Everybody knows what time is or, better, everybody believes to know what it is. But ask people to define time, and the majority will be unable to do it. Among all the living creatures only men is aware of the importance of the notion of time, the others have no idea of what the future means, and this is also probably true for the past. In the past time was thought to run in cycle. What happens today happened already before, and will happen again. Now, since the invention of the clocks, time is thought to run linearly.
Until the beginning of the 20th century, people thought that time was absolute, that is, it is the same to all observers. The discovery that the speed of light was the same to all observers moving at various speeds led to the theory of relativity, and this destroyed the notion of absolute time. In clear, time is different for different observers.
Time can be seen as a mathematical concept that has some analogies with a line -straight or circular, depending if one sees it as linear, or running in cycle. Since it has only length, it is similar in all its parts, and it can be described as a succession of similar instant, or as the continuous flow of one instant.
To unify gravity with quantum mechanics one has to introduce the concept of "imaginary time", that is the same in all direction of space. In the same way that a person can move in one direction or in the opposite, according to the Unified Theory one can go forward and backward in imaginary time as there is no meaningful difference between both directions in this case. With real time, it is different, of course. Where does this difference between the past and future time comes from? And why can we remember the past, but not the future? The answer to these questions is not yet fully known.
The scientific laws do not make a difference between the past and the future or, better, the laws of science are unchanged under the combination of the symmetries known as C (changing particles into anti-particles), P (taking the mirror image), and T (reversing the direction of motion of all particles) (see § 12- Elementary particles, Facts and Theories on how the matter is made). We have seen that the scientific laws that govern the behaviour of matter are unchanged under the combination of the two operations C and P. That means that life would be the same on a planet if their people were mirror images of us and were made of antimatter.
Moreover, if the scientific laws are unchanged under the combination of symmetries C and P as well as C, P, and T, then they must be unchanged under the symmetry T alone. However, there is a difference between the backward and forward direction of real time in life. For instance, if we film a cup falling from a table onto the floor and breaking into pieces, running it backward would see the pieces coming together again, and the restored cup going up on the table. This does not happen in our in real life experience. It does not happen because this goes again the second law of thermodynamics that says that in a closed system, disorder, or entropy, always increases with time. Disorder increases when a cup falls and breaks into pieces, but decreases when it collects itself together.
The increase of disorder with time is a direction or an "arrow"
of time; it distinguishes the past from the future. We have more that one
such arrow of time:
- The thermodynamics arrow of time indicates the way the entropy, or disorder,
increases.
- The psychological arrow of time is the direction in which we feel the
time passes, remembering the past but not the future.
- The cosmological arrow of time is the direction in which the universe
is expanding.
Let us assume that a system starts in ordered state. It will evolve according to the laws of science, and it is more probable that the system will become dis-ordered rather that stay ordered, as there are more dis-ordered states and the disorder will increase with time. But if the system -let us take the universe as an example- starts in a completely dis-ordered state, disorder cannot increase any more. Disorder could either stay constant, and there would be no thermodynamic arrow of time, or it could decrease and, in this case, the thermodynamic arrow of time points in the other direction of the cosmological arrow. These two cases do not conform to our experience.
If the universe is finite but has no boundary condition, edge or singularity, then the beginning of time would have been a regular, smooth point in space-time, and the universe would have started to expand in a smooth and ordered way. However, it could not have been uniform because this goes against the uncertainty principle of quantum theory. There had to be some small differences in the density and velocities of the particles. The no-boundary condition would impose that these differences be as small as possible but compatible with the uncertainty principle. During the expansion of the universe the differences would increases in time. In the regions of higher density the expansion would have been slowed down by gravity effect of the extra mass. These regions would stop expanding, and eventually collapse to form galaxies, stars and human beings. This universe that started in a well-ordered state, would become dis-ordered, and this is compatible with the thermodynamic arrow of time.
Let us now see what would happen if the universe stopped expanding and,
instead, started contracting. Would the thermodynamic arrow change direction
and the disorder decreases? If this happened people would remember the future
instead of the past. However it has been shown that the collapse of the
universe is different from its expansion. During the collapsing phase the
no-boundary condition would impose the disorder to go on increasing, and
the thermodynamic and the psychological arrows of time would not reverse
while the universe contracts. The same is true within a black hole.