A PAST chairman of this Group, Professor Woodger, has a capacity
for saying profound things lightly. I should like to quote one of
them. It occurs in his book Physics, Psychology and Medicine. He is
discussing some prevalent errors concerning the nature of reality and
'Another tenet of this philosophy seems to be that everything that is,
is in a big box called Space, which is floating down a river called Time.
Consequently if anything (except the river!) is not in space, it is just not
This is the philosophy that Professor Woodger rightly invites us
to reject. He might have issued the invitation with a parade of
learning and abstruse logic; but the uncompromising simplicity of
the form in which Woodger presents this erroneous view of reality
embodies a criticism of it by implication that is both more cogent and
more precise than a learned dissertation could be.
We are all prone to adopt the big box view of reality and we have
to understand why it is wrong. It contains two errors.
The first is the assumption that only those things with location have
reality; that anything not in space is 'just not at all', or, more shortly
still, what is nowhere is not. 'Nowhere' and 'non-existent' are
regarded as synonyms, and according to this school, space itself is not
necessarily real but everything is real that is in space and nothing, except
perhaps time, is real that is not in space.
There are, of course, those who would like to adhere to this school
and yet doubt whether it is correct to identify 'nowhere' with
'non-existent'. With the leaning towards compromise of the woolly-minded they then prefer to identify it with 'not quite'. In other
words they introduce the view that there are degrees of reality in the
same way as there are degrees of temperature or degrees of hardness.
What is nowhere is not quite real, they would say. Some things are
to them more real than others. According to this remarkable interpretation of the concept 'real' they say that particles are the most real
of all. These they think of as consisting of a substance, which they
might call particle stuff. Particles are regarded as interacting with
other things that are several degrees less real, such as waves. The very
real particle stuff and the not so real waves are then regarded as having
their existence in time, which is hardly real at all. They are also said
to have their existence in the big box space, about the reality of which
they do not care to think. Mass and electrical charge, being properties
of the particle stuff, are placed high on the reality scale. Extension,
being a property of space is placed low.
If the course of events is ever subjected to control it is taken for
granted, by adherents of this school, that the controlling influence
consists of particle stuff. Having heard of servo-mechanisms and
feed-back they say that the controlling influence must necessarily be a
part of a closed loop and, moreover, a part consisting of material
substance. They find a place for it in the big box. As nothing is
believed to exist unless it has location in the big box it is regarded as
unscientific, bad philosophy, or logically absurd to postulate a controlling influence without location.
Be it admitted that all things possessing physical reality do occur in
the big box. The error is to assume, indeed to take it for granted, that
physical reality is the only kind of reality. I have myself attacked this
somewhat fashionable but, nevertheless, naive view on many occasions
and propose to leave it at that for the moment. I want to pass on to
the second error implicit in the big box philosophy.
The second error concerns the nature of space. The view that
space is a container was held almost universally until early in this
century. It is true that some denied it, among them Leibniz, and some
doubted it, among them perhaps Newton. But since the success of
Newtonianism the doubts were never clamorous. When it was said
that all physical things are in space I do not think that it would have
occurred to many to question the appositeness of the preposition 'in'.
Yet doubts ought to have arisen. If space were the container of
physical reality it would be relevant to ask how full is was. How
much reality must be put into a given region of space so that it may be
100 per cent full? How much would make it 50 per cent full? Do
the actual contents of space fill it up to just as much as it can hold? If
something more came into space than is there already would reality
overflow and spill into the river Time? If the big box were filled
with radiation only, how much would there be to fill it? How much
particle stuff, alternatively, is needed to fill the box?
I hope such questions seem as absurd to you as they do to me.
What I want to make clear is that we ought not to have had to wait for
relativity theory before we abandoned that queer notion of space
implicit in the big box philosophy.
