by Reginald O. Kapp
To be Valid, a Theory of Gravitation must be Based on the Principle of Minimum Assumption
A considerable portion of the foregoing chapters has been concerned with two hypotheses. The first is that of the continuous origin and extinction of matter, which I have called here the Hypothesis of the Symmetrical Impermanence of Matter. Although I published this hypothesis as long ago as 1940, the present book is almost the first record of a serious attempt to explore its implications. The second hypothesis is that of the expansion of space, which has already received wide, if not yet universal, support.
It has been shown here that the evidence for both hypotheses is strong and abundant. It is observational as well as inferential. One must not, of course, exclude the possibility that the whole of this evidence may some day be refuted. Alternative explanations may be found for each piece of observational evidence in turn; the Principle of Minimum Assumption, which is the basis of the inferential evidence, may be proved false and have to be abandoned; the arguments that I have been presenting may prove to contain faulty logic; an error may be found in the mathematics by which relativists have inferred the linkage between ponderable matter and space.
Evidence is never so conclusive that anyone should be discouraged from attempting to refute it, and in this instance such an attempt might well lead to a discovery of importance. But the search for means of refuting an hypothesis should include the search for means of testing it, be it by observation or by experiment. Its implications should be worked out and so formulated that one can say: 'If this hypothesis is true, one should expect so-and-so'. One can then make the observation, conduct the experiment, and find out thereby whether the hypothesis has support or not.
This was the method pursued in Part Three for testing the Hypothesis of Symmetrical Impermanence. If this hypothesis is true, it was argued, one should expect to observe spiral nebulae. That they had already been observed made it appear, perhaps, that the hypothesis was justified by its explanatory power rather than by its power of prediction. But there is really no difference. Whether one says that an hypothesis explains or predicts depends, as I have pointed out before, on whether the observation to which the hypothesis refers has preceded or followed it.
Here, in Part Four, three further pieces of evidence will be presented. They are, respectively, gravitation, the occurrence of stars, and their rotation. The first of these will be discussed in this chapter, the second and third in Chapters 27 and 28.
What is to be presented here can be regarded in several different ways. From one point of view it constitutes two new theories, one about the cause and nature of gravitation, the other about the process by which stars are formed. But from another point of view it constitutes confirmation by observation, and in a sense by experiment, of the validity of both Symmetrical Impermanence and general relativity. As both these hypotheses are inferences from the Principle of Minimum Assumption, what is presented here can, more basically, be regarded as a demonstration of the great unifying power of this principle.
Let me follow here the line of reasoning by which, in fact, I arrived at the new theory of gravitation. I did not do so in a deliberate attempt to solve the riddles that were presented in Chapter 22. At the time I was but dimly aware of these riddles and had come to regard them as largely beyond the scope of scientific inquiry. What I was concerned with instead was a means of testing the Hypothesis of Symmetrical Impermanence. During my search I found that the behaviour of ponderable matter in the vicinity of a massive body provides such means.
As discussed in Chapter 14, the rate of origins is constant per unit volume and the rate of extinctions constant per unit mass. For reasons given in Chapter 24 and Appendix H, the origin of matter and the origin of space occur in association and the extinction of matter and the extinction of space also occur in association.
From these considerations, it follows that the gross rate of expansion of space per unit volume is everywhere the same, while the gross rate of contraction is everywhere proportional to the mass density. When the two rates are superimposed, one obtains the net rate of expansion per unit volume, which is positive when the mass density is below the equilibrium value and negative when the mass density is above this value. In other words, a very tenuous region expands and a dense one contracts.
It has already been explained that for this reason the rate of contraction must exceed that of expansion within our galaxy, and must greatly exceed it within every star. The suggestion has been made in Chapter 24 that the contraction might just conceivably be observed for the galaxy as a whole. It would be so if one could measure a reduction in the red shift of the spectrum of the light from distant stars. But the effect would be very slight and might not be measurable. However, a moment's thought will show that one ought to expect the contraction of space within large masses to show another, and much more conspicuous, effect.
When the rate of contraction varies from place to place, it must result in noticeable strains. An analogy is a tablecloth that has been splashed with a chemical substance. If this is of the kind that causes the fabric to shrink, and if it lands on the cloth in spots, the spots will be areas of shrinking, while the surrounding cloth will not shrink. The result will be that the spots are surrounded by puckers and bulges.
If the cloth is patterned, any lines through and near the spots that were previously straight will have become curved after the chemical has done its work. Suppose that a teacher of geometry had previously drawn lines and triangles on the cloth in order to demonstrate one of Euclid's theorems to his pupils. The lines and triangles will have been distorted by the action of the chemical and will no longer serve as a means of demonstrating Euclidean geometry.
It has been inferred above from Symmetrical Impermanence and general relativity that every heavenly body is analogous to a spot on the tablecloth. It is a region of local shrinking. So the space around it is strained, distorted. Lines in the neighbourhood that would be straight if the body were not there will be curved as a consequence of the extinctions that are occurring in the body. In the region around it Euclidean geometry will not hold; it will be replaced by another kind.
Such is the prediction that is inferred, without any additional hypothesis, from Symmetrical Impermanence and general relativity. Can it be verified? Can one think of an observation or an experiment by which to test it?
This was the question that I put to myself a number of years ago when I was seeking for means of testing Symmetrical Impermanence by observation or experiment. It came as something of a shock at the time that one would be able to observe the effect of the extinction of matter on the geometry of space by the movement of a body free of restraint. If the space was flat, such a body would move with a constant velocity, which means with zero acceleration. But according to relativity theory the body would have a finite acceleration if the space was curved.
