It should be stated that for most of physics, there is no real preference for the arrow of time. Most of the processes which are described in physics are symmetrical over time, including all of quantum physics and relativity. The uncertainty principle, and relativistic length contraction/clock slowing work exactly the same in a time-reversed world as compared to our own. This is due to the fact that most basic physical processes as described in those theories are reversible. Richard P. Feynman was once asked during one of his lectures on QED about time-reversed particles. He noted that if you have a film of a person who is merely flipping dominos on a table, the process looks the same whether the tape is going in forward or reverse.

In all of the sub-atomic world, there is only one (current) example about the preference for the forward arrow of time: neutral Kaon particles decay into their constituents about one trillion times more rapidly than Kaon particles can be created from their constituents. Needless to say, (due to the rarity of Kaon particles in the everyday world) this one example does very little to help explain why time seems to go in a forward direction.

Enter thermodynamics and statistical mechanics. In short, it was derived that in a large system of many small reversible processes the entire system has the highest probability of evolving into the state with the highest entropy. This behaviour is labeled the second law of thermodynamics. According to statistical mechanics, there are no real irreversible processes, just unlikely ones. So, it's possible to have a broken egg reform itself, it just has a infinitesimally small probability of occuring. Comparing the probabilities of egg breakage to egg formation it would seem that there is a preference to the forward passage of time (the direction of greater entropy).

Interestingly, in a time reversed world, a person would not remember the future and gain memories of the past as he/she went back in time. Memory formation is linked to the second law of thermodynamics, the process of making memories increases the entropy of the universe. If we lived in a time reversed world, people would lose memories instead of gaining them.