbital velocity. They are fully sustained at any altitude however, cushioned by cooperative interactions from the impulses of quanta and the process of action resonance though they require just as much extra energy to raise them individually in the gravitational field as molecules in two different orbits with the same difference in altitude would require. Compared to being sustained in free orbit, the kinetic energy acquired in supporting each molecule in the atmosphere against falling in the gravitational field is much less. Resonant exchange of quanta with other molecules in the atmosphere amplifies the dispersive force, exerting a buoyant effect. This interaction within and between classes of molecules is augmented by collisions, characteristic of particles undergoing Brownian motion. Indeed, in action resonance theory (Chapter 2), collisions correspond to events in which changes in the degree of screening by the matter of molecules leads to the emission and the absorption of quanta. Such energy and action transitions are considered to occur as equilibrium processes, since the quanta emitted and absorbed in collisions are closely matched. Molecules are not free to fall in the gravitational field since any tendency to descend will be countered by a greater rate of impulses as a result of the shorter mean free path of molecules between collisions at the higher density of molecules. Any tendency to rise will be countered by gravity and the lower density of impulses from quanta needed to sustain each molecule. Of course, individual molecules can readily exchange positions as an action exchange process, leading to diffusion. Thus, any gas molecule at sea level may eventually reach the top of the atmosphere by replacing another that descends, given sufficient time. The molecules in the atmosphere, as a result, are not dynamically and energetically independent of each other as they would be if travelling at orbital velocity in the earth’s field without collisions. Through interaction, all molecules at the same gravitational potential will be constrained to reach the same temperature; molecules at other gravitational potentials will tend to reach the same minimum value of action and entropy. This will allow adiabatic expansion of

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a rising parcel of recently heated gas molecules by convection in which the action of individual molecules, as a result of being constantly minimised by action resonance, will remain constant. Such adiabatic expansions are well recognised as being isentropic, so that both the action and the entropy remain the same. As discussed in Chapter 4, the increased action and entropy resulting from greater space per molecule is exactly compensated by the decreased action and entropy resulting from cooling. The actual temperature at any altitude in an ecosystem will be a complex function of the current intensity of solar energy or from any other source, the molecular density and heat capacity of the earth’s surface, the rate of energy flux in surface materials and in the atmosphere, the molecular composition of surface materials and the atmosphere and their capacity to absorb particular frequencies. In principle, from detailed knowledge of energy fluxes, the heat capacity of the materials in ecosystems and the necessity for overall energy balance, it should be possible to compute the current temperature at any site. However, it must be understood that this is a highly dynamic quality because of the non-equilibrium conditions implied by variable fluxes of energy. As a result of the variation in the flux of solar energy there will be a diurnal cycle in the magnitude of the atmosphere’s molecular action and entropy. In periods while the intensity of quanta delivered to the earth’s surface is increasing with time, so will the process of transfer of quanta to the atmosphere, local warming generating winds (increased winding resonance). Each of these processes involves the application of torques, generating action (torque x time = action; @ = mr2ω). These adjustments occur in pursuit of equilibrium, generating work and limiting the scope for increasing temperature. But the equilibrium achieved is transient or metastable. Once the peak for the input of radiation has passed, the process of increasing action and entropy will reverse and both these properties will commence to decline. Thus, molecules cycle periodically with respect to their action and entropy. It should be noted that the stages of increasing action (ante-meridian and between the winter and summer solstices) correspond to a net absorption and retention of radiation in the atmosphere while the declining stages (postmeridian and between the summer and winter solstices) involve net excess of radiation of quanta into space and a loss of atmospheric action. Table E.1 Orbital potential energies for hydrogen (2), nitrogen (28.01) and carbon dioxide (44) Property Radius = r H2 N2 CO2 x 10-8 cm Energy U = -mr2ω2 U = -mr2ω2 U = -mr2ω2 12 12 x 10 ergs x 10 ergs X 1012 ergs C = 3.98652x1020 Ca=Celerity=a3earthϖ2

6.371 6.372

2.0960849 2.0957559

29.3258224 29.3212201

46.1239607 46.1167221

6.373

2.0954271

29.3166193

46.1094859

∆U = -mr2ω2 x 1016 ergs

∆U = -mr2ω2 x 1016 ergs

∆U = -mr2ω2 x 1016 ergs

3.2890 6.5780

46.0230 92.0310

72.386 144.748

Energy difference Sea level 1 km altitude 2 km altitude

6.371 6.372 6.373

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It is instructive to consider energy levels for gas molecules regarded as in free orbit. Use of the celerity for the planet earth (Cearth = mearthG, ignoring the mass of the molecule) enables calculation of the change in potential energy for orbital motion of a single molecule of the three gases hydrogen, nitrogen and carbon dioxide at sea level, one km and two km elevations, assuming there was no atmosphere. The relevant calculations are given in Table E.1. Although the orbital kinetic energies are consistent with extremely high kinetic temperatures of many thousands of degrees, such elevated temperatures could only be possible at extremely high altitudes with extremely long mean free paths of gas molecules and low probability of collisions. In fact the high density of gas at low altitude and its physical coherence with the earth’s surface as a result of high collision frequency in denser atmospheres allows the gas molecules to be sustained in the gravitational field by Brownian movement; this results from the action exchange forces of thermal radiation at much lower temperatures.