Be that as it may, it was Einstein who showed more cogently than
anyone had done before why it is wrong to regard space as the container
of reality. (But it is only fair to add that Newton seems to have had
his doubts about it, and Leibniz certainly did.) When attributing
physical properties to space Einstein obliged us to replace the word
'container' by the word 'constituent'. Space, we learnt from him,
is a constituent of the material universe and not its container.
We learnt if half a century ago. But we are in danger of forgetting
it. Today general relativity occupies only a very small part of the
undergraduate teaching in physics and astronomy, if it is taught at all
at that level. Post-graduate studies are necessarily devoted to other,
usually more recent, subjects. Even special relativity does not receive
the same attention from scientists today that it did in the 1920s. It is
found that a physicist or engineer can do all that he needs when working
with particle accelerators if he has familiarised himself with the relativity equations and the rather specialised notation that they employ.
Pre-occupation with meaning, such as was common in Eddington's
day, is no longer necessary. It suffices for practical purposes to know
how to use the letter symbols.
The academic syllabus does not have room for everything. Very
few physicists and astronomers are engaged on work that calls for any
knowledge of general relativity. Those few who have made a deep
study of the subject have been stimulated by intellectual curiosity
rather than by practical needs. Nevertheless, I have reached the
conclusion that those few may be able to contribute much useful
knowledge. Let them be encouraged. Perhaps it is just because
I have little specialised knowledge myself that I view the progress of
science from a little distance. What I see leads me to believe that some
aspects of the physical world can be more profitably explored by one
who takes as his starting point the position that was occupied in the
1920s than by one who sets out from the position more usually occupied
today. In Eddington's time the focus of interest was the interaction
between space and ponderable matter. That subject is rarely discussed
today. Now the focus of interest is more often the interaction between
particle and particle. So I want this paper to serve as a reminder of
the great work done by Einstein, Eddington, and others. I propose
to suggest lines for future study that are stimulated when one places
oneself in thought in the atmosphere of the 1920s.
Let me draw attention to another of the defects in the pre-Einstein
view. This view obliged us to think of every bit of ponderable matter
as having two environments. One of these was called 'space', the
other 'luminiferous ether'. The two environments were said to be
quite distinct. Most of us regarded space as featureless, as such that
any one part was in every respect exactly the same as every other part.
The only property that could be attributed to space viewed in that
way was extant, but even that property had little meaning, if any, so
long as the extent was considered to be infinite.
In contrast to the featureless space we thought of the luminiferous
ether as featured. Its various parts were said to be subjected to a
variety of strains. These strains were considered to be electrical and
magnetic. For some reason gravitational strains were not postulated.
Gravitation was regarded as a phenomenon about which the less said
To explain the presence of the various strains a variety of physical
properties was attributed to the ether, such as elasticity, density, inertia.
One of Einstein's great contributions to science was to show that
there is no need to postulate two environments. One will do. I
think this was as great a contribution to philosophy as to science.
It is now recognised that a space of which no part is distinguishable
in any way whatever from any other part is not observable by any
physical means. Its nature is, therefore, purely conceptual. It is
difficult, if not impossible, to argue that a featureless space has any
physical meaning. Things would happen just as they do with or
without a space of that kind. Of the two environments assumed for
every body, reality could be assigned to one only.
This reasoning could have left scientists with the luminiferous ether,
thought of as differing from one place to another, as being featured;
and the features being considered such as to influence measuring
devices, and as to be observable.
The measurable features, in the environment of ponderable matter,
all have something in common which can be expressed by a single
word, namely, field of force. Such fields are measured and described
in terms of their intensity, which is more precisely called their potential
gradient. There are at least three kinds of field, electric, magnetic,
and gravitational; so the environment of a given quantity of ponderable matter may contain three different kinds of potential gradient.
Each of these may vary both in magnitude and direction. At least the
electric and magnetic potential gradients may also vary with time at any
given point. When they do so they are called waves. The physical
effect on ponderable matter of these potential gradients is always of
the same kind, namely, that of accelerating the ponderable matter.
