25.1: To be Valid a Theory of Gravitation must be Based on the Principle of
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 in 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.
25.2: Gravitation as a Consequence of the Extinction of Matter
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 ex-
tinction 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
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
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
25.3: The New Theory Developed
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
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 con
formity 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.
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