by     Reginald O. Kapp

Vol. VI No 23 1955
Thomas Nelson & Sons Ltd Edinburgh 9


LET me begin by setting down in tabular form all possible hypotheses about the origin and disappearance of matter.




Hypotheses about the duration of matter and energy in the past

Hypotheses about the duration of matter and energy in the future

(A1) All matter and energy has existed for all time

(B1) All matter and energy will continue for all time

(A2) All matter and energy has existed for approximately the same time, which is the time that has elapsed since 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 was completed.

(B2) All matter and energy will continue to exist for approximately the same time, which is the time that will elapse until the End of the World. According to this hypothesis, no particle will continue 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 is completed.

(A3) Any particle of matter or quantum of energy may have existed for any time. 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

(B3) Any particle of matter or quantum of energy may cease to exist at any time. 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

Any hypothesis in the left-hand column can be coupled with any in the right-hand one. The nine combinations thus obtainable cover between them every logical possibility concerning the total duration of matter. When one couples (A1) with (B1), (A2) with (B2), or (A3) with (B3), one obtains a symmetrical hypothesis. Only these three together with the unsymmetrical combination of (A1 with (B3) have their supporters and call for critical study.

On this occasion I propose to consider first the hypotheses about the duration of matter in the past and then those about its duration in the future. It will be found that all of them except {A3) and (B3) have to be rejected for various scientific reasons. Unless one decides to form no opinion at all about the duration of matter one has therefore provisionally to adopt the one according to which the period of existence of a particle of matter or of a photon is indeterminate both in the past and in the future. This is not, be it admitted, because the hypothesis of the indeterminate duration of matter and energy can be proved valid. It is because this is the only one that no one has succeeded in proving false, the only one that can survive critical study. It is reached by a process of elimination. A scientist may with good reason suspend judgment; but it is not legitimate for him to adopt any other combination than (A3) with (B3) unless he can (a) overcome the scientific objections to his choice and (b) provide a positive justification for it other than that of pure faith.

2 The hypothesis of continuous existence in the past

This is an appropriate description of (A1). It has to be rejected for the simple reason that a number of observable processes in a self-contained system, tend asymptotically towards a limiting condition. If the hypothesis were true every asymptote would have been reached by now and the universe would be very different from the one that we live in. This follows from the fact that many physical processes are irreversible. So the universe must either have existed for a finite time (A2), or it is not a self-contained system (A3). This point can best be explained with the help of a few examples.

(1) During every energy change in a self-contained system the total potential energy in the system decreases and the total kinetic and radiant energy increases by the same amount; a self-contained system being one into and out of which no energy or matter passes. This is no more than one formulation of the second law of thermodynamics.
Another formulation is to say that the entropy in a self-contained system tends asymptotically to a maximum limiting value. Both statements mean the same thing. If (A1) were valid there would be no more available potential energy; the limiting value for entropy would have been reached by now; no energy changes could occur. So one must conclude that (A1) is not vahd. Either the time during which energy changes have been occurring is finite, as is asserted by (A2), or the universe is not a self-contained system, as is asserted by (A3).

(2) The movement of all bodies in a field of force is a one-way movement. The direction is from a position of higher to one of lower potential. If one does not limit the meaning of the word 'falling' to movement towards the centre of our earth but allows the word to stand for movement in the direction of any field of force it is quite precise to say that bodies moving in a field of force are always falling. They go on falling until they lodge on a place from which they can fall no farther. During the process they gain kinetic and lose potential energy; they conform to the second law of thermodynamics. In fact the law according to which movable bodies always fall as far as they can is but one particular illustration of the more general second law of thermodynamics; it is really implicit in what was said under (1) above.

Had all matter and energy been in existence for all time every object would, by now, have fallen as far as it could. The asymptote would have been reached for which no movement in the direction of a field of force was occurring. But in fact about half the matter in the universe exists in interstellar space and is still in process of falling on to stars; on our earth rain falls from clouds and the water of our rivers falls down inclined planes into the sea. By this special application of the second law of thermodynamics the bodies that are still falling cannot have been doing so for all time. Each of them must have come into existence a finite time ago. Once again (A1) is ruled out.

(3) Eddington proved mathematically that an Einstein universe could only both contain matter and be stable if it were either expanding or contracting. Observation of distant nebulae shows a shift of all the lines of their spectrum towards the red end. This is spoken of as the red shift. It seems to be proportional to the distance from us of the observed object. Its simplest interpretation is that of Doppler effect, and if this is correct it shows that the nebulae are receding from us with a velocity proportional to their distances. So the red shift has been interpreted as observational confirmation of theory and as proof that the universe is expanding. One can only refute this conclusion if one does two things. One must find (a) a substitute for the Einstein universe, such that it would be stable without expanding, and (b) an alternative explanation of the observed red shift. The attempts at both made so far amount to little more than surmise.

If the whole of the matter and energy in the universe have existed for all time and the expansion has been unidirectional the density of matter in space must have reached asymptotically the value zero by now. But it is not zero. So, yet again, those who accept the hypothesis of an expanding universe must also reject hypothesis (A1).

