Page 74 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 9
because we measure time in the direction in which disorder increases You can’t have a safer bet than that!

But why should the thermodynamic arrow of time exist at all? Or, in other words, why should the universe be in
a state of high order at one end of time, the end that we call the past? Why is it not in a state of complete
disorder at all times? After all, this might seem more probable. And why is the direction of time in which
disorder increases the same as that in which the universe expands?

In the classical theory of general relativity one cannot predict how the universe would have begun because all
the known laws of science would have broken down at the big bang singularity. The universe could have
started out in a very smooth and ordered state. This would have led to well-defined thermodynamic and
cosmological arrows of time, as we observe. But it could equally well have started out in a very lumpy and
disordered state. In that case, the universe would already be in a state of complete disorder, so disorder could
not increase with time. It would either stay constant, in which case there would be no well-defined
thermodynamic arrow of time, or it would decrease, in which case the thermodynamic arrow of time would point
in the opposite direction to the cosmological arrow. Neither of these possibilities agrees with what we observe.
However, as we have seen, classical general relativity predicts its own downfall. When the curvature of
space-time becomes large, quantum gravitational effects will become important and the classical theory will
cease to be a good description of the universe. One has to use a quantum theory of gravity to understand how
the universe began.

In a quantum theory of gravity, as we saw in the last chapter, in order to specify the state of the universe one
would still have to say how the possible histories of the universe would behave at the boundary of space-time in
the past. One could avoid this difficulty of having to describe what we do not and cannot know only if the
histories satisfy the no boundary condition: they are finite in extent but have no boundaries, edges, or
singularities. In that case, the beginning of time would be a regular, smooth point of space-time and the
universe would have begun its expansion in a very smooth and ordered state. It could not have been
completely uniform, because that would violate the uncertainty principle of quantum theory. There had to be
small fluctuations in the density and velocities of particles. The no boundary condition, however, implied that
these fluctuations were as small as they could be, consistent with the uncertainty principle.

The universe would have started off with a period of exponential or “inflationary” expansion in which it would
have increased its size by a very large factor. During this expansion, the density fluctuations would have
remained small at first, but later would have started to grow. Regions in which the density was slightly higher
than average would have had their expansion slowed down by the gravitational attraction of the extra mass.
Eventually, such regions would stop expanding and collapse to form galaxies, stars, and beings like us. The
universe would have started in a smooth and ordered state, and would become lumpy and disordered as time
went on. This would explain the existence of the thermodynamic arrow of time.

But what would happen if and when the universe stopped expanding and began to contract? Would the
thermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts of
science-fiction-like possibilities for people who survived from the expanding to the contracting phase. Would
they see broken cups gathering themselves together off the floor and jumping back onto the table? Would they
be able to remember tomorrow’s prices and make a fortune on the stock market? It might seem a bit academic
to worry about what will happen when the universe collapses again, as it will not start to contract for at least
another ten thousand million years. But there is a quicker way to find out what will happen: jump into a black
hole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole
universe. So if disorder were to decrease in the contracting phase of the universe, one might also expect it to
decrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make money
at roulette by remembering where the ball went before he placed his bet. (Unfortunately, however, he would not
have long to play before he was turned to spaghetti. Nor would he be able to let us know about the reversal of
the thermodynamic arrow, or even bank his winnings, because he would be trapped behind the event horizon
of the black hole.)

At first, I believed that disorder would decrease when the universe recollapsed. This was because I thought that
the universe had to return to a smooth and ordered state when it became small again. This would mean that
the contracting phase would be like the time reverse of the expanding phase. People in the contracting phase
would live their lives backward: they would die before they were born and get younger as the universe

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