Black body radiation From the Stefan-Boltzmann law, the radiancy (Rλ) is proportional to the fourth power of the temperature: Rλ = σTe 4 (i); Rλ = radiancy, σ = 5.5597 x 10-5 ergs sec-1 cm-2 K-4, Te in degrees K, Incidentally, the theory of black-body radiation recognises that only radiation emitted from the interior of a heated cavity (i.e. via a small window) obeys equation (i) exactly. Whenever the intensity of radiation from the surface of a heated body is considered, an emissivity factor less than 1.0, which is different for different materials, must be introduced (Halliday and Resnick, 1977, p. 1093). When a correction factor for emissivity (e), is included, a new equation is generated: Rλ = eσTe 4 Using action theory, we can investigate the reason for the departure of the emissivity from 1.0. As an experiment, the exterior surface can be firstly enclosed in a secondary spherical shell, also at T. We then predict that the emissivity of the initial exterior viewed through a second window would now be 1.0 and no correction is required. Mutual exchanges of quanta of the same frequency distribution would bring both cavity regions into equilibrium and the spectrum from the exterior surface of the primary shell would now be of the same radiancy and peak wavelength as the interior of the primary cavity. If we now remove the secondary shell and allow the black body to radiate freely to the surroundings the emissivity (e) will immediately begin to fall below 1.0, reaching a steady state value (e.g. for tungsten at 2000 K, e is 0.259). We may assume that there is an imbalance in the directional density of impulses from quanta at the heated surface. There will now be a greater flux of actons to the surroundings than from them and the temperature of the surface layer will be different from that of the internal surface; atoms near the surface now receive a greater rate of impulses from the interior than the exterior and the tendency will be to accelerate these atoms very slightly towards the exterior as a result of the imbalance of forces. This imbalance is a function of the temperature gradient between the black body and the surroundings. It should be noted that the temperature (i.e. the frequency spectrum) of the radiation emitted from the surface need not fall below that of the cavity as a result. The peak of the radiation spectrum from the surface will depend on the net outcome of the non-equilibrium condition. For example, radiation from the exterior will be blueshifted when reflected from approaching molecules, affecting the overall spectrum by an amount depending on the temperature difference. Action model A qualitative action resonance model of a radiating body, hotter than its surroundings, suggests the following:

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•

Adding quanta (e.g. electrical heating) results in random oscillations in the quantum states of the molecules in the system, reducing their kinetic energy but increasing their potential energy and subsequent re-emission of quanta, increasing their kinetic energy by an equivalent amount. This is based on the relationship for potential energy (see action discussion on Bohr hydrogen atom), U = mc2 – mv2 and ∆U = hν - ∆mv2/2. A heated body is, by definition, not at equilibrium with its surroundings. Consequently, it will radiate more energy than it receives and its surface will tend to cool compared to the interior, where heating takes place. The degree of cooling and the resultant surface temperature will depend on factors affecting the conductivity of energy, providing a unique emissivity (e) for each substance. Thus ceramics, with low energy conductivity, will have a high radiancy and high emissivity because they maintain their surface temperature higher while metals with high conductivity and more rapid cooling, will have a relatively low emissivity. Denser materials also contain less energy at a given temperature, also affecting the potential radiancy. This is because the heat capacity of different substances at the same gravitational potential is not proportional to density but to the number of atoms per unit volume. It is curious that a higher emissivity, by this analysis, actually corresponds to a lower capacity to emit radiation by a particular substance. Obviously, it is always possible to raise the non-equilibrium surface temperature of a radiating body, by increasing the energy flux to the surface, but the internal black body temperature will then be higher.

•

By adding sufficient heat to radiating bodies to maintain equality of temperature or internal torque (T = mv2/2) we automatically set the celerity for each heated substance to a specific value such that the change in potential energy for quantum re-arrangements and the size of the quanta emitted or absorbed are equal for different substances. This occurs at an energy density giving equal temperature where celerity (rv2) must be approximately inversely proportional to the mass of each substance, given equal numbers of atoms per unit volume. This follows since mv2 = 3kT and hence mrv2 =3rkT, where r is a statistical radius. Materials at the same temperature are subjected to the same torque and consequently, the rate of change in action is the same for all materials. The magnitude of the quanta emitted or absorbed in transitions between two action states is given by: = (nhωn - mhωm)/4π hν (n,m) = me rn2ωn 2/2 - me rm2ωm 2/2 = ∆T = -∆E = ∆mv2/2 Since each atom in a heated substance such as a metal is involved in a large number of atomic interactions, there is an equivalent large number of quanta of different magnitudes emitted and absorbed as it undergoes Brownian motion.

•

Since the pressure and temperature (torque) depend on the radiant density and its frequency we have kT = hνi T = hc/kλi λiT = hc/k = 1.4387238 cm.degrees Kelvin This constant is almost five times greater than the constant observed in the analogous Wien displacement law for black body radiation, 0.2898 cm.degrees Kelvin. This discrepancy, suggesting a higher temperature for a given mean wavelength than is actually observed, is no doubt a result of the marginal properties of quanta and the statistical distribution of action states for surrounding atoms. A mathematical demonstration of this exact statistical relationship would be useful and not too difficult to obtain.

