The End of Time: The Next Revolution in Physics

The End of Time

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The End of Time The Next Revolution in Physics

Julian Barbour

OXFORD UNIVERSITY PRESS

OXFORD UNIVERSITY PRESS

Oxford New York Athens Aut·kland Bangkok Bogot:1 Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madnd Melbourne Mexico City Mumbai Nairobi P quite close to my own present pmition. Ill' has since !Jacl-;ed away somewhat, and now advocates an interpretation of quantum mechanics in which history is the fundamental concept. I should also li!-;e to express my thanl-;s here to Dieter Zeh. Zeh, who was in this hminL"iS long hdore me, also made me realize the importance of Mott's wori-;, and, crucially, alerted me to Bell's paper. TherL' arc not many physicists who tai-;e the challenge of timcll'ssness utterly seriously, !Jut Dieter Zch and his student Clam Kiefer, from both of whom I hJ\'e gained and learned much, arc two of them.

CHAPTER 21• THE MANY-INSTANTS INTERPRETATION Bell's 'Many-Worlds' Interpretation (p. 299) In his 'cosmologicJI interpretation' of quantum mechanics, Bell combined clements derived from both Everett and the de Broglie-Bohm interpretation (see the note to Chapter 19). In fact, Bell's account of his mixed interpretation is rather terse, and can be misunderstood. I am most grateful to Fav Dowi-;er and Harvey Brown for drawing my attention to an error I made in rqJOrting Bell's idea in my first draft of this boo!-;. In this section I follow their interpretation of Bell, which I am SUIT is what he did mean. The Many-Instants Interpretation (p. 302) I hope I have made it clear that probability 'to be experienced' or 'to exist' is a problematic concept. If consciousness is determim'd by '>tructurc, the consciousness is already in the Nows and must be experienced irrespective of their probabilities. What role remains for probabilities"! It is a very difficult issue. Probability is already puuling in ordinary quantum mechanic>, and even in classical physics. Cold water could boil spontaneously, but we never seL' this happen. Standard probability arguments suggest that what is pos,ihll' but hugely improbable will not be experienced. Much 'uggests that probabilities in somL' form arc inescapable in quantum theory simply because it explores mutually exclusive pmsi!Jilities. Instants of time arc natural candidates for the ultimate exclusive possibilities. If certain very specially structured instants do get hugelv larger probabilities than others, and arL' the ones habitually expcril'IlCed, that must, I feel, count as explanation. But as an indication of the depth of this problem, I add here in Box 16 an edited email exchange I had with Fay Dowh'r of Imperial College, London. l had especially asl-;cd her to read my first draft, since she is a very clear tl!ini-;cr !Jut is sceptical about both many worlds and canonical quanti;ation, the approach to quantum gravity that I favour.

CHAPTER 22• THE EMERGENCE OF TIME AND ITS ARROW Soccer in the Matterhorn (p. 307) In the second edition of File l'ilysiwl Hasis of tl1e I lirclfiou uf ri111c. /l'11 savs that the intrinsic dvnamical asymmetry of quantum

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gravity 'offers the possibility of deriving an arrow of time (perhaps even without imposing any special conditions)'. Timeless Descriptions of Dynamics (1) (p. 309) For specialists: for each stage of

a perturbation expansion, Mott always chooses a kernel in an integral representation corresponding to outgoing waves. However, nothing in the mathematics rules out the (occasional) choice of incoming waves. This would mess up everything. (2) (p. 309) I should emphasize that Mott, like Bell, never used any expression like

'time capsule', and clearly did not think in such terms about alpha-particle tracks. Neither did Mott's work on alpha-particle tracks seem to have prompted him to any intimations of a many-worlds type interpretation of quantum mechanics. I learned this from Jim Hartle. Over a decade ago, when collaborating with Stephen Hawking in Cambridge, jim lodged at his college, Granville and Caius (featured famously in Chariots o(Firc), which was also Mott's college. Over dinner Jim asked Mott whether his paper had not led him to anticipate some form of Everett's idea, and was told no. Apparently, all the 'young Turks' followed the Copenhagen line without hesitation at that time. Shortly before his death about two years ago, when he was still mentally very alert, I contact Mott and asked if I could talk to him about his paper. Alas, he was too ill to keep the appointment, telling his secretary he was very disappointed 'since the man wanted to talk about work I did nearly sixty years ago'. A Well-Ordered Cosmos? (p. 321) This final section follows closely the final sec-

tion of Barbour (1994a).

