TOWARDS A UNIFIED COSMOLOGY

by     Reginald O. Kapp

PART II - THE PAST AND FUTURE DURATION OF MATTER

Chapter 3 - Hypotheses About the Origin of Matter


3.1: A List of Possible Hypotheses
As I have shown elsewhere,1 all hypotheses about the duration of matter that anyone has so far been able to put forward comprise a combination of one of those in the following (A) list with one in the (B) list:

(A)
Hypotheses about the Duration of Matter and Energy in the Past

(Al) All matter and energy have existed for all time.
(A2) All matter and energy have existed for approximately the same length of time, i.e. from the date of the Creation. According to this hypothesis no particle has existed for a longer time than has elapsed since the Creation began nor for a shorter time than has elapsed since the process of Creation was completed.
(A3) Any particle of matter or quantum of energy may have existed for any length of time. As will be shown later, this is a way of saying that matter and energy are originating without cause, continuously, at random, and not as a result of anything in the existing state of affairs.

 

(B)
Hypotheses about the Duration of Matter and Energy in the Future

(Bl) All matter and energy will continue to exist for all time.
(B2) All matter and energy will continue to exist for approximately the same length of time, which is the time that will elapse until the End of the World. According to this hypothesis no particle will last for a shorter time than will elapse up to the beginning of the End of the World nor for a longer time than will elapse until the process of destruction is completed.
(B3) Any particle of matter or quantum of energy may cease to exist at any time. As will be shown later, this is a way of saying that matter and energy are disappearing without cause, continuously and by extinction, at random, and not as a result of anything in the existing state of affairs.

There are in all nine possible combinations. Three of these are obtained by combining respectively (Al) with (Bl), (A2) with (B2), and (A3) with B3). They are symmetrical. The remaining six combinations are all asymmetrical. As every one of the combinations is just as much an hypothesis as any other, each has to be assessed by the criteria that are applied to hypotheses when a choice has to be made between them. One of these is the criterion of minimum assumption, Occam's razor. Let us first assess the various possible hypotheses about the past and future duration of . matter by this criterion. Assessment by other criteria is, of course, also necessary and will follow later.

3.2: The Hypothesis of Continuous Existence in the Past
In this chapter the hypotheses in the (A) list only will be discussed. Those in the (B) list will be discussed in Chapter IV.

(Al) fails badly by the criterion of minimum assumption. As will be shown below, it can be maintained only with the help of a number of assumptions that are far from minimum ones.

A minimum assumption is recognized, it will be remembered, by use of the word 'any' in its formulation. The statement that all matter and energy have existed for all time precludes the use of this word and would seem to bring (Al) into conflict with the criterion of minimum assumption. But this is not the major objection. I should feel diffident about applying the criterion thus rigorously. In spite of verbal appearances it is just possible that 'all time' is really less of an assumption than 'any time'. So I should hesitate to dismiss (Al) simply because its formulation does not contain the word 'any'.

Irreversible Processes: The true objection is deeper and stronger. It is that many other very specific assumptions are implicit in (Al). This becomes apparent as soon as one tries to reconcile this hypothesis with a simple fact of observation. This is that the world we live in is a changing one. Let me show why this presents us with a serious difficulty as soon as we try to support (Al).

Certain observed processes are irreversible. The most familiar of them is the process of falling. Things fall from a region of higher to one of lower potential and not vice versa', in colloquial terms things fall downwards and not upwards. One can describe the process as that of following a potential gradient and its result is such that the total potential energy is reduced by the process, it being converted into kinetic energy. As is well known, the conversion of potential into kinetic energy is equivalent to an increase in entropy and is a manifestation of the second law of thermo-dynamics.

Another manifestation of the same law is the equipartition of energy between colliding particles. When a particle that is at rest, but free to move, is hit by a moving particle, the one at rest acquires kinetic energy at the expense of the one that hits it. Again, when two particles of irregular shape collide some of their kinetic energy of rectilinear motion is translated into that of spin. It is easy to deduce from these facts that, given sufficient collisions between moving particles, there will be a tendency for those that began with little kinetic energy to acquire more and for those that began with much to lose some of it. Eventually, therefore, the average kinetic energy in any sample large enough to be typical will be the same as in any other. The temperature of a body is proportional to the average kinetic energy of its component particles. Two substances in which the particles have different average kinetic energies are therefore at different temperatures. When they are brought into contact the kinetic energies come to be shared equally and the temperature difference is smoothed out. This is but another way of saying that heat flows by conduction from hotter to cooler bodies and not vice versa.

