Does conservation of information mean that the direction of causality is arbitrary? If it is the case that the information content of the universe is conserved, and the past can be constructed from a complete knowledge of the future just as easily as vice versa, then is there any reason to conceptualize the past as causally preceding the future, or do the terms "past" and "future" simply refer to "the direction of time in which entropy decreases" and "the direction in which it increases," respectively? If it's the latter, then does the universe's lower entropy in the past explain why information about the past is macroscopically accessible to us, but information about the future is not?
EDIT: To be more specific, the Second Law of Thermodynamics describes entropy as increasing "over time." By "over time," I assume it means "as we observe the past, followed by the future." My question is this: given conservation of information, is there an equally valid alternative way of describing time in which the Second Law states that entropy decreases over time, but "over time" is considered to mean "as we observe the future, followed by the past"? Is this alternative description, combined with complete knowledge of the final state of the universe, sufficient to reconstruct the entire history of the universe farther and farther into the past in such a way that the future appears to causally determine the past, just as we perceive the past as causally determining the future?
 A: Leaving aside the issue of wavefunction collapse, physics is deterministic. So if you have some system like a gas and you know the exact positions and velocities of all the gas molecules you can predict the evolution of the system forwards and backwards in time. So you can start with a future state and work backwards to desciribe a past state.
However thermodynamics is based on average properties, and it discards the detailed information we need to do this calculation. For example the temperature of a gas is related to the velocity distribution of the gas molecules in a precise way described by the Maxwell-Boltzmann distribution. However this distribution averages out the velocities of the individual particles so that detailed information is lost and cannot be recovered from the shape of the distribution.
As a result it isn't possible to use the second law in reverse to describe the evolution of a system backwards in time. When you evolve a system forwards in time there is more than one past configuration that could result in the same future entropy. So when you evolve backwards there's no way to know which of the possible past configurations to head towards.
Whether this means there is a fundamental asymmetry in time is a matter of opinion. The asymmetry is a result of discard information about the system as we evolve it forwards in time, so my view would be that it is our description of the system that is time asymmetric and not the system itself.
