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First, I hear that, on a whiteboard, one may casually invert causality and run time in reverse.

Next, I hear that there are interpretations of QM, like Chaitin's Great Programmer interpretation or de Broglie-Bohm pilot-wave theory, in which we can imagine a universe as being totally described by a configuration, or state, of particles and waves, as well as a set of rules describing how to obtain a configuration's successor. For example, our universe might have a ruleset resembling the Standard Model. As I understand it, the biggest trick with these theories is always remembering that there must be parts of the configuration which aren't fully knowable or measurable. Chaitin uses uncomputability and de Broglie-Bohm uses hidden variables.

Putting these two ideas together, it seems that one must be able to run QM backwards, traversing from "future" configurations to "past" configurations, in a deterministic way. Thermodynamics would appear to be flipped, of course, but everything would still be well-defined, right?

So, now let's consider two pairs of virtual particles. I'd normally call them "Alice" and "Bob", but we'll go with $A^+$ and $A^-$ for the first pair, and $B^+$ and $B^-$ for the second pair. We generally would expect that $A^+$ and $A^-$ will annihilate each other shortly, and similarly for $B^+$ and $B^-$. However, what if we placed our pairs next to each other, and they were pairs of the same sort of particle? Then, it would be legal for $A^+$ to combine with $B^-$ and $B^+$ with $A^-$, right? This suggests to me that there's a way to custom-build situations where two configurations lead to the "same" future, in that the observables of the futures are indistinguishable, but the hidden variables (pilot-wave) or uncomputable real (GP) differ, so that they will diverge again.

We could then imagine that there are actually many configurations for which the hidden parts differ, but the observable parts are the same, based on this idea of overlapping possibilities. And, in particular, we could imagine that perhaps there are situations where the observable parts of two configurations are the same during some span of time. Indeed, perhaps two configurations might have multiple spans of time in which they are observably the same, with intermittent periods of being different.

This reminds me all of Everett's many-worlds interpretation, in which we could imagine many universes that all experienced today (December 7, assuming I finish writing this soon!) roughly the same, apart from some slight differences in Brownian motion in various fluids around the planet, like the upper atmosphere, the Pacific Ocean, etc. These universes, as traditionally described, and as animated by many made-for-television documentaries, form a tree, a basic mathematical structure where parent nodes in the past relate to child nodes in the future via possible evolutions.

However, we can reverse everything, can't we? So surely we can view the many-worlds interpretation, tree and all, in the direction of the past! Parent nodes will be in the future, and child nodes will be in the past. Putting this together, from our current vantage point, we can see a pair of trees branching off into our past and our future.

But some of those possible futures and pasts might overlap, as described earlier. In that case, we don't really have a tree. We do have a graph of all universes (or of the multiverse, if you prefer that term) which seems to provide a foundation for two kinds of analysis. First, path equivalency: when do two different paths lead to the same configuration? And second, meta-universal statistics: are some configurations likelier than others by virtue of having more paths through them or other structural biases? I don't know yet, but I'd first like to know how shaky the ground is beneath these questions!

So, my question is, where did I make a mistake in my thinking? Alternatively, if I didn't, does this imply anything especially interesting? Has anybody else come to this conclusion before?

Edit: A few touchups and also removal of irrelevant wankery. To answer the first question, I was wrong to assume that it's possible to construct universes which alias each other in observable configurations.

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closed as unclear what you're asking by sammy gerbil, Jon Custer, glS, John Rennie, Bill N Dec 11 '17 at 20:25

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  • $\begingroup$ You are asking too many questions for this forum. Anyway the many worlds interpretations is just that, interpretation, the mathematics are the same and there is no predictability, because it models the same reality. Mathematics models reality, it does not create it. Identical states in quantum mechanics are bounded by the Heisenberg uncertainty principle. $\endgroup$ – anna v Dec 8 '17 at 5:59
  • $\begingroup$ Within experimental errors and the HUP elementary particle scattering experiments add up identical pathways to get at scattering crossections to check with theoretical predictions. The arrow of time is an observational reality modeled by thermodynamics. There is not a single experimental evidence that the arrow of time can reverse in the real data. $\endgroup$ – anna v Dec 8 '17 at 5:59
  • $\begingroup$ Sorry, I fear I misphrased something. I am talking about a thought experiment here, and I'm not actually demanding that any sort of time machine exist. (Also, sorry for asking too many questions! How many questions can I ask?) $\endgroup$ – Corbin Dec 8 '17 at 6:10
  • $\begingroup$ one to two or sometimes more if they are simple and clearly labeled. Chceck my model is unlimited. The answer to "identical states" is that quantum mechanics with its commutators of operators does not have physical, i.e. measurable, "identical states" by construction of the theoretical model. $\endgroup$ – anna v Dec 8 '17 at 7:12
  • $\begingroup$ There are quite a few confusions here. As far as I can tell you're asking a general question about the time-reversibility of quantum mechanics. This is a definite physical statement and hence has no dependence on which interpretation you use, so there's really no need to invoke many worlds or de Broglie-Bohm and especially not both of them! $\endgroup$ – knzhou Dec 8 '17 at 11:05
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I will answer the title of the question:

Can two distinct quantum universes ever have the same configuration, and what does it mean for many-worlds?

The many worlds interpretation is just that, a different way of interpreting the mathematics of quantum mechanics, with no predictions for any differences that would allow to make a distinction with the Copenhagen interpretation taught in schools.

The mathematics of quantum mechanics is probabilistic, enclosing the Heisenberg uncertainty principle, HUP, in the algebra of commutators of the quantum mechanical operators. This means that there exists an inherent uncertainty within the quantum mechanical model of the system, so that for example one may not know accurately the momentum of a particle at a specific location, but only above a limit Δ(p)xΔ(χ) given by the HUP. So identical systems cannot exist.

So the answer is that at our present knowledge, experimental and theoretical, two distinct universes cannot be in an identical state due to the HUP.

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  • $\begingroup$ Isn't such uncertainty only limited to certain interpretations of QM? I got the impression that there are several interpretations of QM which are deterministic but not wholly observable. $\endgroup$ – Corbin Dec 8 '17 at 15:24
  • $\begingroup$ As the physically measurable quantities are the same in all "interpretations", what holds for one holds for all, imo. Particularly the many worlds interpretation which just considers the mathematical parts as existing as other worlds must inherently have the HUP in its setup. $\endgroup$ – anna v Dec 8 '17 at 15:30
  • $\begingroup$ @annav, Apologies for this science fiction conjecture, but is it possible that the two universes could be pass through each other, coexist on different wavelengths, like a ghost, anything like that at all? And don't laugh at me. $\endgroup$ – Len Feb 15 '18 at 18:43
  • $\begingroup$ @Len not within standard model physics . The calculations that give rise to probable worlds are not in the usual space dimensions. One would have to build a specific mathematical model , non mainstream for something like that, but there is no indication to necessitate such work. $\endgroup$ – anna v Feb 15 '18 at 18:51

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