When this insight was gained a name was needed for the collection
of potential gradients that surrounds any given quantify of ponderable
matter. 'Luminiferous ether' might have been retained for this were
it not that its verbal currency had been depreciated by sundry misapprehensions. Hypothesis had, for instance, endowed the ether with
the properties I have already referred to; elasticity, density, inertia.
But no such properties could be attributed to places where there was
no ponderable matter. The only observed, or even inferred, physical
features of the environment were various potential gradients, some
static and some alternating, some bound to a particle and some moving
freely with the velocity of light; and so the many properties that had
been attributed to the ether proved both inappropriate and too
numerous to make this term suitable. If the word 'space' suggested
something too abstract, the words 'luminiferous ether' suggested
something too concrete.
Perhaps the non-committal word 'environment' might have been
a good choice. It could have been justified scientifically; for it is
strictly accurate to say that a quantity of ponderable matter is surrounded by an environment that has physical properties and one has to
be very cautious about saying anything more than this. But to use
'environment' in this way would have been to raise the word to the
status of a technical term and to use it, moreover, in an unfamiliar
context. 'Collection of potential gradients' could also have served
for these are, literally, all that one needs to postulate as occurring
between one bit of ponderable matter and another. Whether the
container of the potential gradients be called space or luminiferous
ether is immaterial. The point is that the concept of a container is
unnecessary. The potential gradients are observable by their effects.
But, everything would happen as it does whether these gradients have
a container or not.
But neither 'environment' nor 'collection of potential gradients'
would ever have succeeded in ousting the established word 'space'.
So I think that Einstein showed a sound intuition when he retained
this word while changing its meaning from that of a featureless
container to that of a synonym for featured environment. But when
the word 'space' is used in relativity theory with its new and precise
meaning, it does not at the same time represent the vague concept that
it does in everyday speech. It has become a technical term.
Another piece of insight gained from relativity theory was that
the properties previously attributed to the luminiferous ether could not
be attributed to the environment of ponderable matter. It appeared
at least possible that they could all be replaced by one single property
described as 'curvature'. It was from the identity of inert and
gravitational mass that Einstein arrived at the conclusion that a field
of force, at least when the force is gravitational, is a region for which
the geometry of space is non-Euclidean, and he used the expression
'curvature' as a means of describing the departure from Euclidean
geometry for the space in which there is a potential gradient. This,
too, became a technical term with a unique and precise meaning in
The conclusion startled the scientific world. Until then we had
regarded curvature as a purely geometrical property. That it could
be regarded as a physical one caused scientists to revise their notions
about the nature of matter. How, it came to be asked, could something as apparently abstract as a curvature of space interact with
something apparently as concrete as a material particle? The question
is as puzzling today as ever it was.
The best answer will eventually come, I am inclined to think, from
a revision of our notions about what is abstract and what is concrete.
In making a distinction between these we tend to be enslaved by the
organs of sense perception with which we, as human beings, happen
to have been endowed. We call those things concrete that we can
perceive with the help of these organs and those things abstract that
cannot be so perceived. But this is a surmise and I do not propose to
pursue this line of thought any further here.
Relativists have succeeded in showing good reason why gravitational potential gradients should be identified with a condition of space
appropriately called its curvature. But they have not yet succeeded
in showing the same for electrostatic and magnetic potential gradients,
though some of them still hope to do so. The effort to do this is
called the search foi a unified field theory. Anything that I, or anyone
else, can say today about the relation between space and matter may
have to be modified if and when the search has succeeded. For this
reason, if for no other, whatever can be said at present must inevitably
not only leave some insistent questions unanswered, but also be very
Should it ever be shown that electric and magnetic potential
gradients are regions of curved space we must expect the kind of
curvature to differ basically from the kind that is identified with a
gravitational potential gradient, for there is no known interaction
between gravitational fields and the other two kinds. A change of
the charge on a body having inert mass does not change the behaviour
of the body in a gravitational field. A change in the potential gradient
of a gravitational field does not affect the forces between electric
charges placed in it. Gravitational masses that do not carry electric
charges and are not magnetically polarised fall with the same acceleration through an electric field (provided there is a gravitational one to
fall in) irrespective of its intensity. In other words, electric charges
behave in the same way in gravitationally curved as in flat space.