There are many other irreversible processes. Electric charges tend to neutralize each other. Chemical reactions tend to be such that the resultant compounds are less reactionable than the substances from which they were formed. Exothermic reactions, in which heat is liberated, are more probable and frequent than endothermic ones, in which it is absorbed; and so forth.

Such irreversible processes tend towards a terminal condition. If things keep on falling, the time must come eventually when everything that can fall will have done so until it can fall no further. If bodies in motion keep on interacting, the time must come when the total kinetic energy is shared equally between all of them. If heat keeps on flowing from hotter to cooler bodies, temperatures throughout the universe must eventually be equalized; the world must reach the condition called by German philosophers the 'warmetod' (heat death). Similarly all electric charges must be neutralized and all chemical compounds reach a state in which they cannot act chemically on each other.

All this can be expressed as a principle that I propose to call the Principle of Stabilization. By this principle processes in a self-contained system tend to reduce their causes. If such processes continue for long enough all causes must be reduced so much that they cease to operate. When this has happened there can be no more change.

But we do observe change around us. Things do continue to fall. The ponderable contents of the universe have by no means reached positions where they can fall no further. About one-half of these contents exist in the form of a thinly diffused gas in interstellar space. All parts of this gas are in some gravitational field, for such a field surrounds every star and stretches into the outer distance, where, though very faint, it exerts a finite pull on every molecule of the diffuse interstellar gas. So this gas must be falling very slowly towards the nearest stars. The terminal condition, in which all of the interstellar gas has completed its falling, is still a long way off.

Similarly, great differences of temperature are still observed. Heat in large amounts is flowing from hot to cool surfaces. Interacting bodies are still far from sharing their kinetic energy equally. Particles in collision still impart considerable increases in spin to each other. Electrical and magnetic potential gradients abound. Highly reactionable chemical substances are found throughout the universe. In short, what makes for change is to be found in abundance. The hypothesis of continuous existence in the past (Al) fails to explain this.

(A.I) Can be Saved only by Piling Hypothesis upon Hypothesis: When an hypothesis fails to explain observed facts one has the choice between two alternative courses. The first is to abandon the hypothesis in favour of another one with superior explanatory power. The second is to retain the hypothesis and to combine it with further ones in such a way that the combination does explain the observed facts. One could, for instance, attempt to reconcile the hypothesis of infinite past duration of matter with the observation of present change by adding sundry additional hypotheses about the laws of physics.

A collection of carefully reasoned papers on the age of the universe has appeared in The British Journal for the Philosophy of Science.2 There, several of the additional hypotheses are mentioned that might serve to save (Al) and they are critically discussed. I do not want to cover more of the same ground here than is absolutely necessary, but I do want to emphasize that all attempts to save (Al) have to be rather desperate and cannot be reconciled with the way a physicist regards the material universe.

It could be thought that, perhaps, those processes that seem to us to be irreversible are really cyclical. The expansion of space is one of these; it has actually been suggested that it may alternate with contraction and be analogous to the motion of a pendulum, which slows down as it approaches the limit of its swing and then reverses. In the above-mentioned collection of papers J. T. Davies says 'it is impossible to say whether an expansion might not be merely a phase of a more complex phenomenon such as pulsation'. Ernst J. Opik speaks of 'the collapsing Universe rebounding from the elastic forces of the nuclear fluid at a state of maximum compression'. On this hypothesis the moment when any given irreversible process began is not a starting point but only a turning point.

This hypothesis can sound plausible when it is applied to the expansion of space. But this expansion is only one of a great number of processes that are found to be irreversible. If we are to develop a sound cosmology we dare not overlook any of the others, and when it is applied to other processes the hypothesis of a pulsating universe can sound plausible only so long as one thinks of these processes in a vague and abstract way. If we think of entropy only as an algebraic symbol in a mathematical expression, we shall find no difficulty in believing that in a self-contained system its rate of change may sometimes be positive and sometimes negative. Perhaps, we might then say, the second law of thermo-dynamics defines cyclical and not unidirectional processes; perhaps during infinite time a tendency for the entropy of a self-contained system to increase alternates with a tendency for it to decrease. Perhaps a tendency for processes to reduce their causes alternates with a tendency for them to increase their causes.