BOX 16 An Email Dialogue DOWKER. It seems to me that you provide no scheme for making predictions, and I would further claim that no such scheme can exist which contains the two aspects that are fundamental to your scheme: canonical quantum gravity (COG) and the Bell version of the many-worlds interpretation (MWI). BARBOUR. I think you are right, subject to what one means by prediction. cannot make the kinds of prediction you want, and you correctly identify the reasons. I feel the arguments for COG and MWI outweigh desire for predictions of the kind you would like. DOWKER. I freely admit that I am rather attached to the notion of the universe

(and I) having had, and being about to have, a continuous history. But my criticism here is not the absence of history in your approach, but, to repeat, that

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there is no way to make predictions about the results of our observations. In my view this is a deficiency that cannot be overcome. Whatever else science tells us about the world, it must allow us to make predictions about our observations that we can check. BARBOUR. I am not sure we can impose such a criterion on Nature. The Greeks

had the notion of saving appearances (finding a rational explanation for the phenomena we observe) that is already very valuable. You may be asking more of Nature than she is prepared to give. DOWKER. In backing up this criticism I shall focus on the aspect that I am most familiar with and on which I have most confidence in my own views, which is the aspect of the interpretation of quantum mechanics. I am pleased that your book draws attention to the work of Bell on the many-worlds interpretation, since it has not had the recognition it deserves. In my view his version is the only well-defined many-worlds interpretation (I'll call it BMW!) that exists in the literature. BARBOUR. I agree it is well defined, but with reservations about the role of time. The time of an observation, like any other observable, must be extracted from present records. When you start to ask how that is done in practice and how Nature does put time into the records, I think things may become less well defined. I do believe that almost all physicists this century have blindly followed Einstein in declining to try to understand duration at a fundamental level A lot of the first part of my book is about that. I think my position might be stronger than you realize. DOWKER. I think that neither your version (which I'll call JMWI) nor BMWI allows us to make predictions about what we observe (so I disagree with Everett's statement 'the theory itself predicts that our experience will be what it in fact is'). Let me take your version. There we have many configurations at time t. The most serious problem is that in a scheme like yours, in which all the possibilities are realized, there is no role for the probabilities. The usual probabilistic Copenhagen predictions for the results of our observations cannot be recovered. An excellent reference which analyses the MWI literature and the various attempts to derive the Born interpretation from MWI is Adrian Kent [1990, International Journal of Modern Physics, A5, 1745]. Adrian concludes that they fail I 'II just state again the main reason that they fail: when all the elements in a sample space of possibilities are realized, then probability is not involved. Your idea is that it is the sample space itself, i.e. how many copies of each configuration are included in the sample space, which is determined by the (squares of the) coefficients of the terms in the wave function. That is all well and good (if bizarre). But there's no reason then to call those numbers probabilities, and no

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way to recover the probabilistic predictions of Copenhagen quantum mechanics. In fact the MWI proponents themselves agree that the failure to reproduce the Copenhagen predictions is a problem and do try to address it, but without success. BARBOUR. I accept that this is a strong critique. I nevertheless feel that my