3 The hypothesis of past infinite existence

This is an appropriate name for (A2). It accords with the theological doctrine that an Act of Creation was performed once, and once only, in a remote past, differently dated, in thousands of years by some, and in millions by others. The reason why it has to be rejected is not, as for {Al), that it is incompatible with undisputed scientific facts and laws. The reason was hinted at when I first discussed this hypothesis in 1940 and gave it the name 'Once-upon-a-time theory'. Like a fairy tale it fails to conform to the principle of economy of hypotheses.

(A2) asserts that in the whole of infinite time two moments have had a unique significance. One is the commencement, the other the completion date of the universe. During the interval between these significant moments one is asked to believe that the most fundamental laws of physics, the nature of material systems, those features by which we recognise matter and energy when we encounter them, were different from what they have been ever since. 'Once-upon-a-time' hypothesis {A1) asserts by implication: 'the law of conservation of energy was suspended; all sorts of things happened that could not happen now. That was during the time, which may for all that we know have been very long or very short, between the moment when the first proton appeared in our universe and the moment when the very last one arrived in its allotted place. But immediately after that happy event all the laws of physics were imposed with the rigour that they have now. And they have never been suspended again.' It is alien to the spirit of science to postulate conditions of that sort. The mildest comment that can be made on (A2) is that physicists do not have a place in their science for events of which the type does not repeat itself.

4 The hypothesis of continuous origin

This is an appropriate name for (A3). When I first advocated it in 1940 in my book Science versus Materialism1 I called it ‘The At-any-time Theory'. The word 'any' hints at the absence from the all-too specific hypotheses implied in (A1) and (A2). The same hypothesis has since been independently advocated by Hoyle,2 and and by Bondi and Gold,3 with much more supporting evidence than I provided. It has been supported by McCrea.4 Their contribution was to formulate it in mathematical language and present it in quantitative terms. They were led to undertake this task by two considerations. Firstly, extrapolations by which to arrive from various different observations at a date for the Creation that is implied in (A2) led to conflicting results; secondly, neither (A1) nor (A2) could be reconciled with a principle known as 'The Perfect Cosmological Principle', according to which, apart from unimportant differences, the universe presents the same aspect at all parts of it and at all times. The conclusion reached by such distinct lines of reasoning have been received with scepticism in some quarters, but never disproved.

5 Disappearance by extinction or by removal?

If new matter has been originating for all time it is necessary to explain why we do not observe an infinite amount of it. In other words the origin of new matter must be balanced by the disappearance of old. And the disappearance must be genuine, absolute. It cannot, of course, consist in the conversion of matter and/or energy into something else. Nor can what has disappeared leave any trace. If it did we should observe an infinite accumulation of traces. So much is agreed by all those who support (A3). But two quite distinct assumptions have been made about the manner of the disappearance. The first may be called disappearance by extinction, the second disappearance by removal. The hypothesis of disappearance by extinction is an appropriate name for (B3). The reason that led me to couple it with (A3) when I first put it forward in 1940 and in subsequent contributions 5 was again the principle of economy of hypotheses. To the question for how long a given particle must exist the answer 'it may be for any time' is less of a hypothesis than either the answer 'it must be for all time' or 'it must be for the finite time that will elapse until the End of theWorld'.

On this view there is no need to assume that the rate of origin and the rate of disappearance are everywhere and at all times equal. For they are not assumed to influence each other. The difference between the two rates may be positive in one part of space-time and negative in another. The universe as a whole may be sometimes expanding and sometimes contracting, depending on whether the rate of origin for the whole happens to exceed or fall short of the rate of extinction. If one sets out to avoid any and every unsupported hypothesis one is left with the very barest minimum of assumptions. One must either abandon the subject or assume complete randomness. Anything more is based on faith and not on facts.

The hypothesis of disappearance by removal rejects (B3) and assumes that every particle that has once come into existence will continue for all time, as assumed in (B1), or at least until the End of the World, as assumed in (B2). The advocates of this hypothesis account for the observed finite density with which matter is spread over space in an ingenious way. They point out that, as matter originates, space must expand to accommodate it. And as matter is assumed to have been originating for an infinite time space is assumed to have acquired an infinite volume and to be expanding at an infinite rate. Thus disappearance is not regarded as extinction but as removal to distant regions.

It might be thought for a moment that the removed matter would continue to leave traces with an observer here and now, so that there would be an infinite accumulation of traces. But it would not be so. There is a limiting distance, beyond which objects in an expanding universe recede with a velocity greater than that of light. An observer can receive no evidence, even in theory, of the present or past existence of such objects. Their removal carries, one might say, all traces with it. There is something attractive, almost poetic, in the picture of heavenly bodies drifting on and on, eternally, into infinite space. Yet I find myself unable to reconcile it with a rather important and fundamental scientific principle.