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Bohr Hydrogen Atom In the quantum model of the hydrogen atom proposed by Nils Bohr it was assumed that the negatively charged electron moved in a circular orbit around the much heavier positively charged proton as the nucleus. Using Newton’s second law of motion of the electron, the stationary states involve equating the centrifugal force tending to cause linear inertial motion of the electron with the attractive Coulomb’s force. This approach enables the hydrogen atom to be considered as an independent object, without external forces being needed to provide its stability. Then, by balancing these two forces, the electron is considered to travel indefinitely on a curved path: F1 = ma = mv2/r (centrifugal or inertial force) F2 = e2/r2 (Coulomb force) So e2/r2 = mv2/r From this, the kinetic energy is given by T = 1/2mv2 = e2/2r The potential energy U of the proton-electron system is given by U = V(-e) = - e2/r where V = e/r is the potential in volts of the electron at the radius of the electron. This assumes that the potential energy approaches zero when r increases to large values. Then the total energy E of the atom is E = T + U = -e2/2r Note the equivalence of the total energy to the negative of the kinetic energy or to half the potential energy. It follows that the speed (v) of the electron, its rotational frequency (νo), its linear momentum (p) and its angular momentum (L) can be expressed as v = (e2/mr)0.5 νo = v/2πr = (e2/4π2mr3)0.5 p = mv = (me2/r)0.5 L = mvr = (me2r)0.5 The quantum condition was introduced by Bohr that the angular momentum of the electron is restricted to units of h/2π. (n=1, 2, 3 …m…∝). Then And So

En = -e2/2r = - nhv/4πr = -2π2e4m/h2n2 Em – En = 2π2e4m/h2 (1/n2 - 1/m2) = hνm-n νm-n = 2π2e4m/h3 (1/n2 - 1/m2)

The emission and absorption spectra of hydrogen (H) then correspond to transitions between different quantum states, indicated by n, m or ∝. A selection of lines of the hydrogen spectrum is given in Table E.1, where the series known as the Lyman, Balmer and Paschen spectral lines are shown.

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Quantum mechanics also proposes that exact knowledge of the position of an electron is not possible because of the uncertainty principle. However, insofar as a physical model of atomic structure can have any validity at all, the Bohr model continues to be employed for purposes of illustration.

Action revision of the H atom In action resonance theory the cause for stability of the hydrogen atom and other atoms differs, although similar equalities between key parameters still exist. The physical model of action theory involves a large ensemble of hydrogen atoms, free to exchange radiation as energy and momentum within the ensemble. Bonding is not achieved by an attractive central force, but by the balance of internal impulses (tending to dissociate the electron from the proton) and external impulses (tending to associate them). Furthermore, the dynamic concept of energy as resonant, continuously generating the action of particles in molecules must be borne in mind. The action resonance theory predicts that a hydrogen atom free of such impulsive interactions with other hydrogen atoms in the rest of the universe via quanta would be unstable. 1. As indicated in Chapter 2, all action exchange forces are considered to be dispersive, delivered locally by the impulses associated with ground state energy and quanta (actons), always conserving momentum. These quanta are distributed randomly in space. There is no role for attractive force fields of constant intensity with time, such as that proposed in the Coulomb law. On the contrary, the force fields generated by energy (which are consistent with the Coulomb law) must act intermittently (transmitted at the invariant speed of c); thus, the position and speed of an electron at any instant relative to the proton reflects the current detailed balancing of impulses from energy received from all directions. 2. A critical feature of the action field is the mutual screening effect exerted by the field of dense nucleons (protons) and orbiting electrons on the local intensity of actons; a proportion are deflected by reflection or scattering so creating a protected zone or niche where the dispersive force is diminished, but which is instantaneously filled. The shape of this protected niche for an electron is conic by extension through the proton, but rotating to project in all directions in an isotropic field with a spherically symmetrical nucleus. Its effect will vary inversely with the square of the range or radial separation, providing a tendency for the speeding electron in the hydrogen atom to fall towards the proton by the greater rate of impulses of quanta emanating from the hemisphere distal to the proton. Newton’s principle of inertia (proposing continuing motion in a straight line, in the absence of forces) is instantaneously operative. But the actual path of motion depends on the net impetus provided by the impulses of quanta and these occur with such great rapidity that motion in a straight line can never be observed. The apparent “attractive” influence on the electron generated by nuclear screening will be diminished by opposing impulses emanating from the hemisphere proximal to the nucleus. Statistically, the net (negative) magnitude of impulses resulting from this screening effect of the nucleus centripetally accelerates the electron towards the proton by a value which is just matched by the centrifugal acceleration from impulses provided by the extra motion of the electron relative to the proton. So the electron is sustained in its trajectory. An electron in motion ‘views’ more of the universal field over time than an electron stationary relative to nearby nucleons would do. The centripetal ‘attraction’ logically varies inversely with the square of the separation (∝1/r2) since the screening surface as a proportion of the total spherical surface delivering impulses (4πr2) varies in this manner. The net change in the rate of fall towards the central body or acceleration (rω2) simply represents the difference (∝ω) in the rates of impulses of actons received from the distal and proximal hemispheres.