scheme does in principle have predictive strength. If you could see Platonia and Born's probability density concentrated incredibly strongly on a tiny proportion of its points that all turn out to be time capsules as I define them and Bell describes them, would you not find that impressive, and something like a rational explanation for our experiences/ DOWKER. As well as the MWI, you base your conjecture of timelessness on the technical result that when a canonical quantization scheme is applied to general relativity, the wave function cannot contain the time. My understanding of the state of affairs in canonical quantum gravity is that. because of this, no one knows how to make the kind of predictions we'd like to make: explanations such as 'What happens in the final stages of black hole collapse I', 'Why is the cosmological constant so very small?', etc. BARBOUR. I agree with your first example (and do not think it is too seriousthere may be questions that it is JUSt not sensible to ask), but in principle my scheme could predict that virtually all time capsules will appear to have been created in nearly classical universes with a very small cosmological constant After all, that is what our present records indicate. If all probable configurations seem to contain records that indicate a small cosmological constant, I am okay. DOWKER. My reaction to the situation is that formulating general relativity in a canonical way has been shown to be the wrong thing to do--we did what we weren't supposed to-divided up space-time into space and time again. Even if it wasn't clear from the beginning that it would be incredibly difficult to maintain general covariance of the theory whilst trying to treat space and time differently, I find the lack of any insight into how to recover predictions within the canonical quantum gravity program convinces me that we should look elsewhere for a quantum theory of gravity. BARBOUR. As he was creating general relativity, Einstein was convinced general covariance had deep physical significance. Two years later, correctly in my opinion, he completely abandoned that position. In my opinion, general covariance is an empty shell (I say something about this at the end of Chapter 10 and in the notes to it). I believe it is not possible to give any meaning to the objective content of general relativity without saying how the three-dimensional slices in space-time are related to each other. That is the very content of the the-

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ory. That is why I think the arguments for canonical quantum gravity are very strong indeed. The constraints of the canonical theory are its complete content. DOWKER. Having made my basic points, let me now just say that I find it

incredibly hard to understand how, as a solipsist of the moment, you must view science and the scientific enterprise. BARBOUR. Answered above I think. Science should explain what we observe. We habitually observe and experience time capsules. Even granting the real difficulties with calling the square of a static amplitude a probability, should it turn out that the Wheeler-DeWitt equation does strongly concentrate the square of the amplitude on time capsules, I think that would be an incredibly strong and suggestive result. DOWKER. Take the idea that a good scientific theory should be falsifiable. BARBOUR. I think my idea is falsifiable in the following sense. There may well

be configurations of the universe with records of my idea and mathematical proofs that the Wheeler-DeWitt equation most definitely does not concentrate the square of the amplitude on time capsules. If I too am in them, I would have to say my proposal for an explanation of why we think time flows has failed. DOWKER. That presupposes that there will be a future in which we can try new experiments that test the theory and find that these experiments may be in contradiction to our predictions. The very word 'prediction', which I have used so many times in this letter, is laden with time-meaning. A prediction is a statement of expectation of something that will happen. Prediction is the lifeblood of science. How could we do science without it? BARBOUR. I totally agree about the importance of prediction. But it does not

necessarily have to involve time in the way you suggest. From observations of one side of the Moon, astronomers tried to predict what was on the other side. They got it wrong when the other side was seen. I do not think time comes into such predictions at all significantly. Consider, as Jim Hartle once did when he was quite close to my present position, geology. The rocks of the Earth hardly change. Suppose the idea of continental drift had been proposed before America had been discovered. It would have predicted the existence of America and the geology of its east coast (the west of Ireland exactly matches Newfoundland, I believe). Again, time is not essentially involved in this prediction. I think Bell puts my case very well: 'We have no access to the past. We have only our "memories" and "records". But these memories and records are in fact present phenomena.' The italics are Bell's. Predictions are always verified in the present. That is my apologia.

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Notes Added for This Printing.

