Yes, reversible laws of physics are possible. State1 can cause state2, and state2 can cause state1.
Here is the question: Do you pick a state for state1 and then figure out what state2 should be from it (that is, cause state2)? Or do you pick a state for state2 and figure out what state1 should be (causing state1)?
If you have a "starting state", it doesn't matter if the time is reversible. All states will be caused by the starting state propagating forward in one direction. This is exactly what we seem to observe in the real universe. The big bang starts the universe and everything appears to be a chain of cause and effect from it. We never observe events that are caused by things in the future. Glasses do not spontaneously assemble themselves out of shards and fly on top of tables. Photons do not just spontaneously fly from all directions in space to form sensible images on Earth.
Now you might say "what if the universe somehow decided on all the states at once". Well that isn't what appears to be true in our universe for one (or you'd have things spontaneously happening in the future and then rippling effects back in time, rather than the other way around.) Second it might not even be possible. In order to do that you'd have to try every possible combination of states and see which ones are valid. Does writing down every possible combination of bits create universes? Even if you apply some rule to them to check if they are "valid" universes?
I think that "real" universes like ours have to have a chain of causation like that.
Here is the question: Do you pick a state for state1 and then figure out what state2 should be from it (that is, cause state2)? Or do you pick a state for state2 and figure out what state1 should be (causing state1)?
If you have a "starting state", it doesn't matter if the time is reversible. All states will be caused by the starting state propagating forward in one direction. This is exactly what we seem to observe in the real universe. The big bang starts the universe and everything appears to be a chain of cause and effect from it. We never observe events that are caused by things in the future. Glasses do not spontaneously assemble themselves out of shards and fly on top of tables. Photons do not just spontaneously fly from all directions in space to form sensible images on Earth.
Now you might say "what if the universe somehow decided on all the states at once". Well that isn't what appears to be true in our universe for one (or you'd have things spontaneously happening in the future and then rippling effects back in time, rather than the other way around.) Second it might not even be possible. In order to do that you'd have to try every possible combination of states and see which ones are valid. Does writing down every possible combination of bits create universes? Even if you apply some rule to them to check if they are "valid" universes?
I think that "real" universes like ours have to have a chain of causation like that.
Here is a better description of this line of thought than mine: http://lesswrong.com/lw/fok/causal_universes/