TOWARDS A UNIFIED COSMOLOGY

by     Reginald O. Kapp

PART II - THE PAST AND FUTURE DURATION OF MATTER

Chapter 4 - Hypotheses About the Disappearance of Matter


4.1: The Alternatives
To obtain a complete hypothesis about the duration of the contents of the material universe one must combine one of the three hypotheses in the (A) list at the beginning of Chapter 3 with one of the three in the (B) list. The (A) list, it will be remembered, is concerned with the past and the (B) list with the future duration of matter. Of the nine possible combinations eight have to be eliminated.

The elimination cannot be based on scientific proof, for it does not appear that any one of the nine combinations can be proved false. But if one abandons the criterion of proof and adopts instead the criteria of minimum assumption, maximum explanatory and unifying power and satisfactory evidence, most of the combinations can be eliminated without much difficulty. It has already been shown that (Al) and (A2) fail badly by these criteria and I shall have several further occasions to confirm their inadequacy. So there remains only (A3) in the (A) list.

Of those in the (B) list it will be convenient to consider (B2) first, for this is the one that it is easiest to eliminate. (B2) is the hypothesis that the whole contents of the material universe will have ceased to exist after a definable time in the future. Apart from having the doubtful virtue of giving a very literal interpretation to the theological doctrine of the End of the World it has nothing to recommend it.

Consider its implications. Unless the further strange hypothesis is added that a process can be completed in zero time, supporters of (B2) must assume that a moment will arrive during the future year T1 A.D., when the extinction of the contents of the material universe will begin and they must assume a later moment during the year T2, when the process of extinction will be complete. Perhaps the hypothesis that a process can be completed in zero time would find supporters among laymen. But physicists do not know of any observation, experiment or line of reasoning by which to justify such an hypothesis.

If we believe that extinction is prevented in our time by certain specific physical laws, we could support (B2) only by assuming that these laws will be suspended for a period dating from the first of the two significant moments in the year T1 and lasting until the second significant moment in the year T2. We should, however, have to assume that the suspension will be one-sided, permitting the extinction of mass and energy but prohibiting the origin of anything new. It would be interesting to work out the implications of this hypothesis in detail. A physics from which one basic law was removed would differ in many other respects from that with which we are familiar.

From the moment when this new physics applies and matter begins to behave in new strange ways it would have to be assumed that the contents of the material universe will be dwindling until finally just one elementary component will be left. Then this, too, will disappear to mark the great transition from something to nothing.

This hypothesis can no more be disproved than its counterpart (A2), which assumes the same process in reverse for the past. But both are equally foreign to the physicist's habits of thought. The picture that they present looks more absurd the more closely it is examined; and this is just as true when the picture is relegated to a remote past as when it is relegated to a remote future. It is therefore not at all surprising that (B2) has no serious supporters among scientists, but it is surprising that (A2) has. Why, one is led to ask, should anyone who cannot believe that the laws of physics will ever be changed in the future believe that they may have been changed once upon a time in the past? Why should the notion of two specific, unrepeated and unrepeatable moments in the years T1 and T2 A.D. be rejected while the same notion is not even critically discussed when it is applied to the years T1 and T2 B.C.? Why should anyone who finds the notion of a future transition from something to nothing unacceptable be able to accept the notion of a past transition from nothing to something ? I do not know the answers to these questions, but the fact remains that attempts to justify (A2) by extrapolation from present observations have, at the time of writing, become fashionable and are being seriously discussed among scientists, while an attempt to justify (B2) by similar methods has not yet been made and would probably be deprecated.

Whatever it may be that causes (A2) to appear attractive need not, however, concern us here. (Al), (A2) and (B2) must all be dismissed by those who become aware of the tangle of additional hypotheses that are needed to preserve them. There remain thus for serious consideration only two of the nine possibilities: the combinations of (A3) with (Bl) and of (A3) with (B3). The former assumes that every elementary component of the material universe may have come into existence at any time and that a conservation law prohibits it from ever ceasing to exist. It attributes to each component a finite past and an infinite future, i.e. it assumes that one cannot trace the existence of any given component indefinitely back into the past, but that one can predict an indefinitely long future for it. (A3) coupled with (Bl) assumes a combination of past impermanence with future permanence. It can be called the Hypothesis of the Asymmetrical Impermanence of Matter. The combination of (A3) with (B3) can then be called the Hypothesis of the Symmetrical Impermanence of Matter; it assumes impermanence both for the future and for the past.