As mentioned at the end of the Preface and at various places in the Notes, there have been some promising developments of the ideas presented in this book since it was sent to press in spring 1999. They are contained in two joint papers published electronically and available on the web: julian Barbour and Niall () Murchadha, 'Classical and quantum gravity on conformal superspace', http//xxx.lanl.gov/abs/gr-qc/9911071 and julian Barbour, Brendan Z. Foster, and Niall () Murchadha, 'Relativity without relativity', http//xxx.lanl.gov/abs/grqc/0012089 [the xxx is correct[. The potential significance of the first paper has already been explained on p. 349/350. At this stage, I do not wish to make any firm statements about this new work since it is incomplete and has not yet been exposed to scrutiny by other physicists, but I can at least give some idea of what is at stake. The basic issue is the status of the relativity principle. When Einstein and Minkowski created special relativity, they deliberately made no attempt to explain the remarkable structure that their work had brought to light: the existence of spacetime and its associated light cone, both being ret1ected in the Lorentz invariance of the laws of nature. They adopted Lorentz invariance, which assumes the existence of length, as the basis of physics. In small regions of spacetime, this still remains true in general relativity. Taken together the two papers cited above suggest that all of the presently known facts of relativity and electromagnetism can be derived in a new and hitherto unsuspected manner from three assumptions: 1) an independent time plays no role in dynamics; 2) best matching (pp. 116/7) is the essential element in the action principle of the universe; 3) any theory satisfying these principles must have nontrivial solutions. It is the third assumption that makes a dramatic difference. Hitherto, in common with other colleagues, I had assumed (see p. 181) many different theories could satisfy the first two conditions, but, as my collaborator Niall c) Murchadha discovered, this is not the case. The reasons for this and its remarkable potential consequences are spelled out in the second cited paper. It is frustrating not to be able to say more at the present moment, but at a time of uncertainty about the final outcome it is better to say less rather than too much. My website (julianbarbour.com) will carry more detailed information. I conclude with some additional comments that have mostly already appeared in the UK paperback. My website now carries an email dialogue between myself and Don Page (whom Hawking, in A Hrir.f History of' Time, credits with pointing out, with Raymond Lat1amme, 'his greatest blunder'). I think Don has made some interesting and valuable comments, including both valid criticism of some points but also reassurance on other issues on which I had doubts. Don is another person who takes the timelessness of physics utterly seriously, and, in fact, our views are very close. He has written several papers on the problem of consciousness and quan-

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tum mechanics (Sensible Quantum Mechanics). Full details can be found on my website. I should also like to mention here an idea that Dieter Zeh put forward in the meeting at Huelva in Spain at which I conducted my straw poll. This is that the universe must, of necessity, always be observed as expanding. I find this an intriguing idea and, if it is correct, it would fit beautifully with the open-ended, flowerlike structure of Platonia. I think Dieter's idea, which I hope is correct though I have hedged my bets in this book, influenced me somewhat in the writing of Box 3 and parts of the Epilogue. I regret that in the final chapter I made no mention of the idea of inflation, which is explained in a gripping and candid book by Alan Guth that I have at least now included in the books recommended for further reading. From reading Guth's book I also learned that an interesting proposal of a mechanism for the 'creation of the universe' was made by Edward Tryon in 1973. I should also have mentioned that in 1982 Alexander Vilenkin proposed an influential alternative proposal to Hawking's no-boundary idea (1981) and that Jim Hartle played a significant role in its development, which culminated the Hartle-Hawking wave function. My apologies to these authors (none of whom have registered any complaint). Details can be found in Guth's book. It has also been pointed out to me by several email correspondents that there is a clear anticipation of some of my ideas about time in Fred Hoyle's novel October the First Is Too Late, which Paul Davies discusses in his About Time. Sir Fred's 'pigeonholes' are essentially my time capsules. American reviewers and correspondents also noted a similarity with the philosophy of time that underlies Kurt Vonnegut's Slaughterhouse Five. Having now read the book, I can confirm that this is the case. Of course, as I make clear in the text, john Bell also formulated the idea of time capsules (without giving them any name) quite clearly long before me. Another correspondent, Andrew Clifton, regretted that I had not devoted at least a few words to demolishing the idea that there really is a 'moving present'. I think he was right. Happily, David Deutsch has done the job very well in his The Fabric o(Rea/ity. I should also like to thank Damien Broderick, who has reviewed my book for The Australian, for drawing my attention to various misprints. It is also now clear to me that in the body of the text I should have said more about possible ways in which my ideas could be refuted. A theory is no use to science unless it is capable of disproof. In the email exchange with Fay Dowker, I did mention the possibility of mathematical disproof of my conjecture that the Wheeler-DeWitt equation concentrates its solutions on time capsules. However, I think that (in normal parlance) that might take decades. Something that might occur much sooner is a completely convincing definitive form of superstring theory (or some other unified theory) that reintroduces an external time (string theory does currently use background structures). That would kill my idea. My own feeling is that in fact superstring theory will, if and when it is found, turn out to be timeless.

