My understanding is that, if information in the universe cannot be lost, it will always be possible (in principle) to tell which prior state of the universe has led to the current state. Is this true regardless of whether the universe is said to evolve deterministically or indeterministically?
Also, does this imply that, unless the universe had been forever cycling back to this exact current state via the exact same course of evolution, this current state of the universe will be forever lost in the future, regardless of whether the universe is said to evolve deterministically or indeterministically.
If this is indeed a true implication of the law of conservation of information, and if it is indeed the case that the universe was not cycling back to this exact current state, then it would seem to me that it may be possible for this universe to return to a state that is only almost identical to the current state, but one that must nevertheless be distinguishable from the current state however similar the two states are. Is this correct? Also, I wonder whether these states which are not identical with the current state but are almost indistinguishable from it are infinite in number. If so, then perhaps it is physically possible for the universe to forever return to an infinite number of states which are similar to this current state but not identical to it?