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Therefore rω2=C/r2 So r3ω 2 = rv2 = C, where C is a constant for a nucleon or set of nucleons of given mass called the celerity, indicating radius (r) and frequency (ω) during circular trajectories (or their mean values for elliptical orbits). The magnitude of the celerity is assumed here to be a fixed property of the central, more massive material body. Furthermore, the screening effect of the proton would only be exerted over a minute proportion of the area of the field (1 part in 353,778,481, assuming the true radius of the proton is its Schwartzchild radius where orbital velocity would be the speed of light (see Table E.1)). In fact, the value of the celerity for any two particles must be interactive, varying in a manner depending on the geometric properties of the field and with other properties of the interacting bodies, such as their density. Note that in very close approaches, screening effects will vary in a highly complex manner, but in a way predictable from the action model. 3. The actual trajectory taken by the electron relative to the proton will represent a path of least action, indicative, on average for a large number of hydrogen atoms, of the dynamic transient equilibrium provided by all impulses from quanta. Obviously, this average path of least action for a particle of such low inertia as an electron will be far from smooth and there will always be uncertainty concerning its current position. This position depends on all its previous history, modified by the direction of the most recent impulse. Since impulses effectively arise from an infinite number of past and present sources (but always from the past and never from the future) this direction cannot be ascertained. Furthermore, any attempt to measure the current position of an electron must alter its position. . 4. The greater relative speed of the electron enables it to exert a proportionately greater screening effect for the nucleus from the impulses from quanta emanating from the distal hemisphere. Overall, the combination of greater speed and a smaller screened surface area to be traversed by the electron means that this capacity to deflect quanta distally is inversely proportional to the fourth power of the quantum number (∝ 1/n4). Bonding between the electron and the proton in the hydrogen atom can thus be considered as caused by these mutual reductions by the proton and the electron in the rate of momentum transfer or dispersive force carried by quanta between these particles. The equilibrium separation between the proton and the electron will depend on the position of balance of all impulses from both hemispheres and the interactive screening. This position will vary with the energy density of the system, as a result of the relative influence of screening and direct dispersive force between the proton and the electron. 5. As the radiant energy is quantised in sets of impulses of given frequencies, so the relative positions of the proton and electron will be quantised. It is observed that the angular momentum (or action) in particular is quantised. Thus, me r2ω = nh/2π ( n = 1,2, 3, ……) Such quantisation in action depends on the constancy of torque x time, operative during orbital transitions between stationary states. 6. We can conclude from the above relationships that me r2ω 2/2 = K = meC/2r, so that the kinetic energy is inversely proportional to the radius, and mer2 ω = @ = meC/rω, so that angular momentum or action is inversely proportional

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to mean velocity. Making the arbitrary and erroneous assumption that the potential U = - mer2ω 2 = -meC/r energy approaches zero as r becomes extremely great1, then So E = - mer2ω 2 /2 = -meC/2r We can make the following conclusions regarding the manner of variation of the parameters involving celerity (C), action (@),velocity (v), momentum (p),kinetic energy (K) = negative of total energy, radial frequency (ω), rotational frequency (ω/2π = νr), and acceleration (rω2 = v2/r), with values for the least energy orbital shown in the table. Table E.2: Action parameters for the Bohr hydrogen atom Parameters Dimensions Quantum variation

Ground state value

Celerity

C= r ω = rv

1

2.528569x108 cm3.s-2

Action, angular

@=nh/2π = mer2ω =

n = 1,2,3,4,…m,….. ∞

1.054573x10-27 erg.s

momentum

merv

Radius

R

n2

5.291772x10-9 cm

Velocity

rω = v

1/n

2.185933x108 cm.s-1

Linear momentum

p=merω = mev

1/n

1.992854x10-19 g.cm.s-1

Kinetic energy

T=mer2ω2/2 = mev2/2

1/n2

2.178961x10-11 ergs

Radial frequency

ω

1/n3

4.1308148x1016 rad s-1

Rotational frequency

ω/2π = νr

1/n3

6.579684x1015 rev s-1

Acceleration

rω2 = v2/r

1/n4

9.029684x1024 cm.s-2

3 2

2

“Schwarzschild” radius = 2.81341244x10-13 cm, where Rsc2 = C

These relationships and the variation of parameters with quantum number make it relatively simple to calculate values of energy and radial frequency . Table E.3: Quantum numbers, energy and radial frequency n = quantum number Total energy ωn = frequency x 10-15 rad s-1 -mev2/2 = hν∝ 12 x10 ergs ∝ 1/n2 ∝ 1/n3 1 21.78122 41.324056 2 5.445395 5.165507 3 2.420136 1.530520 4 1.361326 0.645688 5 0.871249 0.330592 6 0.605034 0.191315 7 0.444515 0.120478 8 0.340332 0.080711 9 0.268994 0.056686

Then the exact spectra can be calculated as a simple function of the rotational frequency of the electron. In action resonance theory, this geometrical model of the hydrogen atom can be given 1

In fact, the potential energy clearly must have a minimum value of zero and all real values must be positive. The arbitrary choice of the zero value at infinite dissociation is a misleading fiction, but was convenient in the absence of knowledge of absolute energy values. Here, we retain this traditional method, but we point out that Einstein has shown that the maximum potential energy is E = mec2

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more credence than the Bohr model is currently accorded in quantum mechanics. For the delivery of impulses by quanta of particular frequencies, the rotational frequency and the radial separation of the electron from the proton are key parameters, since they would control the frequency of impulses. An electron close to the nucleus experiences greater screening. The shorter radius also determines that the electron can be sustained with fewer quanta. Thus, an acton or actons with an assumed mass of 7.3725 x 10-48 g travelling at the speed of light can traverse the length of the ground state radius of 5.291 x 10-9 cm the huge number of 5.665256 x 1018 times a second, potentially delivering 2.504292 x 10-18 g.cm s-1 of dispersive impulses from 861 transits per orbit of the electron. Since these impulses would actually be delivered randomly over the surface of the sphere they will be reduced by a probability factor of 1/4π to 1.9928523 g.cm x 10-19 s-1, a value the same as the momentum of the electron. This is a simple result of the ratio of the average speed of the electron and the speed of actons or light (c), which has the value of 137.0 (= 861/2π). In order to raise the electron to a higher quantum state, or to carry out the complete dissociation of the electron, a larger number of actons as a quantum of energy would be required. These impulses (and others from the proximal hemisphere) would contribute a positive dispersive force between the proton and the electron. They would be opposed by impulses from the distal hemisphere, resulting in progressively curved motion towards the proton. For orbits with greater values of n than one, the force delivered by one acton is progressively reduced in proportion to the increase in radius because transmission at c cm s-1 takes longer (∝ x4, x9, x16, ---x n2). The distal hemisphere therefore progressively absorbs additional quanta as the radius increases. Consequently, a relationship between the frequency of the quanta absorbed by the system or emitted by it and the frequency of revolution of the electron, that can be observed by experiment as spectra, would be expected. In fact, the frequencies of the emissions can be considered as governed by the ratio of the radii of the respective stationary states, or by the difference in the rate of change of action between the states. Thus the frequencies of the emitted or absorbed photons are given by

