24.1: Inferential and Observational Evidence
What has been said in the last chapter about the impossibility of understanding some of the notions with which physics is concerned in the representational sense of the word 'understand' applies forcibly to the notion of
expanding space. It defies every effort of the visual imagination. But we have,
nevertheless, two kinds of evidence for it: inferential and observational.
In physical science we are rarely satisfied about the validity of any
statement unless it has the support of both these kinds of evidence. The
inferential evidence for the performance of a machine is, for instance,
provided by calculations made before the machine is even in the blueprint
stage. We regard it as nearly, but not quite, conclusive. The observational
evidence is provided by tests made with the machine after it has been built.
If they confirm the calculations, we are satisfied. Similarly, both kinds of
evidence are usually provided by a teacher who is lecturing on one of the
generalizations of physics. He first deduces the generalization from first
principles by making drawings and calculations on the blackboard and
then confirms what he has just inferred by an experimental demonstration.
If our reasoning were infallible, one of the two kinds of evidence alone
would suffice. But we cannot be thus sure of ourselves. When there is only
inferential evidence, one is justified in asking whether this may not be
based on false premises or faulty deduction. When there is only observational evidence, this may be open to different interpretations; we are
justified in doubting whether one may draw the stated general conclusion
from a particular case. But when there are both kinds of evidence, each
supports the other.
It is only because the notion of expanding space has this dual support
that it is widely, though not perhaps universally, accepted. It will suffice
here to refer quite briefly to the two kinds of evidence for it.
The inferential kind was provided first, and by those who had mastered
the relativity equations. 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 reasoning alone.
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 inferential evidence.
When there is such good agreement between prediction and observation, it is usual in physics for the conclusion to be accepted without further
question. If it was not so for the notion of expanding space, the reason is
not far to seek. This notion cannot be understood representationally any
more than the notion of the electron can, and 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
Should a convincing alternative explanation of the red shift be found
the situation would be that inference supported the notion of expanding
space while observation failed to support it. The calculations made by
relativists would then have to be re-examined. It really ought to be done
simultaneously with the search for an alternative explanation of the red
shift. If this has not happened, it is probably because the mental effort or
understanding the calculations and examining them critically is considerable. It is far easier to invent an hypothesis by which to explain the red
shift or explain it away.
But unless both the inferential and the observational evidence are
effectively shaken, the wisest course is to come to terms with the notion of
expanding space, whether we find it attractive or not. And it has so far not
been effectively shaken. So we must, I am afraid, be content to do with
this notion of expanding space what we have had to do with the notion
of the electron: form our private mental images of it from time to time;
but always remember that these images are wrong. Experience with the
electron has shown that we are rarely misled by doing so, provided we
recognize the inadequacy of the images and are prepared to replace them
by others if and when occasion demands. Experience has also shown that
images, false though they be, are sometimes helpful, sometimes even
24.2: How to Interpret the Notion of Expanding Space
Thus forewarned let us try to reach, if not representational understanding of, at least some valid statements about, expanding space.
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 the pursuers.
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 have 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 moving.
If this were our own galaxy, it would be moving away from A, ie 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.
It is amusing and instructive to try to find a mathematical formula that
would express a force of repulsion between nebulae in an expanding space;
for the attempt is bound to fail. The velocity of recession as viewed in one
particular direction is:
dl/dt = Hl
where l is distance and H is Hubble's constant. It has a value of 185
kilometres per sec per megaparsec. The acceleration is:
A d2l / dt2 = Hdl / dt = H2 l ......... (24a)
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 ......... (24b)
where m was the mass of our receding galaxy. But this would be an absurd
conclusion. According to equation (24b), 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 / l 2
Here the force exerted by m1 on m2 is the same as that exerted by m2 on
m1. But if equation (24b) meant anything, which it does not, one would
have to express the force exerted by m1 on m2 as m2 H2l and that exerted
by m2 on m1 as m1 H2l. 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 m1 relative to m2 is - 1/2G m2 / l2, and the
acceleration of m2 relative to m1 is -G m1 / l 2. The total acceleration of
the two masses relative to each other in expanding space is:
Atotal = kH2 l - 1/2G( m1 + m2 ) / l 2 ......... (24c)
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. For the distance, l, is the only variable in the
term that defines the effect of expanding space.
