4.1: The Alternatives
To obtain a complete hypothesis about the duration of the contents of
the material universe one must combine one of the three hypotheses in the
(A) list at the beginning of Chapter 3 with one of the three in the (B) list.
The (A) list, it will be remembered, is concerned with the past and the (B)
list with the future duration of matter. Of the nine possible combinations
eight have to be eliminated.
The elimination cannot be based on scientific proof, for it does not
appear that any one of the nine combinations can be proved false. But if
one abandons the criterion of proof and adopts instead the criteria of
minimum assumption, maximum explanatory and unifying power and
satisfactory evidence, most of the combinations can be eliminated without
much difficulty. It has already been shown that (Al) and (A2) fail badly by
these criteria and I shall have several further occasions to confirm their
inadequacy. So there remains only (A3) in the (A) list.
Of those in the (B) list it will be convenient to consider (B2) first, for
this is the one that it is easiest to eliminate. (B2) is the hypothesis that the
whole contents of the material universe will have ceased to exist after a
definable time in the future. Apart from having the doubtful virtue of giving
a very literal interpretation to the theological doctrine of the End of the
World it has nothing to recommend it.
Consider its implications. Unless the further strange hypothesis is
added that a process can be completed in zero time, supporters of (B2)
must assume that a moment will arrive during the future year T1 A.D.,
when the extinction of the contents of the material universe will begin
and they must assume a later moment during the year T2, when the process
of extinction will be complete. Perhaps the hypothesis that a process can
be completed in zero time would find supporters among laymen. But
physicists do not know of any observation, experiment or line of reasoning
by which to justify such an hypothesis.
If we believe that extinction is prevented in our time by certain specific
physical laws, we could support (B2) only by assuming that these laws
will be suspended for a period dating from the first of the two significant
moments in the year T1 and lasting until the second significant moment in
the year T2. We should, however, have to assume that the suspension will
be one-sided, permitting the extinction of mass and energy but prohibiting
the origin of anything new. It would be interesting to work out the implications of this hypothesis in detail. A physics from which one basic law was
removed would differ in many other respects from that with which we are
From the moment when this new physics applies and matter begins to
behave in new strange ways it would have to be assumed that the contents
of the material universe will be dwindling until finally just one elementary
component will be left. Then this, too, will disappear to mark the great
transition from something to nothing.
This hypothesis can no more be disproved than its counterpart (A2),
which assumes the same process in reverse for the past. But both are equally
foreign to the physicist's habits of thought. The picture that they present
looks more absurd the more closely it is examined; and this is just as true
when the picture is relegated to a remote past as when it is relegated to a
remote future. It is therefore not at all surprising that (B2) has no serious
supporters among scientists, but it is surprising that (A2) has. Why, one is
led to ask, should anyone who cannot believe that the laws of physics will
ever be changed in the future believe that they may have been changed
once upon a time in the past? Why should the notion of two specific,
unrepeated and unrepeatable moments in the years T1 and T2 A.D. be rejected
while the same notion is not even critically discussed when it is applied to
the years T1 and T2 B.C.? Why should anyone who finds the notion of a
future transition from something to nothing unacceptable be able to
accept the notion of a past transition from nothing to something ? I do not
know the answers to these questions, but the fact remains that attempts
to justify (A2) by extrapolation from present observations have, at the time
of writing, become fashionable and are being seriously discussed among
scientists, while an attempt to justify (B2) by similar methods has not yet
been made and would probably be deprecated.
Whatever it may be that causes (A2) to appear attractive need not, however, concern us here. (Al), (A2) and (B2) must all be dismissed by those
who become aware of the tangle of additional hypotheses that are needed
to preserve them. There remain thus for serious consideration only two of
the nine possibilities: the combinations of (A3) with (Bl) and of (A3) with
(B3). The former assumes that every elementary component of the
material universe may have come into existence at any time and that a
conservation law prohibits it from ever ceasing to exist. It attributes to
each component a finite past and an infinite future, i.e. it assumes that one
cannot trace the existence of any given component indefinitely back into the past, but that one can predict an indefinitely long future for it. (A3)
coupled with (Bl) assumes a combination of past impermanence with
future permanence. It can be called the Hypothesis of the Asymmetrical
Impermanence of Matter. The combination of (A3) with (B3) can then be
called the Hypothesis of the Symmetrical Impermanence of Matter; it
assumes impermanence both for the future and for the past.
