Page 75 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 9
contracted.

This idea is attractive because it would mean a nice symmetry between the expanding and contracting phases.
However, one cannot adopt it on its own, independent of other ideas about the universe. The question is: is it
implied by the no boundary condition, or is it inconsistent with that condition? As I said, I thought at first that the
no boundary condition did indeed imply that disorder would decrease in the contracting phase. I was misled
partly by the analogy with the surface of the earth. If one took the beginning of the universe to correspond to
the North Pole, then the end of the universe should be similar to the beginning, just as the South Pole is similar
to the North. However, the North and South Poles correspond to the beginning and end of the universe in
imaginary time. The beginning and end in real time can be very different from each other. I was also misled by
work I had done on a simple model of the universe in which the collapsing phase looked like the time reverse of
the expanding phase. However, a colleague of mine, Don Page, of Penn State University, pointed out that the
no boundary condition did not require the contracting phase necessarily to be the time reverse of the expanding
phase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, the
collapse of the universe was very different from the expansion. I realized that I had made a mistake: the no
boundary condition implied that disorder would in fact continue to increase during the contraction. The
thermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, or
inside black holes.

What should you do when you find you have made a mistake like that? Some people never admit that they are
wrong and continue to find new, and often mutually inconsistent, arguments to support their case – as
Eddington did in opposing black hole theory. Others claim to have never really supported the incorrect view in
the first place or, if they did, it was only to show that it was inconsistent. It seems to me much better and less
confusing if you admit in print that you were wrong. A good example of this was Einstein, who called the
cosmological constant, which he introduced when he was trying to make a static model of the universe, the
biggest mistake of his life.

To return to the arrow of time, there remains the question: why do we observe that the thermodynamic and
cosmological arrows point in the same direction? Or in other words, why does disorder increase in the same
direction of time as that in which the universe expands? If one believes that the universe will expand and then
contract again, as the no boundary proposal seems to imply, this becomes a question of why we should be in
the expanding phase rather than the contracting phase.

One can answer this on the basis of the weak anthropic principle. Conditions in the contracting phase would not
be suitable for the existence of intelligent beings who could ask the question: why is disorder increasing in the
same direction of time as that in which the universe is expanding? The inflation in the early stages of the
universe, which the no boundary proposal predicts, means that the universe must be expanding at very close to
the critical rate at which it would just avoid recollapse, and so will not recollapse for a very long time. By then all
the stars will have burned out and the protons and neutrons in them will probably have decayed into light
particles and radiation. The universe would be in a state of almost complete disorder. There would be no strong
thermodynamic arrow of time. Disorder couldn’t increase much because the universe would be in a state of
almost complete disorder already. However, a strong thermodynamic arrow is necessary for intelligent life to
operate. In order to survive, human beings have to consume food, which is an ordered form of energy, and
convert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contracting
phase of the universe. This is the explanation of why we observe that the thermodynamic and cosmological
arrows of time point in the same direction. It is not that the expansion of the universe causes disorder to
increase. Rather, it is that the no boundary condition causes disorder to increase and the conditions to be
suitable for intelligent life only in the expanding phase.

To summarize, the laws of science do not distinguish between the forward and backward directions of time.
However, there are at least three arrows of time that do distinguish the past from the future. They are the
thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction
of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in
which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the
same as the thermodynamic arrow, so that the two would always point in the same direction. The no boundary
proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the
universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to

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