From such observations it has to be concluded that, if electromagnetic potential gradients are, like gravitational ones, curved regions
of space the geometry by which the curvature can be defined can
hardly be of the same Riemannian kind that represents gravitational
potential gradients. This independence from each other of the different
kinds of field takes some accounting for and even leaves room for
doubt whether the electro-magnetic field is, as seems so reasonable to
suppose, a region where the geometry is non-Euclidean. But I have
nothing to contribute to the search for an explanation and do not
propose here to discuss the relation between space and charge or that
between space and magnetism, but only the relation between space and
mass. I have no choice but to discuss this relation as though the only
condition of space by which one region is distinguished from another
is curvature and the only known, kind of curvature is that identified
with the gravitational field. The incompleteness of such treatment is
made obvious by the known facts about electricity and magnetism.
But all that one can do in the present state of ignorance is to see along
what path the incomplete treatment takes one and to hope that better
knowledge of the relation between space and charge will not necessitate
too great a change of direction from that in which the chosen path
I want here to define the limits to our present knowledge of the
relation between space and mass. Relativity theory has contributed a
great deal to that knowledge. But there is still much about which we
are ignorant and questions to which the search for answers is likely to
prove rewarding come under two headings: the action of space on
mass and the action of mass on space.
Let me now turn to the action of space on mass and remind you of
some well-known facts about it.
Relativity theory tells us something about the motion of a particle
to which no force is applied, it being well understood that all statements
about the motion are relative to a given co-ordinate system. The
motion depends, according to the theory, only on the curvature of the
space in which the particle finds itself. If the space is flat, the particle
moves with a constant velocity, which may of course be zero velocity.
If the space is curved, the particle moves with a non-uniform velocity;
it experiences an acceleration or a deceleration.
If a force is applied to the particle its movement is no longer wholly
determined by the geometry of space. A billiard cue can accelerate
a billiard ball in flat space and a shelf can, by exercising a force on
the stone resting on it, prevent the stone from following the curvature
of the space in which it finds itself.
I mention these well-known facts only to bring out what is and
what is not known about the action of space on mass. Relativity
theory defines the property of space by virtue of which it is able to act
on mass; this property is technically called curvature. But relativity
theory does not tell us anything about the property of mass by virtue
of which an unrestrained particle follows the curvature. The property
is given the name inertia, but to name a thing is not to explain it or to
give any sort of information about it. Relativity has some important
things to say about space but fewer about mass. Let me illustrate our
present ignorance about the relation between these two concepts with
the help of an analogy.
When one sees a tramcar turn a corner, one may give the perfectly
true explanation that there are rails for it to travel on. But it is an
insufficient explanation. It says something about the street, but
nothing about the tram. To make the explanation complete one has
to add that the tramcar is provided with flanged wheels, so designed
that they fit the rails.
Similarly, when one sees a stone fall one may give the explanation
that the space in which the stone happens to be is curved and thereby
causes a curved track in space-time. One has then found the equivalent
of the rails that take the tram round a corner. The analogy is admittedly not perfect, for a force is exerted between the tram-rails and
the flanges on the wheels, whereas the stone follows the curvature of
space without any force being exerted on it at all. But the analogy
serves, nevertheless, to show in what way the relativistic explanation
remains incomplete. It fails to include the equivalent of the tram-wheels. What, one is led to ask on receiving the relativistic explanation, is the feature of a particle that causes it to 'engage' with space,
as it were, so that its track in space-time follows the curves? In the
example of the tramcar, steel wheels run on steel rails. When an
unrestrained particle moves in space something is said by relativists to
run on curvature. What is it?