ν

= ω1(1/n2 – 1/m2)/4π = ω1(r1/rn – r1/rm)/4π = (nωn - mωm)/4π.

Mechanistically, the frequency of these photons results from the difference between the products of the quantum number and the radial velocity or frequency of recurrence of the electron in its current state (nωn/2π) and the quantum number and frequency of the recurrence of the electron in any other quantum state (mωm/2π). Intermediate states are unstable because orderly recurrences or juxtapositions of the system’s particles and energy are not possible. Consequently, the photon should not be regarded as an entity existing discretely within the system, but as additional energy completely dispersed within it, absorbed or emitted by the system only as a result of quantum state rearrangements by impulses from actons. Action theory thus proposes a strong causal and mechanistic role for electrons and nucleons in quantum transitions of energy states. Plainly, all of the energy or actons in the system participate in sustaining its action so that ground state energy and even zero point energy should not be ignored just because it is unavailable for emission or absorption. Recognition of these relationships between energy and the action of atoms promises to enable the puzzle of spectra to be unravelled. It is also possible to recognise the following relationship involving respective momentum or total impulse.

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Thus And

ν hν hν/c p

= (nωn - mωm)/4π = (nhωn - mhωm)/4π = (nhωn - mhωm)/4πc = ∆Kinetic energy/c = ∆T/c

So the magnitude of the quantum emitted is equal to the increase in the kinetic energy as the electron falls towards to nucleon. The converse is true when a quantum of radiation is absorbed, which effectively cools down the electron. We point out from this that the change in total energy is equal to the quantum of energy emitted. The change in potential energy is equal to the sum of the quantum emitted plus the increase in kinetic energy. Earlier, U = - me r2ω 2 = -meC/r And E = - me r2ω 2 /2 = -meC/2r = (nhωn - mhωm)/4π hν (n,m) = me rn2ωn 2/2 - me rm2ωm 2/2 = ∆T = -∆E

∆U = hν - ∆ me r2ω 2/2 ∆U = ∆E - ∆T = 2∆E As noted above, the magnitude of the change in total energy (i.e. the photon) is always equal to the change in kinetic energy and that the change in potential energy is actually the sum of energy of the photon and the change in kinetic energy of the electron. Potential energy is thus always a positive value, quite logically decreasing as the electron moves from an infinite radius by the sum of the energy radiated as quanta (the total energy removed from the system) plus the increase in kinetic energy. Assuming that the maximum kinetic energy possible of an electron is mc2/2 (which it would have at the radius of the proton, where mass would be radiant energy) where the potential energy would be zero, it seems clear that the potential energy of the electron at infinity must be mc2. The assumption of zero at infinite radius is therefore in error by -mc 2. Thus

U = mec2 – mev2 = mec2 - meC/r

This implies that the total energy refers to the radiant energy absorbed in the system only. This is all available when the electron is at infinity, plus the potential kinetic energy. Using the same formula as before: E=T+U = mec2 – mev2/2 which is consistent with Einstein’s formula when v =0. Otherwise, the internal energy of the system is simply mc2 minus the radiation emitted from the system. This simple mathematical description of the spherically symmetrical hydrogen atom illustrates some of the key features involved in the action resonance model. Appropriate developments of this approach may provide realistic physical models for more complicated atoms and molecules, generating their spectra. In any such development, the dynamic geometrical structure of the respective nuclei and electron shells must be considered. In particular, the momentum transferred by impulses from quanta must have some correspondence with the change in momentum for the electron. Calculation shows that the linear momenta of the quanta or photons indicated as capable of dissociating electrons (e.g. see Table E.3, n = 1, 2, 3, … m = ∞) are clearly insufficient, since escape requires a doubling in the electron’s initial kinetic energy. However, appropriate resonance may amplify the total impulse. For example, the linear momentum for the photon corresponding to the transition n = 1,∞ is 7.268223 x 10-22 g.cm s-1

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(from Einstein’s equation p = hν/c). This is 274 times less than the linear momentum of the electron in the ground state Table E.2). As discussed above, the addition of one acton of specified mass to the sphere occupied by the electron-proton couple could alter the electron’s momentum by resonant reflections in the couple, effectively altering and straightening its trajectory sufficiently to allow dissociation, but this would take one second. In fact, dissociation does not occur from the addition of energy to one atom. Instead, a large number of actons are added to an ensemble of hydrogen atoms freely exchanging quanta. The dissociation of the first electron is then a cooperative action involving resonance of actons between all electrons and protons in the system and the dissociation of a particular electron is subject to statistical probability. Indeed, the electron that does dissociate is the one that is most probe-able to actons and least subject to deflection by screening in its proximal hemisphere. Table E.4: Calculation of spectral frequencies and wavelengths Spectral series Lower quantum Upper quantum Radiation frequency for no. = n no. = m transition ν = ω1(1/n2 – 1/m2)/4π = ω1(r1/rn – r1/rm)/4π = (nωn - mωm)/4π 1 2 2.46635x1015 Hz 1 3 2.92308x1015 Hz Lyman 1 4 3.08294x1015 Hz 1 5 3.15693x1015 Hz 1 6 3.19712x1015 Hz 1 3.28846x1015 Hz ∞ Balmer

Paschen

Etc.

