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Everett's theory of quantum mechanics is about the wavefunction of the whole universe holistically. If a branching occurs very far away at the Andromeda galaxy, do I also branch? Are branchings global or local? If the branching occurs outside the cosmological horizon, do I branch?

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In the many worlds interpretation (MWI) interpretation of quantum mechanics there is just one single wave function for the entire universe. So there really does not exist the concept of "branching". You can read about it here.

What "branching" really means is that different portions of the wavefunction decohere so that there is no possible communication between the different decoherent portions of the wavefunction.

For example when an electron diffracts and is "detected" in one particular fringe of the diffraction pattern in "our" universe what really happens is that the electron interacts with a large number atoms in the detector and this causes that part (or our branch) of the wave function to decohere relative to all the other portions where the same electron was detected in a different fringe. So, in that sense it is kind of like a branching since our portion of the wavefunction cannot interact with all the other portions which are decoherent.

But there is only one wavefunction for the entire universe so if the universe extends beyond our horizon all of that is also included in the wavefunction of the universe.

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you can always take partial traces of your universe wavefunction to any subsystem that pertains to your local observations. I think you are missing the big point of MWI; it has absolutely nothing to do with decoherence; in the Eistein-Podolsky-Rosen experiment, the decoherence is entirely irrelevant to the scales where measurements are made. The correlations are only due to super-selection rules in the allowed interactions between far-away observers "branches", which even if you dislike the term, is still appropiate –  lurscher Oct 18 '11 at 4:46
Hi @lurscher, please read the wikipedia article I linked - it talks about decoherence all over the place. It makes it clear that the branching is ALL about decoherence. After you read that, let me know if you still think I am wrong and we can discuss it... –  FrankH Oct 18 '11 at 5:24
FrankH, decoherence is strictly speaking, when a basic physical system couples with the environment, and causes random phases to accumulate between the states. the branching, in MWI speak , does occur even in complete absence of interactions with the environment; as long as each observers measure their respective subsytem of the decaying singlet state (i'm referring again to the EPR setup example) they will branch entirely due to superpositions of the decaying products. If true decoherence would take place, then both observers could never agree on their correlations. –  lurscher Oct 18 '11 at 5:52
i'm not sure why the wikipedia article will use the term in that sense. My only guess is that they are using 'decoherence' as a synonym of 'measurement' ,which are certainly related processes, but not the same. –  lurscher Oct 18 '11 at 5:53
I guess we will just have to disagree about what MWI really means. We certainly are not the first two physicists to disagree about the interpretations of QM :) ! I took away my downvote on your answer... –  FrankH Oct 18 '11 at 7:27
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in MWI interpretation, "branching", in the sense that systems will spread across many eigenstates over time, always happens locally. MWI helps understand the EPR experiments precisely because it is strictly a local phenomena; separate observers that measure parts of an entangled system will "branch" locally exactly like the distant component did not exist at all.

Only when both observers join and mutually interact to exchange observation results, their branches will couple selectively to each other in order to preserve globally conserved quantities (like angular momentum)

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First, please note that MWI stands for many worlds interpretation. Second, I think you are wrong. Please see en.wikipedia.org/wiki/Many-worlds_interpretation . Specifically in MWI there are no observers or observations. There is just one single wave function for the entire universe. There really is not "branching" - rather different portions of the wave function decohere so in that way there is no communication between the different decoherent portions of the wave function. –  FrankH Oct 17 '11 at 23:26
thanks for the observations, even if deeply misleaded: If MWI "would not have observers and observations" it would be really useless as an interpretation of quantum processes, which are deeply related to "observations" performed by "observers". To your other comment: "branching", even if meaningless in the usual interpretation of a discrete event implied by the graph analogy, it is nonetheless a insightful intuition tool to comprehend the phenomena. Even if you dislike the term for some reason, that, per se, doesn't make it less appropiate in the sense that i've just explained –  lurscher Oct 18 '11 at 4:36
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One thing is for sure. The branchings can't possibly be microlocal. The example of the fractional quantum Hall effect (FQHE) makes this clear. In FQHE, a Landau level band is partially filled with band electrons and they end up in a highly entangled state approximated by something like the Laughlin wavefunction ansatz. The entanglement for this state can be over macroscopic distances of the order of the mean distance between anyonic excitations. If the sample is pure enough, the entanglement can be over the sample size, but typically, there will be "defects" and the defects are none other than the anyonic excitations. If a superposition of an anyon-antianyon pair and no pair is set up, the resulting branching can't possibly be more local than the distance between the anyon and antianyon.

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Some MWI proponents have tried to get away with an interpretation with no splittings at all, but then, all you are left with is an unstructured Hilbert space which is nothing more than some complex vector space with a norm. Splittings are necessary for MWI to work. This is best done in the Schrodinger picture. How do you define splittings in the Heisenberg picture without secretly smuggling in the Schrodinger picture? It will be an utter mess. Splittings have to respect the quasilocal structure. What other criteria can we have for splittings anyway? Overall, splittings can only make sense locally. Globally, it is always an entangled mess.

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