(Bl) postulates a specific law, which requires that every elementary
component of the material universe shall last for all time. (B3) does not
postulate this nor any equivalent law. It says that any component may become extinct at any moment of time, which is what would happen in the
absence of a law. So (B3) seems to meet the criterion of minimum assumption better than (Bl). But I do not want to exaggerate the importance of
this. I have already said that 'all time' may perhaps be less of an assumption than 'any time'. However, it will emerge from these pages that (B3) also
meets the criterion of explanatory power much better. But this does not
mean that (Bl) can be lightly dismissed. It is arguable that the Principle
of Minimum Assumption may not always apply. (Bl) does have a little
explanatory power. It is, moreover, sanctified by long tradition and has
the backing of considerable authority.
This backing prevents its hypothetical nature from being easily
recognized. We tend, understandably, to believe what we have been taught
and to take for granted that it must have been subjected to the rigid canons
of scientific proof. We are often told that good scientists, following Newton's precept, never adopt hypotheses and so we do not doubt that what
has the backing of their authority must be irrefutable fact. It is a part of
human nature to accept what is easy to believe and to reject what is unfamiliar. For all of these reasons many people are likely to deny hotly
that the permanence of matter and energy (or at least their future permanence) is an hypothesis. They will contend that (Bl) is fact and only (B3)
I think that this view may well have been taken by the more recent
supporters of (A3); for they have all adopted the Hypothesis of the
Asymmetrical Impermanence of Matter1 Otherwise their reason
for supporting (Bl) is not easy to understand. They can hardly have thought
that it was the more attractive alternative. By the unreliable criterion of
attractiveness one should expect symmetrical impermanence to be the
favoured hypothesis. A more probable reason is that (Bl) is so firmly
established and generally accepted that (B3) did not even enter their
thoughts. This surmise is confirmed by the fact that the supporters of asymmetrical impermanence have never undertaken a critical comparison of
the alternatives, as they would surely have done if they had noticed that
there were alternatives.
He who has a new point of view to present cannot afford to ignore
contemporary opinion and so I have to attach much importance to the
relative strengths with which each of the hypotheses in the (A) and (B)
lists is held today. From reading and conversation I have gained the
impression that support for (Al) would be very weak. Many will say that,
in attempting to refute it, I am only flogging a dead horse. But support
for its counterpart (Bl) is likely to be so strong that my attempt to refute it
is likely to evoke a different metaphor: that of tilting at windmills.
Nevertheless, it was a combination of (A3) with (B3) that I advocated
when I first published the hypothesis of continuous origin in 1940 and I
propose to show here that it alone is consistent with a cosmological model
that accords with the observed universe.
Before I leave this theme I should like to emphasize that the words
'origin' and 'extinction' are to be understood literally and not as synonyms
for 'conversion from one form into another'. It would deny my intention
to assume, for instance, that, when matter becomes extinct, something
else, such as energy, must necessarily take its place.
4.2: The Relative Rates of Origins and Extinctions
Let us imagine that a region of space can be so isolated that no matter
or energy passes its boundary. According to the Hypothesis of Asymmetrical Impermanence the content of this region must continuously
increase; for new matter will originate in the region while none will leave
it. According to the Hypothesis of Symmetrical Impermanence, on the
other hand, some matter will be originating in the region and some
becoming extinct, and so the content will not necessarily increase. It will
do so if the rate of origins exceeds the rate of extinctions; but the content
will decrease if the rate of extinctions exceeds that of origins.
If the region is small and the density low, origins and extinctions will
be only occasional and as they are both assumed to be random, they will
occur at irregular intervals. The content may decrease at one moment and
increase at the next. But the larger the region the more such irregularities
will be smoothed out; and if a region be chosen large enough to be a fair
sample of the whole material universe the rate of origin per unit volume
will be the same as for the whole and so will the rate of extinctions.