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Then there is one other quite different way in which my ideas could be disproved. This is if experimental evidence can be found that shows collapse of the quantum wave function to be a real physical process. In this connection, I should like to mention especially an experiment proposed by Roger Penrose to test this very possibility. He is developing it in collaboration with Anton Zeilinger, the Austrian physicist based in Vienna, who has performed so many incredibly beautiful quantum experiments. Penrose, very understandably, finds the many-worlds interpretation of quantum mechanics extremely hard to accept (see my comments about the death of Diana), and with great persistence is trying to find a way round it. He has certainly identified the greatest single issue in modern physics. If his experiment, which could perhaps be performed within a decade, works out in the way he hopes, it will be a huge development and destroy my approach (because it will show that quantum mechanics does not hold macroscopically). The volume containing my paper (Barbour 2000) also contains Penrose's most important paper on the subject, and also a related paper by Joy Christian, who was a student of Abner Shimony. joy, following Abner (see my Epilogue), is trying to establish transience as a real physical thing. I think that if collapse of the wave function could be demonstrated as a real physical phenomenon, that would be true demonstration of something that one might call transience. ]B january 2001

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FURTHER READING

Barrow, john, 1992, flu!orics o( Everything, Oxford University Press, Oxford. Barrow, john and Tipler, Frank, 1986, The 1\nt/zropic Cosmological Antlzropic l'rinciple, Clarendon Press, Oxford. Bondi, Hermann, 1962, Relativity and Co1111110n Seme: A New Approaclz to Eimtein, Dover, New York. Coleman, James, 1954, Relativity fin tlze l,aymmz, William-Frederick Press, New York ( 1990, Penguin, London). ( :oveney, Peter and Highfield, Roger, 1991, Tlze Arrow of Time, Flamingo, London. Davies, Paul, 1991, Tlze Mind o( (;od, Simon & Schuster, New York. Davies, Paul, 1995, About Time: Eimtein's Unfinished Revolution, Penguin Press, l.ondon. l kubch, David, 1997, Tlw Fabric o( Rmlity, Penguin Press, London. Eddington, Arthur, 1920, Space, Time and Gravitation, Cambridge University l're-;s, Cambridge. Einstein, Albert, 1960, Relativity: Tlze Special and tlze General Theory. A Popular Fxpositiun, Routledge, London. (;recne, Brian, 1999, Tlzc Elegant Universe: Superstrings, Hidden Dimemions, and tlze Quest fin tile Ultimate Tlzmry, Vintage Books, New York. Cribbin, John, 1984, In Smrclz o(Sclzrijdinger\ Cat: Quantum l'lzysics and Reality, Corgi, London. Cuth. Alan 11., 1997, Tlzc Inflationary Universe: Tlzc Quest fi;r a New Tlzcory o( Cosmic Origim, Perseus Books Group, New York. Lippincott, Kristen, Eco, Umberto, Gombrich, E. H. eta/., 1999, Tlzc Story of Time, Merrell Holberton, London . [This is a splendid book on the most diverse aspects of time in culture and science.[ Lockwood, Michael, 1989, Mind, Brain and tlzc Quantum, Basil Blackwell, Oxford. Novikov, Igor, 1998, Tlzc Rivero( Time, Cambridge University Press, Cambridge. l'L'nl"