And as we have explained many times, the results of this inference – the retrodictions – always depend on our priors. So the knowledge of the present is enough to calculate the future (classically) or to predict the unique probabilities of various states in the future (quantum mechanically). But it is simply never enough to calculate the unique state or unique probabilities of various states in the past.
The reason has been explained many times. But we can say that at least in the macroscopic context (when some microscopic detailed information is being omitted, e.g. because it’s unmeasurable), different initial states “A,B” in the past may evolve into the same final state “C” in the future.
— Logical arrow of time and terminology
— Lubos Motl
2013.07.20 Saturday ACHK