A naïve question, I'll admit, about entropy and the various arrows of time.
If we have as input the position or momentum (the wave function, I suppose) of every particle, would it then be possible to precisely simulate the universe in reverse? Or does entropy impose a hard-barrier to modelling the past?
More simply perhaps, is it possible to know the exact past state of a closed system from its current state plus the heat it has emitted?
The question is not naive.
In principle, mechanics is fully deterministic and reversible, which means that the equations of motion can be integrated forward or backward in time.
Thermodynamics says this is not possible. The equilibrium state has no memory of its past, the same equilibrium state can be reached from different states.
Philosophers have been scratching their heads trying to reconcile these opposing views. One possible answer is that the equations of motion are extremely sensitive to the initial conditions and the slightest uncertainty will eventually lead to very different predictions after sufficient time, whether in the forward or reverse direction.
Another view posits that it is simply not possible to have all the information needed to solve the equations of motion with sufficient accuracy for all future and past times. To do that we need the precise state of every particle in the universe, including the universe that is not known to us at present, and an exact physical theory of everything.
If we could perform this calculation I would be much more interested in calculating the future rather than the past. This would give me the opportunity to alter the future by drinking tea instead of coffee tomorrow morning, but how can I alter it if my calculation has already told me which drink I will have?
The conundrum goes away if we accept that our perception of nature is fundamentally stochastic and that the determinism of (classical) mechanics is an idealization that works only so far.
