Page 28 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 3
the stars that we can see in our galaxy and other galaxies, the total is less than one hundredth of the amount
required to halt the expansion of the universe, even for the lowest estimate of the rate of expansion. Our galaxy
and other galaxies, however, must contain a large amount of “dark matter” that we cannot see directly, but
which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the
galaxies. Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more
dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies. When we add
up all this dark matter, we still get only about one tenth of the amount required to halt the expansion. However,
we cannot exclude the possibility that there might be some other form of matter, distributed almost uniformly
throughout the universe, that we have not yet detected and that might still raise the average density of the
universe up to the critical value needed to halt the expansion. The present evidence therefore suggests that the
universe will probably expand forever, but all we can really be sure of is that even if the universe is going to
recollapse, it won’t do so for at least another ten thousand million years, since it has already been expanding
for at least that long. This should not unduly worry us: by that time, unless we have colonized beyond the Solar
System, mankind will long since have died out, extinguished along with our sun!
All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand
million years ago) the distance between neighboring galaxies must have been zero. At that time, which we call
the big bang, the density of the universe and the curvature of space-time would have been infinite. Because
mathematics cannot really handle infinite numbers, this means that the general theory of relativity (on which
Friedmann’s solutions are based) predicts that there is a point in the universe where the theory itself breaks
down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science
are formulated on the assumption that space-time is smooth and nearly fiat, so they break down at the big bang
singularity, where the curvature of space-time is infinite. This means that even if there were events before the
big bang, one could not use them to determine what would happen afterward, because predictability would
break down at the big bang.

Correspondingly, if, as is the case, we know only what has happened since the big bang, we could not
determine what happened beforehand. As far as we are concerned, events before the big bang can have no
consequences, so they should not form part of a scientific model of the universe. We should therefore cut them
out of the model and say that time had a beginning at the big bang.

Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention.
(The Catholic Church, on the other hand, seized on the big bang model and in 1951officially pronounced it to
be in accordance with the Bible.) There were therefore a number of attempts to avoid the conclusion that there
had been a big bang. The proposal that gained widest support was called the steady state theory. It was
suggested in 1948 by two refugees from Nazi-occupied Austria, Hermann Bondi and Thomas Gold, together
with a Briton, Fred Hoyle, who had worked with them on the development of radar during the war. The idea was
that as the galaxies moved away from each other, new galaxies were continually forming in the gaps in
between, from new matter that was being continually created. The universe would therefore look roughly the
same at all times as well as at all points of space. The steady state theory required a modification of general
relativity to allow for the continual creation of matter, but the rate that was involved was so low (about one
particle per cubic kilometer per year) that it was not in conflict with experiment. The theory was a good scientific
theory, in the sense described in Chapter 1: it was simple and it made definite predictions that could be tested
by observation. One of these predictions was that the number of galaxies or similar objects in any given volume
of space should be the same wherever and whenever we look in the universe. In the late 1950s and early
1960s a survey of sources of radio waves from outer space was carried out at Cambridge by a group of
astronomers led by Martin Ryle (who had also worked with Bondi, Gold, and Hoyle on radar during the war).
The Cambridge group showed that most of these radio sources must lie outside our galaxy (indeed many of
them could be identified with other galaxies) and also that there were many more weak sources than strong
ones. They interpreted the weak sources as being the more distant ones, and the stronger ones as being
nearer. Then there appeared to be less common sources per unit volume of space for the nearby sources than
for the distant ones. This could mean that we are at the center of a great region in the universe in which the
sources are fewer than elsewhere. Alternatively, it could mean that the sources were more numerous in the
past, at the time that the radio waves left on their journey to us, than they are now. Either explanation
contradicted the predictions of the steady state theory. Moreover, the discovery of the microwave radiation by
Penzias and Wilson in 1965 also indicated that the universe must have been much denser in the past. The
steady state theory therefore had to be abandoned.

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