2 2 2 2 2 2 3 3 3 3 3 3 3 n

3 4 5 6 7 ∞ 4 5 6 7 8 9 ∞ m

0.45656x1015 Hz 0.61659x1015 Hz 0.69058x1015 Hz 0.73077x1015 Hz 0.75500x1015 Hz 0.82216x1015 Hz 0.15986x1015 Hz 0.23385x1015 Hz 0.27440x1015 Hz 0.29827x1015 Hz 0.31400x1015 Hz 0.32479x1015 Hz 0.36538x1015 Hz (nωn - mωm)/4π

Wavelength of emitted quantum λ = c/ν nm 121.6 102.6 97.2 95.0 93.8 91.2 656.3 486.2 434.1 410.2 397.1 364.6 1875.1 1282.0 1092.5 1005.1 954.8 923.0 820.5 c/ν

One might regard excitation by a linear train of quanta of appropriate frequency repetitive impulses of 91.2 nm wavelength as sufficient to dissociate the electron. However, the notion of energy being distributed randomly on isolated one-dimensional photons as streams of linear momentum, able to act independently on isolated electrons in this fashion, without a full complex of sustaining dispersive impulses from actons distributed in a time-variable three-dimensional matrix, is misleading. For one thing, it fails to consider the variable inertia (I = mr2) of electrons and that changes in their action state will be governed by the radial parameter (r) that determines the outcome of torque x time (mr2ω2 x t = mr2ω). Ignoring these facts can lead to fallacies regarding mass-energy equivalence and estimates of the momentum carried on photons. Of course the physical parameters given in the action model of the hydrogen atom can only represent statistically-averaged values. Examination of the actual trajectories of electrons

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would be anticipated to reveal erratic if rapid motions more akin to those of Brownian particles than the idealised smooth circular orbits of the Bohr model. Obviously, each impulse would be expected to alter trajectories by alteration in r,ω and all derived properties such as action. Also the greatest care must be taken to consider that the continuous nature of action resonance stressed here means that frequency, momentum, action and energy take on an abstract quality that does not allow one to isolate these properties from the interaction between energy (acton exchanges) and the physical dimensions of the matter in which they occur. For example, photons such as those emitted in strongly heated hydrogen as its characteristic spectra can only be detected in resonant systems that can also vibrate at the appropriate frequency. Therefore, considering the nature of quanta independently of the material context in which they generate action may be misleading, particularly when concepts such as mass, frequency and velocity are considered. As mentioned above, the mass-energy equivalence proposed by Einstein is particularly difficult to reconcile when these properties are considered as static. In due course, the full range of descriptive and predictive successes obtained from quantum mechanics using the Schrödinger equation and matrix mechanics may be explained using the action resonance revision.

Celerity A new property introduced in action theory to indicate the mutual acceleration of one body towards the other. The value of the celerity is a function of the quantity of matter (i.e. mass in a body) and in general, the gravitational celerity is estimated by multiplying mass (m) by the universal gravitation constant (G).

Couple A couple is a pair of equal forces acting on the same body in opposite directions and in parallel lines. We can generalise this idea to include any pair of orbital bodies.

Dimensions, physical; dimensional analysis All physical and chemical properties must be expressed based on some system of units. Each unit is expressed in terms of primary dimensions of mass (M, m) length (L, r) or time or relative motion (T/t, ω). In action resonance theory mass (m), radial separation (r) and relative angular velocity (radians per second, ω) are the basic physical dimensions, consistent with the primary principle of conservation of the impulses from actons as the basis of force. Mass as a quantity of matter provides the measure of the propensity to interact by action exchange forces, radial separation provides spatial coordinates and extends the distribution in space of matter, and angular velocity provides a measure of relative motion (or of time). All other physical and chemical properties are derived from these dimensional parameters. As a result, dimensional analysis can provide a useful means of examining physical and chemical problems. For example, the physical dimensions of equalities must also be equal, providing a means of checking the accuracy of mathematical equations. During most of the 20th century, there has been an increasing tendency to neglect dimensional analysis. Progressively, physical and chemical theories have been expressed with units of more obscure physical meaning. The naming of units after prominent scientists, perhaps an expression of the ‘cult of personality’ in science, has accelerated this tendency towards use of units with obscure dimensions. The Système Internationale (SI) of units, set up in the latter half of the century to achieve uniformity, actually cemented this trend.

