Page 73 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 9
and that these two arrows necessarily always point in the same direction. If one assumes the no boundary
condition for the universe, we shall see that there must be well-defined thermodynamic and cosmological
arrows of time, but they will not point in the same direction for the whole history of the universe. However, I
shall argue that it is only when they do point in the same direction that conditions are suitable for the
development of intelligent beings who can ask the question: why does disorder increase in the same direction
of time as that in which the universe expands?

I shall discuss first the thermodynamic arrow of time. The second law of thermodynamics results from the fact
that there are always many more disordered states than there are ordered ones. For example, consider the
pieces of a jigsaw in a box. There is one, and. only one, arrangement in which the pieces make a complete
picture. On the other hand, there are a very large number of arrangements in which the pieces are disordered
and don’t make a picture.

Suppose a system starts out in one of the small number of ordered states. As time goes by, the system will
evolve according to the laws of science and its state will change. At a later time, it is more probable that the
system will be in a disordered state than in an ordered one because there are more disordered states. Thus
disorder will tend to increase with time if the system obeys an initial condition of high order.

Suppose the pieces of the jigsaw start off in a box in the ordered arrangement in which they form a picture. If
you shake the box, the pieces will take up another arrangement. This will probably be a disordered
arrangement in which the pieces don’t form a proper picture, simply because there are so many more
disordered arrangements. Some groups of pieces may still form parts of the picture, but the more you shake
the box, the more likely it is that these groups will get broken up and the pieces will be in a completely jumbled
state in which they don’t form any sort of picture. So the disorder of the pieces will probably increase with time if
the pieces obey the initial condition that they start off in a condition of high order.

Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’t
matter what state it started in. At early times the universe would probably be in a disordered state. This would
mean that disorder would decrease with time. You would see broken cups gathering themselves together and
jumping back onto the table. However, any human beings who were observing the cups would be living in a
universe in which disorder decreased with time. I shall argue that such beings would have a psychological
arrow of time that was backward. That is, they would remember events in the future, and not remember events
in their past. When the cup was broken, they would remember it being on the table, but when it was on the
table, they would not remember it being on the floor.

It is rather difficult to talk about human memory because we don’t know how the brain works in detail. We do,
however, know all about how computer memories work. I shall therefore discuss the psychological arrow of
time for computers. I think it is reasonable to assume that the arrow for computers is the same as that for
humans. If it were not, one could make a killing on the stock exchange by having a computer that would
remember tomorrow’s prices! A computer memory is basically a device containing elements that can exist in
either of two states. A simple example is an abacus. In its simplest form, this consists of a number of wires; on
each wire there are a number of beads that can be put in one of two positions. Before an item is recorded in a
computer’s memory, the memory is in a disordered state, with equal probabilities for the two possible states.
(The abacus beads are scattered randomly on the wires of the abacus.) After the memory interacts with the
system to be remembered, it will definitely be in one state or the other, according to the state of the system.
(Each abacus bead will be at either the left or the right of the abacus wire.) So the memory has passed from a
disordered state to an ordered one. However, in order to make sure that the memory is in the right state, it is
necessary to use a certain amount of energy (to move the bead or to power the computer, for example). This
energy is dissipated as heat, and increases the amount of disorder in the universe. One can show that this
increase in disorder is always greater than the increase in the order of the memory itself. Thus the heat
expelled by the computer’s cooling fan means that when a computer records an item in memory, the total
amount of disorder in the universe still goes up. The direction of time in which a computer remembers the past
is the same as that in which disorder increases.

Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within our
brain by the thermodynamic arrow of time. Just like a computer, we must remember things in the order in which
entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time

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