But when one thinks of the concrete reality that finds its generalization in the second law, those 'perhapses' fade to an unconvincing pallor. The law expresses, among other things, the fact that colliding bodies tend with time to share their kinetic energies equally. Perhaps, one is led to assume, there have been times when a body that was at rest and was hit by a moving one imparted kinetic energy to the body that hit it and lost some of its own (non-existent) kinetic energy. Perhaps spinning bodies once-upon-a-time gave up their spins on collision and converted their spin energies into energy of rectilinear motion. Perhaps at one time gravitation was reversed and things fell up instead of down. Perhaps inert chemical substances used to act on each other and cinders converted themselves into coal. Perhaps heat used to flow from the cooler to the hotter surface. Perhaps electrical potential gradients used to grow steeper when charges were neutralized. Perhaps the laws of physics are not universal but change from time to time. Perhaps the Cosmic Statute Book comes up for periodic revision. Perhaps the last occasion was the precise moment when a pulsating universe had reached its maximum concentration and began to expand. Perhaps all the present irreversible processes started together just then. If we attempt to save (Al) we shall run the risk of drowning in an ocean of strange hypotheses.

Most, if not all, of them are untenable anyhow. That objects of irregular shape tend to spin when they collide is not the consequence of a transcendental law but of simple mechanics. It can be easily shown that there are innumerable ways of colliding that cause spin for one way that does not. The laws of physics allow the objects to collide in 'any' way and so nearly all collisions are of the spin-causing kind. The irreversible process by which rectilinear motion tends to be converted to spin does not arise from a specific law but from the absence of a specific law. To say that 'perhaps' it was the other way about at one time is to say that perhaps there was a specific law at that time to control collisions, a law that has since been struck off the Statute Book.

It can, moreover, be shown that many of the so-called laws that seem to show processes to be irreversible are merely true by definition. One defines a field of force in terms of the direction in which things fall in it. To say that they fall in the opposite direction is to contradict the definition. One defines temperature gradient similarly in terms of the direction in which heat flows. To say that it flows from the hotter to the cooler surface is implicit in the definition. This is why, if we seek to offend against the rule of Economy of Hypotheses in the forlorn hope of saving (Al), we shall do so in vain. There would rarely be the need to reproach us for piling one hypothesis on another. One could refute us by logic.

For the foregoing reasons the notion that the whole existing contents of the material universe have existed for all time seems, today, to have but few sponsors among serious scientists, whether the notion be of a universe in a process of unidirectional change or of pulsation. It fails badly by any acceptable scientific criterion and certainly by that of minimum assumption.

3.3: The Hypothesis of Past Finite Existence
One can explain the fact that there is still change in the universe if one adopts the hypothesis that all the contents of the physical universe have existed for a definable time. This is (A2), and at the time of writing it has considerable vogue. Sundry estimates have even been made concerning the age of the universe.

Irreversible Processes have been Claimed to Provide Evidence for (A2): For this purpose a few of the observed irreversible processes have been used as clocks. It is assumed that the universe started in some specific condition and that it has been departing at a known rate from this condition ever since. The degree of departure is taken as a measure of the time that has been occupied by the process.

One of the clocks is provided by the expansion of space. It is assumed by supporters of (A2) that the whole contents of the universe started in a small volume of very high mass density and have been spreading out more and more ever since. By measuring the rate of expansion and the distance between discrete objects one arrives at the time assumed to have passed since the expansion began. One of the other clocks is the ratio of helium to hydrogen in stars; it is assumed, with considerable justification, that all ponderable matter has begun its existence in the form of hydrogen and that its slow conversion into helium is among the irreversible processes that give a reliable time scale. Another clock is provided by the partition of kinetic energy between stars, and yet another one by the proportion of certain isotopes found in rocks. These and several other clocks give roughly the same age, namely between four and seven thousand million years.

I do not propose to discuss in detail the observations on which the various estimates are based. They have been fully described by others and there is no reason to doubt that the estimated time-interval of some thousands of millions of years has a cosmic significance of some sort. It does not therefore seem likely that hypothesis (A2) will have to be rejected on the grounds that the various clocks provided by irreversible processes are unreliable; the agreement between them is too good for their readings to be lightly dismissed.

But we must take care to draw the correct conclusions from those readings. One may safely conclude that since the clocks were, so to speak, wound up the part of the material universe where we are has been behaving as it does today. But this conclusion is equally compatible with (Al), with (A2), and with (A3), as has been pointed out by sundry writers of the papers that appeared in the above-mentioned 'Age of the Universe' number of The British Journal for the Philosophy of Science.

Supporters of the hypothesis that a pulsating universe has been existing for infinite past time, (Al), could point out that the moment when the clocks started need not be interpreted as a moment of origin; it could equally well be a moment of change in a universe that had existed in a different form before then and had obeyed a different set of laws. The strange collection of hypotheses that would have to be designed in order to save (Al), and that has been mentioned already, may be refuted by various arguments, but it is only fair to add that it cannot be refuted by the evidence of the clocks. Michael Scriven, one of the contributors to the papers on the age of the universe referred to above, speaks of 'phases in the Universe prior to the present "expansion",' as a description of a possible view, though not one to which he seems personally to commit himself. He also asks the pertinent question: 'What is the difference between saying that the Universe has an origin in time and saying that each of the processes of change within the Universe has an origin in time ?' The implication is, of course, that the evidence of the clocks might equally well be used as evidence for the pulsating universe that, according to (Al), would have existed for all time.