6 The error of attaching physical meaning to infinity

In mathematics infinity means just this: however large a number one cares to mention, one could mention a still larger one. The value of this larger one not being stated, the symbol for infinity does not stand for any specific value. Infinity is by intention and definition, an unspecified quantity. But how can a deliberately imprecise mathematical symbol apply to a physical reality? Surely it is axiomatic that there can be no infinite quantity of any physical reality. This helps to explain why, when in the general theory of relativity, space was invested with physical properties, it was also found to be of finite extent. The same reasoning is implicit in the discovery in quantum mechanics that no physical quantity can be infinitely small. Are we now to go back on the insight that these discoveries gave us? And this is what (B1) does when it is coupled with (A3). It postulates a physical space with a rim, or edge, or boundary infinitely distant and receding from us at an infinite speed, at a speed moreover that increases exponentially during a finite time, no matter how short, by an infinite amount. When one sets foot upon the path represented by such a notion one cannot rest content with the may-be comforting concept of a simple infinity. One has to add infinity to function of infinity, over and over again, literally ad infinitum.

Even more disturbing, when one turns one's mind from a contemplation of mathematical abstractions to physical realities, is the notion of centres here and there around which, according to this hypothesis, matter must have been accumulating for all time. To point out that any such centres of accumulation must be in regions from which no trace can reach us is not to deny that their existence is implicit in the hypothesis. For it is assumed that centres of accumulation have begun at all times, some therefore in the infinitely remote past. Matter must have been falling on these for an infinitely long time; they must by now have grown infinitely massive; they must be imparting to all objects within their infinitely extensive, infinitely strong gravitational fields an infinite acceleration; they must be growing at an infinite rate; the gravitational forces at their centre must be infinitely intense; and so must the forces applied by gravitation at any finite distances from them however great these distances may be. Such are some of the conclusions that one has to face when one follows the path that identifies all mathematical symbols with physical realities. Surely when one finds oneself on this slippery slope the wise thing is to retrace one's steps.

Let us remember the alternatives with which the two hypotheses about the manner of disappearance of matter confront us. Each obliges one, admittedly, to surrender something that one may like to believe. One must surrender either the axiom that an infinite amount of a physical quantity is a notion without meaning or the traditional belief in the permanence of matter and energy. But between an axiom based on logic and a belief based merely on tradition a scientist must not hesitate. Belief in the conservation laws is surely the more expendable one.

7 A possible means of deciding between (B1) and (B3) by observation

Both those who couple (B1) and those who couple (B3) with (A3) assume that new stars arise far out in interstellar space as the result of irregularities in the distribution of new matter. Mass densities slightly above the average are assumed to act as centres of gravitational fields and to grow by the capture of further new matter from their vicinity. But a moment's thought shows that the rate of growth cannot be the same for each hypothesis.

According to (B1) a new star must continue to grow without limit. But according to (B3) the rate of growth must become less as the star reaches a very large size and may at last cease altogether or even become negative. The reason is as follows.

To couple (B3) with (A1) is to assert that the rate of origin of new matter is approximately constant per unit volume while the rate of disappearance is approximately constant per unit mass. So a star would lose more matter the larger it was, and its replenishment rate by gravitational capture of new material would have also to increase with increasing size. Hence a growing star would depend on an ever increasing volume of space for new matter; the particles captured would be drawn, on the average, from greater distances; and so the probability that any one of them would reach the star before its disappearance by extinction would decrease as the star grew bigger. In other words, the replenishment rate according to (B3) could not be expected to keep pace with the loss rate; the latter would tend to gain on the former. Should they become equal the star would cease to grow. A consequence is that there must be an upper limit for the size of the star if (B3) is valid, but none if (B1) is.6 (B3) thus predicts that a larger proportion of all stars must occur within a certain size-range than (B1) does. Data concerning the actual size distribution of all observable stars should therefore help towards a decision whether the hypothesis of disappearance by extinction or that of disappearance by removal is the more tenable.

* Read to the Philosophy of Science Group, 14. June 1954

1   R. 0. Kapp, Science versus Materialism, London, 1940, Chapter XXIV
2   F. Hoyle, 'Stellar Evolution and the Expanding Universe', Nature, 1949,163, 196
3   H. Bondi and T. Gold, 'The Steady State Theory of the Expanding Universe', Monthly Notes Royal Astronomical Society, 1948, 108, 252
4   W. H. McCrea, 'The Steady State Theory of the Expanding Universe', Endeavour, 1950, 9, 3; 'Relativity Theory and the Creation of Matter', Proceedings of the Royal Society, 1951, 206, 562
5   R. 0. Kapp, 'Effects of Origin of Matter on Cosmology', The Observatory, 1948, 69, 149; 'Development of the Universe', Nature, 1948, 165, 68; 'Theories about the Origin and Disappearance of Matter', The Observatory, 1953. 73, 113
6   R. 0. Kapp, 'Development of the Universe', Nature, 1948, 165, 687

This paper and any subsequent discussions and rejoinders are reproduced from the British Journal for the Philosophy of Science with the kind permission of the Oxford University Press.
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