I shall return to the question later. For the moment I want to
say a few words about the action of mass on space.
For the sake of convenience I shall again repeat a few well-known
facts. According to Newtonian mechanics a massive body causes other
bodies in its vicinity to be accelerated. To the question why this
happens the answer is that a field of force surrounds the body. But
to the question: what sort of a thing is this field? Newtonian
mechanics has no answer; it can at most provide a name. Newton
did not attempt to explain gravitation; he was content to postulate it.
It is here that relativity theory steps in. It does say what sort of
a thing a gravitational field is, namely a region of curved space. The
answer is justified both because it is methodologically sound and because
it has considerable explanatory power. But it leads to the further
question: why should a massive body cause the space around it to be
curved? Again, relativity says something about space, but nothing
about mass. It is content to postulate the effect of mass on space
without explaining it. It seems to me that this limitation of relativity
theory has not been properly appreciated. I say advisedly 'limitation'
and not 'defect' for it is no defect of a theory to fail to provide 'all
If this particular limitation has not been much noticed and if little
effort has been made during recent decades to get past it, the reason is
I think in a deflection of interest. In the early days of relativity interest
was directed strongly towards the interaction between particles and,
space. Studies in nuclear physics have since then directed more
attention towards the interaction between particles and other particles,
as already mentioned. Both kinds of interaction deserve equal study
and I venture to suggest that a return to the earlier interest would now
When one turns one's attention to this earlier interest, one is led to
remember a view expressed by some relativists of those times. An
elementary particle, it was sometimes said, is, apart from its charge, a
region of gravitationally curved space and nothing else.
Eddington made this point a fundamental one. 'Mass is curvature' he said somewhere. At the time when he was writing there
was the catch-phrase, 'Man is a kink in space-time'. Pre-occupation
with this hypothesis is less insistent today, but not because we are any
nearer either to accepting or discarding it. It is only for the reason
already mentioned, namely that we are today more concerned with
the way particle acts on particle than with the way space acts on
particle. The great attention paid to nuclear physics has diverted
attention from the fundamentals of relativity. But I do not think
that what is at most a slight lack of topicality makes the question
whether mass is curvature or something else any less rewarding now
than it has been in the past.
To avoid the complication of electricity and magnetism I shall
begin by considering only a neutron. What is it made of? Must we
postulate a substance that is different in nature from the technical
concept, space? Shall we find ourselves obliged to speak of particle
stuff' or shall we say, with Eddington, that the neutron consists of
curvature and nothing else? When the question is put with this
disconcerting candour one is inclined to dislike every answer that can
be suggested. But I think that one will have the greatest dislike for
the suggestion that there is something deserving of such a title as
'particle stuff'. One will be inclined to accept the Eddingtonian
answer, if only as the lesser evil. The theory that the neutron
consists of curvature seems better to meet the Principle of Minimum
Assumption and to offer a better prospect of further unification of
If this is accepted, the volume occupied by a neutron is a region of
bound curvature. Within this region the potential gradient does not
change with time in the way it does when the curvature takes the form
of a travelling wave.
I have said a little while ago 'In the example of the tramcar, steel
wheels run on steel rails. When an unrestrained particle moves in
space, something is said by relativists to run on curvature. What is it?
If mass is curvature, the answer is found. Only curvature can run on
curvature. It seems as reasonable a conclusion as one may hope for
so long as one accepts general relativity.
With that hint I should like now to leave discussion of the features
by which one part of a relativistic space is distinguished from another
and to turn to the notion of expanding space.
The theory that space is expanding is supported by two kinds of
evidence, that of inference and that of observation.
The inferential evidence was provided first, and by relativists.
They explained that a cosmological model of which the volume did
not change with time would be unstable. In the sense in which they
used the word 'unstable', a model that resembled actuality would
have to change its volume. This did not prove that space expands.