McCrea has calculated the rate at which the content in mass of the
universe is increasing and finds it to be about 500 atoms of hydrogen per
cubic kilometre per year. According to asymmetrical impermanence this
is the gross rate of origins. According to symmetrical impermanence it is
the net rate given by the excess of origins over extinctions; the gross rate is
greater, and may be much greater.
It is, of course, quite impossible to observe directly the annual arrival
of 500 atoms of hydrogen in a cubic kilometre of space. The mass of
those atoms is very minute and could not be measured even if they could
be assembled at one time and place. But there is an indirect method for
estimating the rate. This is derived from the fact that, as relativity theory
shows, matter and space are inseparable. According to relativity theory,1
space is not regarded as a container but as a constituent of the material
universe. To speak of the origin of matter is the same as to speak of the
origin of space, and if the content of the material universe is increasing its
extent must be doing so too!2 The origin of new matter must therefore
be associated with the expansion of space and the rate at which the
extent of the material universe is increasing becomes a measure of the rate
of increase of its content. This is fortunate. For the rate of increase of
extent is easier to measure than that of content. It is done with the help of
telescopes, and these reveal regions of space large enough to show an
easily measured effect.
As is well known, this effect is manifest as a shift towards the red of the
spectrum lines of very remote objects, called the Doppler effect. A simple
calculation shows that the amount of red shift is proportional to the
velocity with which a remote object is receding. Observation shows that
the amount of the red shift is proportional to the distance of the object.
From these two facts it follows that the velocity with which every object is
receding is proportional to its distance from us. This is what one would
find in a universe that was expanding uniformly and so the expansion of
space is inferred from observation and known facts and without the use
of additional hypotheses. The rate of expansion is expressed by the simple
formula v=Hx, where v is the velocity of recession, x the distance of the
observed star and H a constant known as Hubble's Constant. It represents
the increase of velocity of recession with distance, dv/dx, observed for
every object in a uniformly expanding universe and is given as 145 km/sec
per megaparsec by Opik.3 A more recent estimate is given by Humason,
Mayall and Sandage.4 This is based on the measurement of red shifts.
for nearly 1000 extragalactic nebulae and is 180 km/sec per megaparsec.
These most careful measurements show that the rate of expansion is
nearly, if not quite, constant for all regions of space-time. But they do
seem to show some small lack of uniformity. There may have been a
change during the long period of time that the light from the most distant
nebulae takes to complete the journey that ends in the observers' telescopes. However, it will be shown later that there are good reasons for the
view that the change is not between different periods of time but between
different regions of space, and that it results from unevenness in the
distribution of ponderable matter.
The constancy of the expansion rate, and with it the rate of increase
of the content of the material universe, reminds us of the constant half-lives of
radioactive isotopes. The reason why the disintegration of an atom
of radium is regarded by physicists as an uncaused event is just this constancy, as will be explained in the next chapter. If the half-life of radium
varied, one would look for a circumstance with which the disintegration
was associated and expect to find a causal relation between such circumstances and the disintegration. But the fact that the rate never changes is
taken as negative evidence that the disintegration is uncaused.
The same reasoning applies to the increase in the content of the
material universe. If one regards the unvarying value of Hubble's Constant
as evidence of a constant net increase in the quantity of matter in the
universe, one will also regard it as observational support for the conclusion that origins are random, without cause, and not associated with
anything in the existing state of affairs. If one accepts (B3), one will then
have to take the same view about extinctions. But this aspect of Symmetrical Impermanence will be discussed more fully in the next chapter.
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1See footnotes 4,5, 6 to Chapter 3
2I doubt whether this is implicit in relativity theory, but it has been assumed by
others besides myself. Its justification will be found in Appendix H.
3The British Journal for the Philosophy of Science, November, 1954, Vol. 5, No. 19, 210.
4Astronomical Journal, Vol. 61, April, 1956, pp. 97-162.