It will later become apparent that the evidence of the clocks could also be used to support (A3), the hypothesis of continuous origin. But that can be easily understood only after (A3) has been discussed. Suffice it at the present moment to refer again to the above-mentioned papers, where J. T. Davies shows this cogently when he says 'thus the theory of continuous creation provides us with a picture rather like that of a living population; individuals are born, age and die, but the population may remain in a steady state'. What, in other words, the clocks record is not necessarily the age of the universe as a whole. Each clock may only record the age of the particular part of the universe in which it is placed.

It will appear in due course that one should expect matter that was originating continuously, in accordance with (A3), periodically to form nebulae, like our galaxy. One should expect the various clocks placed in any one of them to record its age and to give consistent readings between themselves.

In short, claims that there is observational evidence for (A2) have, to say the least, been greatly exaggerated. It is doubtful whether there is any evidence at all for it that is not also evidence for either of the other alternatives.

(A2) Fails by the Criterion of Economy of Assumption: Perhaps more scientific considerations will be found some day in favour of the hypothesis of a definable time for the past existence of matter than have been' found hitherto, but while we wait for these we must also assess the hypothesis by the criterion of minimum assumption. By this it fails at least as badly as the hypothesis of past infinite existence. This must cause disquiet to any scientist who is contemplating the hypothesis. To emphasize this disquiet I have on a previous occasion referred to (A2) as the 'once-upon-a-time theory'.3 My reason was that, like a fairy-tale, it fails conspicuously to conform to Occam's razor.

(A2) postulates, for instance, two (and not only one) significant and quite specific moments in all time. The first is the moment at which it has to be assumed that the very first element of the universe came into existence. It is the moment before which it is assumed that there was nothing, The second specific and significant moment of time is the one at which the very last element of the material universe came into its correct position. It is the moment before which is is assumed that the universe was incom- plete, and after which it is assumed that it was complete. These two moments, it is assumed, have never been repeated in the whole of time, Two more-specific assumptions are hard to imagine.

It is alien to the spirit of physics to contemplate unrepeated and unrepeatable events. It is part of the physicist's faith that events are all repeatable whenever similar conditions are reproduced, and that given sufficient time similar conditions will always be reproduced. To postulate two specific moments in time is to reject this. Physicists will be unwilling to do so without a great deal of evidence.

But this is not even the whole of the objection. Hypothesis (A2) implies that the laws of physics, as we know them, did not come into operation until the second of the two significant moments. The implication of the hypothesis is that there was once in the past a period of finite duration between those two moments, which may have lasted for seconds only , or for millions of years, but was in any case finite. From a specific moment in the year t1 B.C. until another specific moment in the year t2 B.C. it is implied that the laws of conservation of energy and of matter were suspended, that they came into force precisely at the second of the two moments, and that they never can be suspended again.

For all that can be proved to the contrary it may have been so. But an hypothesis that implies it cannot be called a minimum one. The belief that the laws of physics hold, and have held, and will hold, everywhere and at all times is a strong one. This is why it demands a substantial intellectual effort to be persuaded of (A2). But the effort has not to be directed at understanding something; it has to be directed at ignoring something, namely the implications of the hypothesis. The period between the beginning of the Creation and the completion of the universe is one that does not bear thinking about. To make (A2) acceptable one must prevent this period from intruding on one's attention. An hypothesis that calls for this ignoble kind of intellectual effort must be suspect. That it fails conspicuously by the criterion known as Occam's razor would not . alone be a sufficient reason for rejection of (A2). But it seems also to fail by all other scientific criteria. The evidence for it is slight and of doubtful validity. It has but little unifying and explanatory power. If it is to be justified at all, it can only be on non-scientific grounds.

3.4: The Hypothesis of Continuous Origin
I doubt whether the hypothesis of continuous origin (A3) would ever have suggested itself if both the other two hypotheses had not proved so unsatisfactory. It is fair to say that I did not arrive at (A3) by a direct approach to the problem but by a process of elimination consisting of the rejection of (Al) and (A2). To be justified, (A3) will have to be free from the glaring defects of the other two hypotheses. It will have to meet the Principle of Minimum Assumption adequately, it will have to manifest greater explanatory power than the other two, and it will need better support from the evidence of observed facts.