The inference would have been equally compatible with a model that
contracted, which it could, of course, not have been doing for an
indefinitely long time without having disappeared. Hence the conclusion that space was, in fact, expanding was first arrived at by
The observational evidence for the same conclusion is well-known.
It is provided by the red shift in the spectrum of the light from distant
nebulae. This shift is interpreted as a Doppler effect and is attributed
to a recession of the nebulae from each other. The magnitude of the
shift is found to a close approximation to be proportional to the
distance of the nebulae. It is the effect that was predicted by the
When a theory has such two-fold support it is usually accepted by
scientists. If the notion of expanding space has not gained universal
support, the reason is not far to seek. The notion is difficult to understand; one cannot form a picture in one's imagination of space itself
expanding. It is only natural to dislike a conclusion that one cannot
fully understand. From dislike to rejection is but a short step, so it
is not surprising that some rather desperate attempts have been made
to find an alternative explanation of the red shift. It has been done, of
course, in the name of scientific caution. But the degree of scientific
caution with which a new idea is greeted is some indication of its
But unless both the inferential and the observational evidence can
be effectively shaken, the wisest course is to do one's best to come to
terms with the notion of expanding space whether one finds it an easy
concept or not. If we cannot hope to relate this notion to anything
with which we are familiar, we should at least try to find some valid
statements about it.
One sometimes says that a fugitive from justice puts space between
himself and his pursuers. One does not mean the expression to be
taken literally. One only means that the fugitive is running faster
than those in pursuit. When he does this he does not create new space
but only causes a larger amount of existing space to separate him from
If the fugitive could literally put space between himself and his
pursuers, he would not need to run away from them. He could sit
down and smoke a cigarette while he put enough space in front of
those who were trying to catch him to make sure that they never got
any nearer. If he did this he would not be moving past objects in
existing space. He would not be moving at all.
It is in this literal sense that, in an expanding universe, space
originates between us and every distant nebula. While the fugitive
from justice is getting further from his pursuers, he is also getting
nearer to the house in which he hopes to hide. But while our galaxy
is being caused by the expansion of space to get further from all other
galaxies, it is not being caused to get nearer to anything.
In this there is a significant difference between changes that result
from the operation of forces between bodies and those that result from
the expansion of space. So long as there are forces, some things get
nearer to others; they overtake other things. But when space-expansion alone determines distances nothing ever gets nearer to
anything else; there is no overtaking; there is not even movement.
It is this last conclusion that makes the notion so difficult to understand. If things get further apart they must, we are inclined to reason,
move relatively to each other. But we have to appreciate that this is
false reasoning. Let me show why as clearly as possible.
Two nebulae, A and B, have been observed and both show the red
shift. One of them, A, is in the part of the sky called North and B is
in exactly the opposite direction, the part called South. When we
are thinking only of A, we may make one of two statements:
(1) The distance between our galaxy and the nebula is increasing.
(2) Our galaxy and the nebula are moving relatively to each other.
We may be inclined to think that these two statements have identical
meanings; and so they would in many contexts. But if we attribute
the red shift to the expansion of space we have to conclude that they
mean different things and that, while (1) is correct, (2) is wrong.
This emerges when the implications of (2) are examined. To say
that our galaxy and the nebula A are moving relatively to each other
may mean that both are moving or that one is at rest while the other
is moving. But it must mean that at least one of the two bodies is
If this were our own galaxy, it would be moving away from A,
i.e. southwards. But when we observe nebula B we have to conclude
that, if our galaxy moves at all, it must be away from B and northwards. A corresponding conclusion would be reached if we used a
nebula in any other part of the sky as an indication of the direction in
which our galaxy was moving. Wherever our choice fell, it would
always cause us to say that we were moving away from the observed
nebula. To say that the expansion of space is causing our galaxy to
move is to say that the movement is in all directions at once! The
correct interpretation of the red shift is, in other words, that our galaxy
is not moving at all relative to any other nebula.
