Page 29 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 3
Another attempt to avoid the conclusion that there must have been a big bang, and therefore a beginning of
time, was made by two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, in 1963. They suggested that
the big bang might be a peculiarity of Friedmann’s models alone, which after all were only approximations to
the real universe. Perhaps, of all the models that were roughly like the real universe, only Friedmann’s would
contain a big bang singularity. In Friedmann’s models, the galaxies are all moving directly away from each
other – so it is not surprising that at some time in the past they were all at the same place. In the real universe,
however, the galaxies are not just moving directly away from each other – they also have small sideways
velocities. So in reality they need never have been all at exactly the same place, only very close together.
Perhaps then the current expanding universe resulted not from a big bang singularity, but from an earlier
contracting phase; as the universe had collapsed the particles in it might not have all collided, but had flown
past and then away from each other, producing the present expansion of the the universe that were roughly like
Friedmann’s models but took account of the irregularities and random velocities of galaxies in the real universe.
They showed that such models could start with a big bang, even though the galaxies were no longer always
moving directly away from each other, but they claimed that this was still only possible in certain exceptional
models in which the galaxies were all moving in just the right way. They argued that since there seemed to be
infinitely more Friedmann-like models without a big bang singularity than there were with one, we should
conclude that there had not in reality been a big bang. They later realized, however, that there was a much
more general class of Friedmann-like models that did have singularities, and in which the galaxies did not have
to be moving any special way. They therefore withdrew their claim in 1970.

The work of Lifshitz and Khalatnikov was valuable because it showed that the universe could have had a
singularity, a big bang, if the general theory of relativity was correct. However, it did not resolve the crucial
question: Does general relativity predict that our universe should have had a big bang, a beginning of time?
The answer to this carne out of a completely different approach introduced by a British mathematician and
physicist, Roger Penrose, in 1965. Using the way light cones behave in general relativity, together with the fact
that gravity is always attractive, he showed that a star collapsing under its own gravity is trapped in a region
whose surface eventually shrinks to zero size. And, since the surface of the region shrinks to zero, so too must
its volume. All the matter in the star will be compressed into a region of zero volume, so the density of matter
and the curvature of space-time become infinite. In other words, one has a singularity contained within a region
of space-time known as a black hole.

At first sight, Penrose’s result applied only to stars; it didn’t have anything to say about the question of whether
the entire universe had a big bang singularity in its past. However, at the time that Penrose produced his
theorem, I was a research student desperately looking for a problem with which to complete my Ph.D. thesis.
Two years before, I had been diagnosed as suffering from ALS, commonly known as Lou Gehrig’s disease, or
motor neuron disease, and given to understand that I had only one or two more years to live. In these
circumstances there had not seemed much point in working on my Ph.D.– I did not expect to survive that long.
Yet two years had gone by and I was not that much worse. In fact, things were going rather well for me and I
had gotten engaged to a very nice girl, Jane Wilde. But in order to get married, I needed a job, and in order to
get a job, I needed a Ph.D.

In 1965 I read about Penrose’s theorem that any body undergoing gravitational collapse must eventually form a
singularity. I soon realized that if one reversed the direction of time in Penrose’s theorem, so that the collapse
became an expansion, the conditions of his theorem would still hold, provided the universe were roughly like a
Friedmann model on large scales at the present time. Penrose’s theorem had shown that any collapsing star
must end in a singularity; the time-reversed argument showed that any Friedmann-like expanding universe
must have begun with a singularity. For technical reasons, Penrose’s theorem required that the universe be
infinite in space. So I could in fact, use it to prove that there should be a singularity only if the universe was
expanding fast enough to avoid collapsing again (since only those Friedmann models were infinite in space).

During the next few years I developed new mathematical techniques to remove this and other technical
conditions from the theorems that proved that singularities must occur. The final result was a joint paper by
Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided
only that general relativity is correct and the universe contains as much matter as we observe. There was a lot
of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and
partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of
Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work

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