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The following link implies that quantum mechanics only violates the "one future" aspect of information conservation:
https://www.physicsforums.com/threads/is-information-always-conserved-in-quantum-mechanics.458985/
How is it possible that we can know that there can only be one past even though any state of any system isn't known from the previous states?

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  • $\begingroup$ How does many possible branches not mean many possible trunks? $\endgroup$ – march Oct 20 '15 at 23:08
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    $\begingroup$ @march Trees aren't time symmetric. Given a known state for a quantum system, the same laws that you use to predict its future as a superposition of outcomes will lead to you to say the same thing about its past. The OP's question is not stupid. $\endgroup$ – Rococo Oct 20 '15 at 23:23
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    $\begingroup$ @Rococo. No question! I agree. I retract my snark. I'll blame it on the monumental pile of grading I have. $\endgroup$ – march Oct 20 '15 at 23:26
  • $\begingroup$ That can get to anyone's head! $\endgroup$ – Rococo Oct 21 '15 at 3:04
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Hopefully someone can come along and give a better answer, but I will put a brief comment as encouragement:

I agree that, naively, one can look at the laws of quantum physics and conclude that there is not one definite past or history that leads to the current universe, for just the same reasons that the current universe's state does not lead to a definite outcome to future experiments. To be precise, it's a straightforward result of the unitarity of time evolution. It's not obvious to me that this is a problem, particularly if you consider the wavefunction to be real, but it is certainly a feature that people don't usually think about.

This is rather similar, although not quite identical, to the Boltzmann brain issue. You can read a lot of arguments about that if you look around (for example, I recommend Sean Carroll's book From Eternity to Here), but a popular one is that we should assume, by some mechanism we don't understand yet, that the universe started with an extremely low entropy. So we have to put a boundary condition on the universe to make any sense of anything, and although it doesn't seem particularly necessary to me one could presumably stipulate that this boundary not be a macroscopic superposition.

Finally, taking an Everettian many-worlds perspective on this question is interesting. The idea in many-worlds is that the total wavefunction of the universe has a sort of fractal shape, with branches that have the same initial state dividing whenever (in some usually undefined way) two parts of some superposition become entangled enough with other things that they could never interfere again. So from this perspective it is actually quite wrong to run quantum evolution backward from your current state, because the state that includes "you" is only part of the total state of the universe. You should actually gather up all the other branches representing different outcomes and apply time evolution to them at the same time. And if you do this, you would actually see all of these branches interfere with each other in such a way that they nicely reduce instead of proliferating and lead back to the one unique past that they all originated from. So this interpretation does appear to naturally have a unique past, something that I don't think I've ever seen discussed...

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  • $\begingroup$ Why would many worlds require a unique past? Couldn't branches join together, just as easily as split apart? $\endgroup$ – user66309 Dec 22 '15 at 9:34
  • $\begingroup$ @user66309 Maybe I overstated the claim here. One must specify the initial conditions in either interpretation. But there does seem to me that in the MWI the number of branches is always increasing (this is very nearly a restatement of the second law of thermodynamics), and to reverse this correctly one must start with all the distinct branches and run them backwards. This seems to me to be different than a Copenhagen-style interpretation, in which you start with only one branch at the present time and therefore they can only proliferate in each direction. $\endgroup$ – Rococo Aug 16 '16 at 3:49
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Take a look at Newton's third law:

For every action, there is an equal and opposite reaction

Change the wording a bit and we can say:

For every past, there is an equal and opposite future

  • What this implies is that there can only exist one past for any given future.

  • This further implies that although any past can have multiple futures, but since only one of the futures succeed in happening, the number of futures are the same as the number of pasts

  • Even more interesting is the fact that since actions do not simply vanish after happening (gravity for example), then whatever action started all reactions still exists. i.e. whatever past started all future-pasts, is still out there.

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