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Table E.5: Dimensional formulae of physical and chemical quantities Quantity Definition Dimensional formula Mass Fundamental M Length or radius Fundamental L Time or Frequency Fundamental T Velocity (v) Distance per unit time LT-1 Acceleration (a) Velocity per unit time LT-2 Momentum (p) Mass x velocity MLT-1 Force (F) Mass x acceleration MLT-2 Angular momentum (L) Momentum x lever arm ML2T-1 or Action (@) Energy x time Energy (U, E, T) Force x distance or lever arm; ML2T-2 Change in action per unit time; Torque Moment of inertia (I) Mass x radius squared ML2 Volume Cubic function of length or L3 radius denoting contained space Concentration Relative quantity of matter per NL-3 unit volume Mass per unit volume ML-3 Density (ρ) Pressure (P) Force per unit area; ML-1T-2 Energy per unit volume Force per unit area per unit ML-1T-1 Viscosity (η) velocity gradient Voltage (V) Square root of force or energy M0.5L0.5T-1 per unit charge Charge (q) Distance x square root of force M0.5L1.5T-1 Current (I) Charge per unit time M0.5L1.5T-2 Electric field (E = iR) Force per unit charge or M0.5L-0.5T-1 voltage per unit length Resistance (R ) Inverse of velocity L-1T Magnetic permeability Inverse of velocity squared L-2T2 of free space (µo); magnetic permeability (µ) Magnetic field strength Magnitude of a magnetic field M0.5L0.5T-2 or intensity (H) (current per unit length) Scalar product of the flux M0.5L0.5 Magnetic flux (Φ) density x area Magnetic flux density or magnetic induction (B = µH) Electromagnetic moment (pm = T/B) Magnetic moment of a magnet (M = L/H) Magnetization (M =B/µo – H) Celerity

Action formula m r ω rω = v rω2 mrω = mv mrω2 mr2ω = mrv mr2ω2 = mv2 mr2 = I r3 Nr-3 mr-3 mr-1ω2 mr-1ω (= mrω2.r /r2.rω) m0.5r0.5ω m0.5r1.5ω m0.5r1.5ω2 m0.5r-0.5ω (rω)-1 (rω)-2

m0.5r0.5ω2 m0.5r0.5

Magnetic flux per unit area at right angles to magnetic force

M0.5L-1.5

m0.5r-1.5

Ratio of maximum torque to magnetic flux density Ratio of maximum torque to magnetic field strength Magnetic moment per unit volume Orbital action x velocity per unit mass of a couple

M0.5L3.5T-2

m0.5r3.5ω2

M0.5L1.5

m0.5r1.5

M0.5L0.5T-2

m0.5r0.5ω2

L3T-2

r3ω2

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By contrast, a rational system more conducive to clarity and understanding would employ units named with more obvious physical meaning, based clearly on functions of these three primary dimensions. One point of view is that the choice of fundamental quantities or units in science is arbitrary. Thus, it would be possible to propose, at least mathematically, that the velocity of light is dimensionless and unity in free space. All mechanical quantities could then be expressed mathematically in terms of mass and time. However, this is an abstract principle quickly leading to conceptual difficulties and certainly not in keeping with the objective realism of action theory. Philosophically, the quantity of matter (mass), of separation or length and angular velocity only can be justified as objective fundamental physical measures. Each of these is extensive and differences in magnitude are based on a simple additive principle. They correspond to our natural way of acting and of thinking. There seems to be no good reason to reject them as the commonsense basis for the primary system of units. On the other hand there remains the question of the choice of units for each of these three fundamental quantities. Throughout this book the centimetre, gram and radians per second have been used as the units of choice, similar to the cgs system used in the first half of the 20th century and for most of the source literature used. In fact, the author prefers to think in this system as more amenable than the SI system based on the metre, the kilogram and the second. Literally, a cubic centimetre and a gram are easier to get one’s mind around than a cubic metre and a kilogram. For water, the cubic centimetre and the gram are equivalent whereas this is not true of a cubic metre and a kilogram, as a cubic metre of water weighs 1000 kilograms. But there is nothing fundamental about any previous system of units and no doubt a better system could be chosen for action theory. Planck (1913, p. 175) drew attention to the possibility of a natural system of units in which each of the speed of light, the universal gravitational constant, Planck’s quantum of action and Boltzmann’s constant would be unity. This required that the unit of length be 3.99 x 10-33 cm, of mass be 5.37 x 10-5 grams, of time be 1.33 x 10-43 seconds and of temperature be 3.60 x 1032 degrees. However, these would not seem very practical units for everyday use in ecosystems. In Table E5, dimensional formulae are given for a range of secondary or derived units. It is of interest that the exponents are not necessarily integral values of the fundamental units, particularly in electromagnetic theory. Traditionally, this has not been widely regarded as a problem. However, it is curious that a voltmeter measures a property with dimensions of the square root of force; since charge is also the square root of force times a radial parameter, the two multiplied together provide force x length = torque or energy. A similar outcome as turning moment or torque is generated when multiplying magnetic induction x magnetic moment, or magnetic field strength x magnetic flux. In action resonance theory, non-integral exponents would be regarded as inimical to the achievement of unification of the different areas of science. An improved system of electromagnetic units based on an action revision, in which torque x time indicates change in action, would not contain this flaw.

Free energy

∆G = ∆H - T∆S and ∆A = ∆E - T∆S Incidentally, the derivation of this equation involves an understanding that ∆G = -T∆S for the whole process. That is, -T∆Suniverse = ∆Hsystem - T∆Ssystem We may then conclude that -T∆Suniverse =

-T∆Senvironment - T∆Ssystem

This perhaps tautological conclusion infers that a negative Gibbs free energy indicates a potential to increase entropy (and action), either inside a system or in its environment.

