Time Reversal Invariance
Time reversal sounds like a science fiction concept. However, time reversal invariance in particle physics is not such an exotic idea. If we look at any particle collision, we can relate it to another particle collision with all momenta reversed in direction and all angular momenta likewise reversed. Since momenta and angular momenta are rates (derivatives with respect to time of some quantity), reversing these quantities is mathematically equivalent to a reversal of the sign of the time variable.
Time reversal invariance is simply the statement that two processes related to one another by a reversal of all momenta and angular momenta have equal rates.
This invariance is exact in strong and electromagnetic processes, but not in weak interactions. It is broken in the same processes that break the combined invariance symmetry CP.
CPT
CPT is the product of the three operations: charge conjugation , parity, and time reversal.
As far as is now known, this appears to be an exact invariance of all processes. This means that any process has a related process with an identical rate, the process to which it is converted by making the three replacements, C, P and T. Experiments have shown that the difference is smaller than 1 part in a million millions (1012)
All particle physics theories are expressed in a mathematical formalism known as relativistic quantum field theory. CPT invariance is an exact property in all such theories. If experiments discover that CPT invariance is not exact, it would require us to develop a new kind of theory.
Microscopic Processes and the "Arrow of Time"
When we watch a movie we can certainly tell if it is running backwards -- improbable events occur such as shards of glass coming together to form a glass bowl.
However, if the movie showed only a single collision of fundamental particles, interacting through the strong or electromagnetic interaction, there would be no way to tell whether it was running backwards or forwards.
Time reversal invariance in the underlying interactions does not lead to time symmetry in the collective behavior of many particles because in collective behavior, the laws of probability come into play as well as the properties of individual collisions. These laws of probability are encoded in physics as the second law of thermodynamics -- this law says entropy increases with time (entropy is a measure of the disorder or randomness of a system).
Clearly such a law has no invariance under a reversal of the time direction. However, the source of this law is simply probability, not microscopic process dynamics. There is no connection between the violation of time reversal invariance in a small fraction of weak processes and the second law of thermodynamics.
As an example of entropy increase, consider a box containing a hundred coins all face up (heads). These are fair coins -- for each coin the probability of a flip from heads to tails is exactly the same as the probability of the time-reversed flip from tails to heads - -the individual processes are symmetric. Now, imagine what happens when the box is shaken up and down. After the box has been shaken for a while the coins will be in a disordered state with roughly equal numbers of heads and tails showing, and no evidence is left of their ordered start. You can shake the box for as long as you like -- it is very improbable that you will ever retrieve the ordered state with all coins face up.
