While coordinate time is arbitrary, proper time is not. And that is the one more accurately described as 'time' in this context.
Entropy is a strange beast and I'm still not convinced I fully understand it (even after the grad courses in stat mech). In a sense, it represents the information loss when we go from a microscopic description to a macroscopic description.
There is even some ambiguity in the concept of the entropy of a system. For example, if there are two gases that are actually different, but for which *we* cannot, at present, distinguish, the entropy can be calculated either with the knowledge of the difference or without it. The answers are different, say, in the case of a separated volume with one on each side. If the separation is removed, one calculation gives a zero entropy change and the other a positive change based on mixing.
The point is that *both* calculation are correct and can be used *as long as we keep our knowledge level the same*.
This arbitrariness comes, in part, from a difference in macroscopic description of the situation and the amount of information loss in the two scenarios.
So, here's the big question: why should there be one consistent direction of time (one half of the light cone) for which information loss always increases? Why does it not vary from spacetime event to another? There is a HUGE symmetry breaking here and I don't at all understand why it is a global rather than a local breaking.
@exchemist or
@ChristineM and
@sayak83 : any ideas?