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Gravitation, Gravity Action resonance theory proposes a simple explanatory mechanism for gravity. Attraction is considered to be the apparent result of cooperative impulsive interactions from actons of ground energy, transmitted between the matter of elementary particles of molecules or bodies made up of molecules. Gravitational forces are regarded as identical in principle to the forces generated at all other scales affecting trajectories in communities of organisms, single organisms, cells, molecules and subatomic systems, although the inertia and degree of coherence of the matter involved varies significantly. Because of their very low inertia, corresponding to a low time rate of incidental impulses, there is much more uncertainty in the case of the trajectories of individual nuclear particles and of electronic orbits. It is conjectured that the quanta of gravity are generally of such low frequency and extremely long wavelength that they can normally be expressed collectively as singular impulses of actons, corresponding to cold, dark, ground energy with an equilibrium temperature almost indistinguishable from absolute zero (the zero point energy). Despite their inherently low frequency and momentum, gravitational actons/quanta are proposed to comprise the vast majority of the energy of ecosystems. Because this ground-state energy is isotropic, continuously balanced in detail by impulses on a time scale of less than 10-22 sec and of extremely small differences in magnitude between adjacent action states, it cannot be readily detected. However, its cumulative effect as vast numbers of impulses is obvious in all irreversible processes that depend on special initial conditions (e.g. the trajectory of a falling apple, rainfall or an aircraft in distress). By contrast, the cooperative sets of actons comprising the energy quanta involved in transitions in action states of molecules, protonic and electronic reactions, correspond to much greater changes in energy content for each change in action state and are therefore easily monitored by suitably responsive detectors. However, these represent only a minute proportion of the total energy available of mc2. Screening from the impulses of actons leads to local coupling between pairs of mutually interactive masses (m1, m2), causing acceleration (rω2) of each body towards the other, generating their relative kinetic energy. Since the magnitude of the instantaneous acceleration from unit mass of the body producing this screening effect must be inversely proportional to the square of the radius of separation we have rω2 = C/r2. Thus r3ω2 = C, the celerity or quickness of action for a body, which is constant for circular orbits but varies for non-circular orbits such as elliptical. These conjectures are consistent with the observations of Johannes Kepler (see Kepler’s laws), who concluded from the accurate astronomical data of Brahe for Mars that planetary orbits are elliptical rather than circular, as proposed by Copernicus. The nature of this motion is codified in his third law: the period of the elliptical orbit T of a planet is related to the semi-major axis of the orbit R by the equation T/2π = R1.5, for an orbital system such as that of the sun and its planets. In action theory, the celerity (C) for a couple formed between a central body and any satellite, a characteristic constant, is given by Ca = a3ϖ2 = r3ω2.. The value of the characteristic celerity will be similar for all other satellites of the central body. In principle, every pair of bodies in the universe will exhibit a characteristic celerity, different for each partner of the couple, which characterises their relative motion. Because this relationship is inversely proportional to the square of their radial separation, since this determines the screening potential, the mutual interaction with distant bodies diminishes very rapidly and soon becomes infinitesimal. For relative motion that is elliptical, a corresponds to the major semi-axis and ϖ to the average angular velocity during an orbit, which equates to the geometric mean of the angular velocities when the radii of action a and b are equal to the major and minor semi-axes respectively (i.e. ϖ = (ωaωb)0.5).

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However, the magnitude of the celerity for any couple is dependent on the total quantity of mutually interacting matter, first recognised by Newton in his theory of gravitation. For mutual interactions proportional to the total mass, as in gravitation, we have: C = r3ω2 = (m1+m2)G, for approximately circular orbital couples, where G is the universal constant of gravitation. Then the gravitational force m1m2G/r2 = m1m2rω2/(m1+m2) = m2rω2 where m1>>m2 or = m2rω2/2 = m2r2ω2 = m1r1ω2 where m1 = m2 and r = r1 + r2. Where this centripetal force is in equilibrium or in balance with an outwardly directed centrifugal force also proportional to the exchange of impulses, a stable orbit is maintained in which r is the constant radial separation for circular orbit or r = a, the semi-major axis for elliptical orbits. Because the true measure of inertia in an impulsive interaction of an orbital couple at equilibrium is the constancy of action or angular momentum, we can write r2ω = @ = nh, arbitrarily setting m2 = 1. Then, for a couple where nh = @ remains constant during the epoch of observation, C = n2h2/r = r3ω2 = rv2; v2 = C/r = n2h2/r2 and v = nh/r. For all other non-dominant couples, the action and the potential energy must constantly vary, corresponding to changing action states and radiant energy exchange. Similar solutions can be obtained for more restricted modes of interaction between particles such as the electromagnetic, dependent on the propensity for mutual resonance between systems of particles such as protons and electrons, but not neutrons. It is evident that the magnitude of the celerity for any couple of bodies depends on the amount of matter they contain ņ a logical assumption of action theory, given the mechanism of acceleration and force if proposes. Another important variable affecting the value of the characteristic celerity, easily predictable from the mechanism of action as the effect of balancing of impulses, is the total radiant energy a system contains, including the zero point energy. This is a result of the change in the relative distribution of matter into action or quantum states with different total energy. Even the value of G, the universal constant of gravitation, is therefore a statistical result which could vary if significant variations in the background zero point energy were possible. This is a possibility which would have implications for the current method of measuring time itself (since it would affect the rate of decay of radio-isotopes), but such variations have not so far been observed by modern scientists. The influence of the geometry of elliptical orbits is worth investigating. In the ellipse shown in Figure E.1, the central body (e.g. the sun) is shown at one focus of the ellipse at F and the orbit of the planet (e.g. the earth) is given by the external oval. It is relevant to action resonance theory that the tangent and its normal drawn at any point P on the orbit bisect the angles between the focal radii F and F,