(Bl) postulates a specific law, which requires that every elementary component of the material universe shall last for all time. (B3) does not postulate this nor any equivalent law. It says that any component may become extinct at any moment of time, which is what would happen in the absence of a law. So (B3) seems to meet the criterion of minimum assumption better than (Bl). But I do not want to exaggerate the importance of this. I have already said that 'all time' may perhaps be less of an assumption than 'any time'. However, it will emerge from these pages that (B3) also meets the criterion of explanatory power much better. But this does not mean that (Bl) can be lightly dismissed. It is arguable that the Principle of Minimum Assumption may not always apply. (Bl) does have a little explanatory power. It is, moreover, sanctified by long tradition and has the backing of considerable authority.

This backing prevents its hypothetical nature from being easily recognized. We tend, understandably, to believe what we have been taught and to take for granted that it must have been subjected to the rigid canons of scientific proof. We are often told that good scientists, following Newton's precept, never adopt hypotheses and so we do not doubt that what has the backing of their authority must be irrefutable fact. It is a part of human nature to accept what is easy to believe and to reject what is unfamiliar. For all of these reasons many people are likely to deny hotly that the permanence of matter and energy (or at least their future permanence) is an hypothesis. They will contend that (Bl) is fact and only (B3) hypothesis.

I think that this view may well have been taken by the more recent supporters of (A3); for they have all adopted the Hypothesis of the Asymmetrical Impermanence of Matter1 Otherwise their reason for supporting (Bl) is not easy to understand. They can hardly have thought that it was the more attractive alternative. By the unreliable criterion of attractiveness one should expect symmetrical impermanence to be the favoured hypothesis. A more probable reason is that (Bl) is so firmly established and generally accepted that (B3) did not even enter their thoughts. This surmise is confirmed by the fact that the supporters of asymmetrical impermanence have never undertaken a critical comparison of the alternatives, as they would surely have done if they had noticed that there were alternatives.

He who has a new point of view to present cannot afford to ignore contemporary opinion and so I have to attach much importance to the relative strengths with which each of the hypotheses in the (A) and (B) lists is held today. From reading and conversation I have gained the impression that support for (Al) would be very weak. Many will say that, in attempting to refute it, I am only flogging a dead horse. But support for its counterpart (Bl) is likely to be so strong that my attempt to refute it is likely to evoke a different metaphor: that of tilting at windmills.

Nevertheless, it was a combination of (A3) with (B3) that I advocated when I first published the hypothesis of continuous origin in 1940 and I propose to show here that it alone is consistent with a cosmological model that accords with the observed universe.

Before I leave this theme I should like to emphasize that the words 'origin' and 'extinction' are to be understood literally and not as synonyms for 'conversion from one form into another'. It would deny my intention to assume, for instance, that, when matter becomes extinct, something else, such as energy, must necessarily take its place.

4.2: The Relative Rates of Origins and Extinctions
Let us imagine that a region of space can be so isolated that no matter or energy passes its boundary. According to the Hypothesis of Asymmetrical Impermanence the content of this region must continuously increase; for new matter will originate in the region while none will leave it. According to the Hypothesis of Symmetrical Impermanence, on the other hand, some matter will be originating in the region and some becoming extinct, and so the content will not necessarily increase. It will do so if the rate of origins exceeds the rate of extinctions; but the content will decrease if the rate of extinctions exceeds that of origins.

If the region is small and the density low, origins and extinctions will be only occasional and as they are both assumed to be random, they will occur at irregular intervals. The content may decrease at one moment and increase at the next. But the larger the region the more such irregularities will be smoothed out; and if a region be chosen large enough to be a fair sample of the whole material universe the rate of origin per unit volume will be the same as for the whole and so will the rate of extinctions.