Are we then to take the view that we alone are at rest and that
nebulae A and B, together with all others, are moving relatively to us?
Are we to adopt the old egocentric universe in which we are located
at a centre from which all effects radiate?
This, we know, cannot be. An observer on any other nebula
would have the same experience as we ourselves here. It would be
just as impossible for him to state the direction in which his nebula
was moving. He could not say that it was moving relative to space
in such a way that space, at one moment in front of it, was behind it
at the next moment. He would say that his nebula was not overtaking
anything, not even empty space; that it was not moving in any
direction; that it was at rest.
We are thus obliged, whether we like it or not, to accept the odd
notion that in expanding space the distance increases between objects
that are all at rest relative to their surroundings. If the nebulae all
seem to drift away from each other, this cannot be attributed to anything that happens to the nebulae but only to what happens to the
space between them.
Even if one succeeds in appreciating the strange fact that, in expanding space, objects remain stationary while the distance between
them increases, one may still, I fear, hanker after a force that drives
them away from each other. It seems, to the way of thinking of most
of us axiomatic, that things can only get further apart if a force is
pushing them away from each other. But a little very simple mathematics shows that the notion of forces of repulsion has to be given up,
however reluctant one may be to do so.
The velocity of recession, as viewed in any one particular direction,
dl / dt = Hl
where l is distance and H is Hubble's constant. To find its value
observations are necessary that cannot be made with very great
precision. Recently it was thought to be 185 km/sec/megaparsec.
But later observations suggest that 100 km/sec/megaparsec may be
nearer to the truth. If H is a cosmological constant and holds for the
whole of space-time the acceleration is:
A = d2l/ dt2 = Hdl / dt = H2l
Here A is the acceleration of one body relative to a single selected
other one, but not the acceleration of any body relative to all other
ones, which would always be zero.
Force is the product of mass and acceleration. If our galaxy were
receding under the influence of a repelling force, we should therefore
give this the value
F = mA= mH2l
where m was the mass of our receding galaxy. But this would be an
absurd conclusion. According to equation (2), the force exerted by
a body on any other one would not be proportional to the mass of
the repelling body but to that of the repelled one.
Such a conclusion cannot, of course, be reconciled with the known
law of gravitational attraction. Consider two bodies with the
respective masses m1 and m2. The gravitational force between them,
which needs the negative sign as it is one of attraction, is:
F = - Gm1m2 / l2
Here the force exerted by m1 on m2 is the same as that exerted by m2 on m1. But if equation (2) meant anything (which it does not), one
would have to express the force exerted by m1 on m2 as m2H2 / l and that
exerted by m2 on m1 as m1H2l . The tiniest repelling mass m1 would
exert a very big force on m2 if this were big.
Let the distinction between a change of distance that is due to
expanding space and one that is due to a force be expressed in a slightly
different way. The acceleration of mass m2 relative to m1 is -Gm2 / l 2,
and the acceleration of m, relative to mi is Gm1 / l 2. The total
acceleration of the two masses relative to each other in expanding
Atotal = kH2l - G( m1 + m2) / l2
This expression shows clearly that the relative acceleration occasioned
by gravity is dependent on both masses as well as on the distance
between them, while the relative acceleration occasioned by the
expansion of space is dependent only on the distance between the
masses. It is a function of space and of nothing else. The conclusion
is disconcerting. But efforts to avoid it have to be rather desperate
and to introduce sundry ad hoc hypotheses. They are not sought so
much by those who accept the relativistic view of space as by those
who reject or have forgotten it.
The proper conclusion is thus, that the distance between things
can increase while the things are at rest relatively to each other. It
is the space between them that originates. The notion of expanding
space is more aptly called the Hypothesis of the Continuous Origin
c/o Kennedy & Donkin
12 Caxton Street
* Chairman's Address to the Philosophy of Science Group, 6th October, 1958
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