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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?

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    $\begingroup$ More on Poincare-recurrence. $\endgroup$
    – Qmechanic
    Oct 25, 2022 at 7:02
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    $\begingroup$ Quite the contrary. Information in an expanding universe is lost all the time. OTOH, in a recurrence scenario there simply is no information... the system will eventually cycle through its entire phase space and there is nothing special about one state over another. The only way to "generate" information in that case is if an external observer makes a selection of what is "important" and what is not. $\endgroup$ Oct 25, 2022 at 7:08
  • $\begingroup$ @FlatterMann Thank you for your response. I have edited my question for fear of miscommunication. Can you reread the question? Are you sure that in a recurrence scenario, the universe must eventually cycle back to the exact same state? The answer in the following page seems to be different: "the [PRT] theorem doesn't guarantee a continuous system will come back to exactly the same state, only arbitrarily close to it." (physics.stackexchange.com/questions/730328/…) $\endgroup$ Oct 25, 2022 at 11:45
  • $\begingroup$ Recurrence scenarios are unphysical. They are a mathematical toy concept of the late 19th century that has next to no application in reality. Yes, we can prove that systems of the kinds we are analyzing in physics have to return to their initial state, but in reality that is a completely meaningless statement because it can not be observed. It is, as my first theory professor put it "intellectual nonsense". Very amusing and that is all that it is. So you can relax, there will never be a copy of you. $\endgroup$ Oct 25, 2022 at 18:59
  • $\begingroup$ Hello @stafusa . Do you know the answer to this question? $\endgroup$ Oct 29, 2022 at 13:28

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