McCrea has calculated the rate at which the content in mass of the universe is increasing and finds it to be about 500 atoms of hydrogen per cubic kilometre per year. According to asymmetrical impermanence this is the gross rate of origins. According to symmetrical impermanence it is the net rate given by the excess of origins over extinctions; the gross rate is greater, and may be much greater.

It is, of course, quite impossible to observe directly the annual arrival of 500 atoms of hydrogen in a cubic kilometre of space. The mass of those atoms is very minute and could not be measured even if they could be assembled at one time and place. But there is an indirect method for estimating the rate. This is derived from the fact that, as relativity theory shows, matter and space are inseparable. According to relativity theory,1 space is not regarded as a container but as a constituent of the material universe. To speak of the origin of matter is the same as to speak of the origin of space, and if the content of the material universe is increasing its extent must be doing so too!2 The origin of new matter must therefore be associated with the expansion of space and the rate at which the extent of the material universe is increasing becomes a measure of the rate of increase of its content. This is fortunate. For the rate of increase of extent is easier to measure than that of content. It is done with the help of telescopes, and these reveal regions of space large enough to show an easily measured effect.

As is well known, this effect is manifest as a shift towards the red of the spectrum lines of very remote objects, called the Doppler effect. A simple calculation shows that the amount of red shift is proportional to the velocity with which a remote object is receding. Observation shows that the amount of the red shift is proportional to the distance of the object. From these two facts it follows that the velocity with which every object is receding is proportional to its distance from us. This is what one would find in a universe that was expanding uniformly and so the expansion of space is inferred from observation and known facts and without the use of additional hypotheses. The rate of expansion is expressed by the simple formula v=Hx, where v is the velocity of recession, x the distance of the observed star and H a constant known as Hubble's Constant. It represents the increase of velocity of recession with distance, dv/dx, observed for every object in a uniformly expanding universe and is given as 145 km/sec per megaparsec by Opik.3 A more recent estimate is given by Humason, Mayall and Sandage.4 This is based on the measurement of red shifts. for nearly 1000 extragalactic nebulae and is 180 km/sec per megaparsec.

These most careful measurements show that the rate of expansion is nearly, if not quite, constant for all regions of space-time. But they do seem to show some small lack of uniformity. There may have been a change during the long period of time that the light from the most distant nebulae takes to complete the journey that ends in the observers' telescopes. However, it will be shown later that there are good reasons for the view that the change is not between different periods of time but between different regions of space, and that it results from unevenness in the distribution of ponderable matter.

The constancy of the expansion rate, and with it the rate of increase of the content of the material universe, reminds us of the constant half-lives of radioactive isotopes. The reason why the disintegration of an atom of radium is regarded by physicists as an uncaused event is just this constancy, as will be explained in the next chapter. If the half-life of radium varied, one would look for a circumstance with which the disintegration was associated and expect to find a causal relation between such circumstances and the disintegration. But the fact that the rate never changes is taken as negative evidence that the disintegration is uncaused.

The same reasoning applies to the increase in the content of the material universe. If one regards the unvarying value of Hubble's Constant as evidence of a constant net increase in the quantity of matter in the universe, one will also regard it as observational support for the conclusion that origins are random, without cause, and not associated with anything in the existing state of affairs. If one accepts (B3), one will then have to take the same view about extinctions. But this aspect of Symmetrical Impermanence will be discussed more fully in the next chapter.

1See footnotes 4,5, 6 to Chapter 3
2I doubt whether this is implicit in relativity theory, but it has been assumed by others besides myself. Its justification will be found in Appendix H.
3The British Journal for the Philosophy of Science, November, 1954, Vol. 5, No. 19, 210.
4Astronomical Journal, Vol. 61, April, 1956, pp. 97-162.

Top of Page

 Title Page      Contents      Chapter 3       Chapter 5             Index