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.