The Beginning of Time
In this lecture, I would like to discuss whether time itself has a beginning, and whether it will
have an end. All the evidence seems to indicate, that the universe has not existed forever, but
that it had a beginning, about 15 billion years ago. This is probably the most remarkable
discovery of modern cosmology. Yet it is now taken for granted. We are not yet certain
whether the universe will have an end. When I gave a lecture in Japan, I was asked not to
mention the possible re-collapse of the universe, because it might affect the stock market.
However, I can re-assure anyone who is nervous about their investments that it is a bit early
to sell: even if the universe does come to an end, it won't be for at least twenty billion years.
By that time, maybe the GATT trade agreement will have come into effect.
The time scale of the universe is very long compared to that for human life. It was therefore
not surprising that until recently, the universe was thought to be essentially static, and
unchanging in time. On the other hand, it must have been obvious, that society is evolving in
culture and technology. This indicates that the present phase of human history can not have
been going for more than a few thousand years. Otherwise, we would be more advanced than
we are. It was therefore natural to believe that the human race, and maybe the whole
universe, had a beginning in the fairly recent past. However, many people were unhappy with
the idea that the universe had a beginning, because it seemed to imply the existence of a
supernatural being who created the universe. They preferred to believe that the universe, and
the human race, had existed forever. Their explanation for human progress was that there had
been periodic floods, or other natural disasters, which repeatedly set back the human race to a
This argument about whether or not the universe had a beginning, persisted into the 19th and
20th centuries. It was conducted mainly on the basis of theology and philosophy, with little
consideration of observational evidence. This may have been reasonable, given the notoriously
unreliable character of cosmological observations, until fairly recently. The cosmologist, Sir
Arthur Eddington, once said, 'Don't worry if your theory doesn't agree with the observations,
because they are probably wrong.' But if your theory disagrees with the Second Law of
Thermodynamics, it is in bad trouble. In fact, the theory that the universe has existed forever
is in serious difficulty with the Second Law of Thermodynamics. The Second Law, states that
disorder always increases with time. Like the argument about human progress, it indicates that
there must have been a beginning. Otherwise, the universe would be in a state of complete
disorder by now, and everything would be at the same temperature. In an infinite and
everlasting universe, every line of sight would end on the surface of a star. This would mean
that the night sky would have been as bright as the surface of the Sun. The only way of
avoiding this problem would be if, for some reason, the stars did not shine before a certain
In a universe that was essentially static, there would not have been any dynamical reason,
why the stars should have suddenly turned on, at some time. Any such "lighting up time" would
have to be imposed by an intervention from outside the universe. The situation was different,
however, when it was realised that the universe is not static, but expanding. Galaxies are
moving steadily apart from each other. This means that they were closer together in the past.
One can plot the separation of two galaxies, as a function of time. If there were no
acceleration due to gravity, the graph would be a straight line. It would go down to zero
separation, about twenty billion years ago. One would expect gravity, to cause the galaxies to
accelerate towards each other. This will mean that the graph of the separation of two galaxies
will bend downwards, below the straight line. So the time of zero separation, would have been
less than twenty billion years ago.
At this time, the Big Bang, all the matter in the universe, would have been on top of itself. The
density would have been infinite. It would have been what is called, a singularity. At a
singularity, all the laws of physics would have broken down. This means that the state of the
universe, after the Big Bang, will not depend on anything that may have happened before,
because the deterministic laws that govern the universe will break down in the Big Bang. The
universe will evolve from the Big Bang, completely independently of what it was like before.
Even the amount of matter in the universe, can be different to what it was before the Big Bang,
as the Law of Conservation of Matter, will break down at the Big Bang.
I think we should interpret these loop divergences,
not as a break down of the supergravity theories,
but as a break down of naive perturbation theory.
In gauge theories, we know that perturbation theory breaks down at strong coupling.
In quantum gravity, the role of the gauge coupling,
is played by the energy of a particle.
In a quantum loop one integrates over… So one would expect perturbation theory, to break down.