Here was the possibility of an experimental test for Symmetrical Impermanence. The hypothesis predicts that a body free from restraint will be accelerated in the vicinity of the Earth. The simple experiment of dropping something shows, of course, that it is so. The experiment is cheaper than many to be seen in laboratories and easier to perform. But cost and difficulty are not good measures of the cogency of an experiment. This one would not be more conclusive if it were rarer, more costly, or more difficult.
The above remarks have been presented in the form of a justification of Symmetrical Impermanence; and that is what they are. I have shown that the cosmological model inferred from Symmetrical Impermanence without any additional hypothesis is such that the region around every massive body is one in which there is a field of gravitational force.
With a small shift of emphasis and slightly different wording the same remarks would have appeared as a new theory of gravitation. The subject is important enough to make repetition in this form excusable.
In Chapter 21 I pointed out that the word 'mass' may mean three things that can be conceptually distinguished. The names given to them were inert, gravitational and attracting mass. Einstein's general relativity is based on the identity of the first two, both numerically and conceptually. Where there is curvature of space, Einstein pointed out, one can infer that a body possessing inert (and therefore also gravitational) mass is accelerated if it is free from restraint. If the body is near an accumulation of inert mass it is observed to be accelerated. We know this from observation that an accumulation of inert mass causes the space around it to be curved. But this fact is derived from observation only and not from inference. It has not been shown that it is in the nature of inert mass to cause curvature. General relativity goes no further than to show that it is in the nature of inert mass to follow curvature. Hitherto we have been able to do no more than believe in a vague way that every particle possessing inert mass carries an environment of curved space around with it, but we have not been able to say why.
The new theory that I am presenting here offers an explanation. The particle, I am claiming, does not carry this hypothetical environment about with it. During the particle's continued existence, it has no attracting mass but only inert and gravitational mass. It is at the moment of its extinction that the phenomenon to which the name attracting mass has been given appears. The extinction of the particle is coupled with the simultaneous extinction of some space; there is a local contraction. This becomes manifest as a local curvature of space, the condition shown by Einstein to define a gravitational field.
Thus gravitation is not the signature tune of matter; it is its swan song.
The local contraction does not remain stationary. One cannot regard it as curvature bound to anything in the sense in which the electric flux around an electron is bound to the electron. As there is nothing to which the gravitational curvature can be bound, it is free in the sense in which the electric flux in a photon of radiation is free. Hence the local curvature that results from the extinction of a particle travels outwards from the site of its source, flattening as it does so. Gravitation occurs in pulses. It is quantized. It has a finite velocity of propagation, though I cannot think of any means of either measuring or inferring the velocity.
The number of pulses of gravitation that emanate per second from any body of which one can measure the attracting mass, ma is very great. Hence they give the appearance of a continuous field. It is the same with a lump of radium. The radiation is quantized but there are so many disintegrations of atoms to provide the quanta that the radiation gives the impression of continuity. It is the same with light from a lamp. Continuous though it seems, it is really intermittent.
According to the traditional theory of gravitation, every particle present contributes its share to the gravitational field. Hence the contribution from each proton or neutron is assumed to be a minute fraction of the total. Though each of these particles is assumed to carry an environment of bound curvature around with it, the curvature around each is regarded as slight.
According to the new theory, on the other hand, the proton or neutron contributes nothing during its continued existence, as has been pointed out already. The contribution comes only from the minute fraction of all those present that happen to be becoming extinct at the moment. The effect of each extinction on curvature at that moment must be correspondingly great. Every extinction, one may say, results in a comparatively powerful jerk to any nearby object in the path of the pulse. The intensity of the pulse, like that of the light from a lamp, diminishes, of course, in conformity to the inverse square law so that the acceleration given to a body by each pulse is less the further away the body is from the site of the extinction that caused it.
Just as an extinction is surrounded by contracting space, so, according to the new theory, an origin is surrounded by expanding space. In this respect, if in no other, origins and extinctions are distinguished only by sign. So the space around an origin must also witness the passage of a pulse, or wave, of curvature. This curvature must have the opposite sign to that of a gravitational pulse. Instead of being a wave of contracting space it is a wave of expanding space. It can aptly be called a wave of anti-gravitation. Its effect must be to accelerate any inert mass over which it passes away from the site where the origin occurred.
It has been shown that the rate of origins must everywhere be constant per unit volume. Although each origin is a centre of anti-gravitation, the random and approximately uniform distribution of these centres throughout space prevents the anti-gravitation from becoming observable. Pulses of anti-gravitation are passing everywhere in different directions and usually cancel each other's effects.
According to the new theory, things do, nevertheless, fall away from the site of every origin in a very tenuous gas. Origins are sources of dispersal, just as extinctions are sources of concentration.
A region, moreover, in which the mass density is below the equilibrium value is one from which more pulses of anti-gravitation emanate than pulses of gravitation. Most extra-galactic space consists of such regions and they must cause inert mass to move out of them. The things that fall towards galaxies are, one might say, being pushed there out of almost empty space as well as being pulled by the galaxies.
So much for a brief outline of the new theory. It will be shown in Chapter 26 that it has sufficient explanatory power to answer the questions raised in Chapters 21 and 22, and it will be shown in Chapters 27 and 28 that it also helps to explain the formation of stars and their rotation.