The above equations are, of course, no more than a mathematical way
of expressing the conclusion already reached without mathematics that
the expansion of space does not cause the bodies in it to move. As they do
not move, they are not accelerated by the expansion of space and are not
subjected by it to any force.
24.3: The Origin of Space and the Origin of Matter
The expansion of space could equally well be called the origin of space.
We may therefore speak of the continuous origin of space as we do of the
continuous origin of matter. Are the two origins coupled? Can there be
origin of space without origin of matter? Are the two kinds of originating
the same process, or are they two separate and distinct processes?
If we could regard space as the container of the physical universe and
ponderable matter as the content, there would be no reason why their
respective origins should be related. A change in the capacity of the
container might well occur without a corresponding change in the quantity
of matter contained in it. One could then say that at a certain mass density
space was quite full; and that at half this limiting density space was only
half-full. There would then be an absolute scale of mass density, as there
is an absolute scale of temperature. But no one has ever looked for such
a scale; no one has ever had the idea that there could be one; no one
believed, even in pre-relativity days, that the expression 'space is as full
of matter as it can hold' would have any meaning. Today relativists are
able to show why, in fact, it has no meaning.
They are also able to show that the origin of space and the origin of
matter are coupled, if not better described as synonymous. McCrea, it
will be remembered, has inferred the net rate of origin of matter, namely
500 atoms of hydrogen per cubic kilometre per year, from the observed
rate of expansion of space.
Yet here, as often in physics, there is a conflict between the two kinds
of understanding. Our misplaced effort at representational understanding
insists on retaining the notion of a purely conceptual, featureless space,
into which particles of matter could be poured; just as it insists on retaining
the notion of a purely conceptual, eventless time along which events are
ranged. It is only deductive understanding that tells us that these notions
are meaningless and that it is absurd to ask whether space is quite full of
matter or only partially full. When visualizing a cosmological model based
on the hypothesis (A2) about the Creation, representational understanding
tries, misguidedly, to picture the featureless space as existing before the
Creation is assumed to have begun, always to be unchanging, and to have
been made the recipient of more and more matter as the process of the
Creation became more and more complete. Those of us who accept (A3)
tend to make the same misplaced effort. But in the battle between the two
sides of one's intellect deductive understanding must win and the effort
at representational understanding must sometimes be abandoned. It is so
here. To speak of the expansion of space is to speak of a space with physical
properties and to imply the continuous origin of matter. It is for this reason
that the observed red shift provides observational evidence for (A3). (I am
only too well aware, let me add, of the conceptual difficulty in the way
of postulating the simultaneous origin of space and matter as well as their
simultaneous extinction. I am hoping that what is said in Appendix H will
help to overcome this difficulty.)
24.4: The Contraction of Space and the Extinction of Matter
If the origin of an elementary component of the material universe, of
what for short I shall call a particle, is associated with the origin of some
space, the extinction of a particle must be associated with the extinction
of some space. A region where the rate of origins exceeds the rate of extinctions must then be one in which space is expanding; conversely a region
where the rate of extinctions predominates must be one in which space is
contracting; and a region in which the rates are equal, i.e. a region at the
equilibrium density, must be one in which the extent of space remains
constant. This suggests a further means of testing the Hypothesis of the
Symmetrical Impermanence of matter by observation.
The average density of the nebulae, including our own galaxy, is much
above the equilibrium value. Space within the galaxy must therefore be
contracting. Instead of showing a red shift the spectra of the light from
stars within the galaxy must therefore show a violet shift. But the shift
is proportional to the product of the rate of contraction and the distance
of the observed star. This product may not be sufficient to reveal a
measurable shift. The Doppler effect occasioned by the relative movement
of stars within the galaxy is likely to exceed that occasioned by contraction and to make the interpretation of the readings uncertain.
