The Constants of Nature

J OURNH TOWA ROS ULTIMATE R€AlIH

11

super- or sub-human in scale. The smallest atoms are 10 billion times smaller than a metre. The Sun is more than 1030 kilograms in mass. In Figure 2.1 we show the span of SizeS and masses of significant objects in the Universe with ourselves added for perspective. We sit in between

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size ra~ges of some important ingredients of the Universe. Our choice of cmtimetres and grams as units places us close to the centre of things. Figure 2. t The mass

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17

J OU R NE Y T OWA R DS ULllloIA TE R E ALITY

specialised scientific conferences. workshops. meetings. discussions. panel discussions and round tables that there is no longer any place for a meettng that covers all of science at a technical level - it would be impossibly big, impossibly lengthy. and well nigh unmtelhglble

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of the partiCipants much of the time. Stoney was an eccentric and original thinker. He was the first person to show how to deduce whether or not other planets m the solar system possessed a gaseous aonosphere. lIke the Earth. by calculating whether their surface gravity was sttong enough to hold on to one. But rus real passion was reserved for his most treasured idea - the 'electron'. Stoney had deduced that there must extSt a basic mgredIent of electric

Figure 2.3 The Irish physicist George Johnstone

Stoney (1826-1911}.'"

36

The Constants oj Nature

Figure 3.1 nse Rosenthal·Schneider (1891-1990).' My opinion now is - stated briefly - that constants of the second type do not exist and that their apparent existence is caused by the fact that we have not penetrated deeply enough. I therefore believe that such numbers can only be of a basic type. as for instance 1t or ~.' What Emstein is saying is that there are some apparent constants which are created by our habit of measuring things In particular units. The radiation constant of Boltzmann's is like this. It 15 just a conversion factor between energy and temperature units, rather like the conversion factors between Fahrenheit and centigrade scales of temperature. The true constants have to be pure numbers, not quantities that have 'dimensions'. like a speed or a mass or a length. Quantities with dimensions always change their numerical values if we change the units in which they are expressed. Even the speed of Itght in vacuum can't be one of the true constants Einstein is searching for. A speed has units of length per unit time and so could not be shown to be some combination of the 'basiC' numbers. like 1t, that

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" Figure 3.3 TI,e pattern with which the observed structures in the Universe fill the size-mass plane is dictated by three factors. TI,e line of conslt2nt atomic density, the line that marks the black hole region within which things woulJ be inside black holes (anJ hence invisible), anJ the line marking the uncertainty principle of quantum mechanics which separates off the quantum region in which the usual concepts of size anJ mass cannot be simultaneously maintained. H-e see that most of the fomiliar strnctures in the universe lie on or close to the line oj constant atomic Jensity. Along this line the mass of soliJ objects is proportional to their IIOlume, or roughly to the cube of their sizes. 21 This is the region that IS guarded by Heisenberg's Uncertamty Principle. Nothing Wlthm It is observable. However, it tells us our third interestmg thing. Notice that tht quantum line mtersects the black hole line.

lbis IS the place where gravity and quantum reality coUide. And what

FU R TH ER. DEE PE R. F EWER

T HE QUE S T FO R A THE UR Y OF EVERYT HI N G

57

Figure 4.1 The irrepressible Mr G.GH. Tompkins, the eponymous hero of George Gamow~ scientific fantasy. Mr Tompkins in Wonderland.8

combine to produce in a world (like ours) where quanrum effects are very smal1,9 Me Tompkins's inttials G.C.H. bear witness to the central importance of the constants of Nature characterising gravity (G), quantum reality (h), and light (t)' We can use them to paint a Simple picture uf thl: curre.spundl:ncl:S bl:twl:l:n diffl:rl:lll law:; uf Naturl:. WI: Ill:l:d

only to appreciate a simple principle. When G is set equal to zero we are turning off the force of gravity and ignoring it; when h is set equal (0 zero we are ignoring (he quantum nature of the Universe, through which energies can only take on particular values, like steps on a ladder. The size of the steps between the rungs are fixed by h. If h were zero there would be no gaps and the energy of an atom could change by any value, no matter how small. 'o Third, when t is set equal to infinity (or, what is the same thmg, II t equal to zero) th~n light signals move with infinite speed. This was the picture of the world in Newton's day, with gravity acting instantaneously between the Earth and the Sun.

FURT HER. DE EP ER. FEWER

T HE O UES T F OR A TH (O RY O F E V( I'; YTHIN G

Figure 4.S Some numerological flights

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75

involving the number

137, compiled by Gary Adamson. enduring in i(S fascination. Our purpose in revealing some of Its examples IS not without a serious object. One of the formulae we listed above bears the name of Arthur Eddington, one of the twentieth century's greatest ascrophysicists. In the next chapter we wi.U look at Eddington more closely. He is a remarkable combination of the

EDD I N G TON S UNriNISHEO

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Figure 5.1 Alben Einstein (md Arthur Eddington tcgether in

Eddington's garden in 1930, photographed by Eddington's sister.) Tbt Einsttin lind tlx Eddington

The Etnstein and the Eddington Were counting up their score The Emstein's card showed ntnety-eight And Eddington's was more, And both lay bunkered in the trap And both stood up and swore. I hate to see, the Einstein said Such quantities of sand;

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'44

The Constants of Nature

Figure 8.1 Why do the cars in the other lane seem to be going

Jaster? Because on tire average they are!6

you anything about whether it is good or bad to change lanes. The grass, maybe, is always greener on the other side. Once we know of a feature of the Universe that IS necessary for the existence of chemical complexity, it is often possible to show that ocher features of the Universe that appear to have nothing to do with life are necessary by-products of the 'necessary' condition. For example, Dicke's argument really tells us mat the Universe has to be biUions of years old in order that there be enough bme for the building blocks of life to be manufacturtd in the stars. But the laws of gravitation tell us that the age of the Universe is directly linked to other properties it displays, like its density, its temperature. and me brightness of the sky. Since the Universe must expand for biUions of years it must become biUions of light years in visible extent. Since its temperature and density fall as it expands it necessarily becomes cold and sparse. As we have

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