A Briefer History of Time – Stephen Hawking
In previous chapters we have seen how our views of the nature of time have changed over the years. Up to the beginning of this century people believed in an absolute time. That is, each event could be labeled by a number called “time” in a unique way, and all good clocks would agree on the time interval between two events. However, the discovery that the speed of light appeared the same to every observer, no matter how he was moving, led to the theory of relativity—and in that one had to abandon the idea that there was a unique absolute time. Instead, each observer would have his own measure of time as recorded by a clock that he carried: clocks carried by different observers would not necessarily agree. Thus time became a more personal concept, relative to the observer who measured it.
When one tried to unify gravity with quantum mechanics, one had to introduce the idea of “imaginary” time. Imaginary time is indistinguishable from directions in space. If one can go north, one can turn around and head south; equally, if one can go forward in imaginary time, one ought to be able to turn round and go backward. This means that there can be no important difference between the forward and backward directions of imaginary time. On the other hand, when one looks at “real” time, there’s a very big difference between the forward and backward directions, as we all know. Where does this difference between the past and the future come from? Why do we remember the past but not the future?
The laws of science do not distinguish between the past and the future. More precisely, as explained earlier, the laws of science are unchanged under the combination of operations (or symmetries) known as C, P, and T. (C means changing particles for antiparticles. P means taking the mirror image, so left and right are interchanged. And T means reversing the direction of motion of all particles: in effect, running the motion backward.) The laws of science that govern the behavior of matter under all normal situations are unchanged under the combination of the two operations C and P on their own. In other words, life would be just the same for the inhabitants of another planet who were both mirror images of us and who were made of antimatter, rather than matter.
If the laws of science are unchanged by the combination of operations C and P, and also by the combination C, P, and T, they must also be unchanged under the operation T alone. Yet there is a big difference between the forward and backward directions of real time in ordinary life. Imagine a cup of water falling off a table and breaking into pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or backward. If you run it backward you will see the pieces suddenly gather themselves together off the floor and jump back to form a whole cup on the table. You can tell that the film is being run backward because this kind of behavior is never observed in ordinary life. If it were, crockery manufacturers would go out of business.
The explanation that is usually given as to why we don’t see broken cups gathering themselves together off the floor and jumping back onto the table is that it is forbidden by the second law of thermodynamics.
This says that in any closed system disorder, or entropy, always increases with time. In other words, it is a form of Murphy’s law: things always tend to go wrong! An intact cup on the table is a state of high order, but a broken cup on the floor is a disordered state. One can go readily from the cup on the table in the past to the broken cup on the floor in the future, but not the other way round.
The increase of disorder or entropy with time is one example of what is called an arrow of time, something that distinguishes the past from the future, giving a direction to time. There are at least three different arrows of time. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.
In this chapter I shall argue that the no boundary condition for the universe, together with the weak anthropic principle, can explain why all three arrows point in the same direction—and moreover, why a well- defined arrow of time should exist at all. I shall argue that the psychological arrow is determined by the thermodynamic arrow, 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 because we measure time in the direction in which disorder increases. You can’t have a safer bet than that!