The relationship between time, relativity and entropy I came across a discussion about the nature of time and whether or not time is an illusion on a physics forum. I'm not so much interested in the philosophical issues regarding time, but the following, which is more related to physics, is something that confuses me:
Is our world a three dimensional world that keeps changing or is it a four dimensional world that remains static?
Relativity seems to say that the world is actually a four dimensional static object, because it is difficult to imagine how the world could be a three dimensional changing world in a spacetime where simultaneity is relative.
On the other hand, statistical mechanics does seem to imply that the world is a three dimensional changing world because entropy increases. The laws of physics are invariant under time reflection, so if the world is a four dimensional static one, why should an arbitrary solution to the laws of physics be the kind of solution were entropy increases in 1 direction of time? I once read somewhere is has something to do with the initial conditions of our universe. This clears things up a little but I'm still confused.
 A: There is an ongoing philosophical argument about this between the presentists (only the present world exists) and the four-dimensionalists (things elsewhere in time exist just as things do elsewhere in space). I personally think relativity theory and especially nontrivial wormhole spacetimes make presentism untenable, but one can make presentist arguments even in time travel situations (see Keller, S., & Nelson, M. (2001). Presentists should believe in time-travel. Australasian Journal of Philosophy, 79(3), 333-345. )
That entropy increases does not necessarily imply presentism. We could imagine a universe that had a preferred direction in space, for example that the CMB was hotter on one side than the other and that travel in that direction would make things warmer. That would not be particularly weird, it is just initial conditions making things anisotropic. Similarly we may argue that it is just initial conditions that give us a time direction where entropy increases that is also roughly orthogonal to spacetime slices where matter is roughly static. A universe where half had high entropy and the other half low entropy from the start would in a sense have a time direction defined by entropy that made an angle to the time direction defined by matter being roughly static. 
But the actual source of time's arrow is still an issue. It is just separate from whether there is just a present. The arrow issue is about the nature of time and entropy, the present issue is about the metaphysics about what stuff actually exists (a full 4-manifold, or an evolving 3-manifold).
