Page 74 - A Brief History of Time - Stephen Hawking
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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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