But there are other ways of testing the hypothesis and one of these can
be usefully mentioned here. It would be provided by spectography.
The light from any nebula passes partly through extragalactic space,
but partly also through a portion of our own galaxy. According to Symmetrical Impermanence the space within this must be contracting, it has
just been said, at a rate given by the excess density within the galaxy over
the equilibrium value. The light from a nebula passes, therefore, partly
through expanding and partly through contracting space. The latter part
of the path will be a small fraction of the whole if the nebula is very distant
and a larger fraction if it is close. The red shift that is observed will depend
on the arithmetical mean of the contraction over the short path within
the galaxy and the expansion over the long path outside.
The nearer the nebula is the greater will be the relative effect of the
contracting portion of the path through which the light travels and the
smaller the red shift. For near nebulae one should therefore expect, on
the average, the value of H to come out rather lower than it would for
Observation of the spectra of a large number of nebulae made in the
United States by Humason, Mayall and Sandage, as mentioned in Chapter 4, suggests that it may be so. The red shift has been found to lead to a
slightly lower value of H for near, than for very distant nebulae. The
difference is hardly great enough to be quite conclusive, but it is in the
direction that Symmetrical Impermanence would predict.
That contraction of space within our own galaxy reduces the red shift
is, however, not the only possible explanation of the observed results. The
greater the distance of a nebula the longer its light has taken to reach us.
We are therefore observing today the spectrum of light that left the nebula
a long while ago. The larger value for the red shift in the light from very
distant nebulae might therefore mean that space was expanding more
rapidly when this light began its journey than it is now.
The rate might thus vary either with time or with locality. But there
seems to be no convincing reason why the variation should be with time,
and the continuous extinction of matter provides a reason why it should
be with location.
The solar system is by no means at the centre of our galaxy; it is rather
far out, though not on the very edge either. So the path of light from a
distant nebula always lies partly within the galaxy within a contracting
region. But the length of the contracting portion of the path differs with
the direction in which the nebula is viewed. It is shortest if it is in a direction
at right-angles to our disc-shaped galaxy.
This may provide means of testing the two interpretations. If the variations in the apparent value of H are with time, the red shift will be the
same for all equidistant nebulae, irrespective of the direction in which they
lie. But if the variations are with locality, the red shift for equidistant
nebulae will be less when the nebulae are so situated that their light
: traverses a large part of the galaxy and greater if the light traverses a
small part. It is conceivable that an analysis of the observations already
made would settle the question whether H is constant in space and varies
with time, or is, as I am claiming, not a function of time but varies in
Space as a function of mass density.
Let the conclusions reached in this chapter be summarized in a few
That space expands has been inferred mathematically from first principles and confirmed by observation. Such attempts as have been made to find alternative explanations for the observations have been far-fetched and unconvincing.
The observed recession of distant bodies cannot be interpreted as
the consequence of movement of the bodies relative to existing space or
attributed to forces of repulsion between the bodies. The only interpretation
to fit the facts is that new space is originating continuously between
the bodies while these may remain stationary.
The expansion of space is coupled with the origin of matter and no
satisfactory hypothesis seems possible according to which the extent of
the universe could change while its content remained constant, why, in
other words, space could originate and matter not do so.
If origins of elementary components of the material universe must be
associated with the expansion of space, the converse must also hold.
Extinctions must be associated with the contraction of space. As, according to Symmetrical Impermanence, origins and extinctions proceed side by
side, any observed expansion must be a net one and represent the difference
between the local gross expansion and the local gross contraction. At the
equilibrium density this net difference becomes zero. Where the density is
below the equilibrium value there is a net expansion, and it is shown by
the expansion of the universe as a whole that the average density for the
whole is below the equilibrium value. In any region of high mass density
there must be a pronounced net contraction.
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