The justification of hypothesis (A3) on the grounds that it involves a minimum assumption was presented when I first advocated this hypothesis in 1940. To emphasize this justification I called it the 'at-any-time' theory. Others have advocated the same hypothesis since and found sundry other reasons for its justification.4,5,6 That it deserves serious consideration is therefore by no means a new claim. Its great explanatory and unifying power will appear in subsequent pages, together with the evidence that supports it. For the moment I shall simply discuss its main features in a little detail.

What is it that Originates? To the claim that matter is originating continuously it is natural to ask In what form?' At the present stage of knowledge concerning the basic constitution of the material universe it is not possible to answer this question with any precision. One would naturally not assume that complex structures come into spontaneous existence completely synthesized. To do so would be to assume that the process of originating was also coupled with a process of ordering to specific forms and that would not conform to the Principle of Minimum Assumption. For this reason none of the advocates of (A3) has suggested that complete molecules of chemical compounds are among the originating bodies. Nor has it been suggested that the nuclei of any of the heavier elements are among them. These are known to be composed of particles that are more elementary than they, such as protons and neutrons, and the minimum assumption is that the originating particles are the most elementary of all. It is, however, impossible to say in the present state of knowledge what the uttermost elementary particles are.

If all so-called elementary particles had the same mass one might regard them as truly elementary. But indivisible particles are known with various inertial masses. It may be that each of them is in some way composite and that the respective masses of the electron, the proton and the sundry mesons are each the consequence of a synthesis from some even more elementary components. One should hesitate to regard any of these particles as the uttermost elementary components of the material universe.

The same objection does not apply to unit charge, which has always precisely the same value on the electron with the negative sign and on the proton with the positive sign. There is, however, convertibility between various elementary particles, such as between neutrons, protons, electrons, positrons and others. A proton may, for instance, convert into a neutron, a positron and a neutrino. One is thereby led to doubt whether unit charge is a quite basic constituent of matter.

It is doubtful even whether the most basic constituents ought to be called particles. For there is also convertibility between particles and photons, as there is between mass and energy. In the sense in which protons and neutrons are common constituents of atomic nuclei some as yet undefined components of matter may be common constituents of positive and negative charges, elementary masses, and photons. If so, these undefined components will be no more like the things of which they are components than neutrons and protons are like the nuclei into which they synthesize.

Bearing in mind that matter is not so much in space as of space, the most accurate description, and a non-committal one, of the uttermost. elementary constitutent of matter may be a bit of differentiated space. But the inseparability of matter and space has not yet become a familiar concept, so I propose to speak here, even more non-committally, of the continuous origin of elementary components of the material universe.

That I have to speak thus non-committally proves that the hypothesis of continuous origin (A3) is incomplete in the form in which I have been able to state it. In the next chapter I shall develop the hypothesis of the continuous extinction of matter and this will be equally incomplete. I have no answer to the important question: 'What is the basic unit that originates and what is the basic unit that becomes extinct?' The question abounds in difficulties. Some of these will be discussed in Appendices G and H.

One of the conclusions to be reached in Appendix H is worth mentioning now, for it will help towards understanding what is said in the main parts of this book. The conclusion to which more than one line of reasoning leads is that a complete atomic nucleus, together with its electric charges, is a basic unit and becomes extinct as a whole.

This conclusion is important. If a part of a nucleus were to become extinct while the remainder continued to exist, this remainder would not only be radio-active: it would also be the nucleus of another element. But observation shows that it is not so. Hence the hypothesis of continuous extinction would have been severely shaken if the line of reasoning followed in Appendix H had led to the conclusion that only a component part of a nucleus becomes extinct at any particular moment.

Even if the suggestions put forward tentatively in Appendix H are corroborated the hypothesis will, however, still be incomplete. Many difficult questions will remain unanswered. In drawing attention to this. I should also draw attention to what I have said on page 16 of the Preface. To say that a theory is incomplete is not the same as to say that it has been falsified.

1 The British Journal for the Philosophy of Science, November, 1955, Volume 6, No 23
2The British Journal for the Philosophy of Science, November, 1954, Vol. 5, No. 19. 3R. 0. Kapp, Science versus Materialism, London, 1940, Chapter XXIV
4 V. Hoyle, Stellar Evolution and the Expanding Universe, Nature, 1949, 163, 196
5 H. Bondi and T. Gold. The Steady State Theory of the Expanding Universe. Monthly Notes Royal Astronomical Society, 1948, 108, 252
6 W. H. McCrea, The Steady State Theory of the Expanding Universe, Endeavour, 1,1950, 9, 3;   Relativity Theory and the Creation of Matter, Proceedings of the Royal Society, 1951,206,562.

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