"A and B perform their measurements at spacelike separation, but each chooses the measurement orientation outside the light cone of the other. There are four possible combinations of results, corresponding to four worlds in the MWI: |+>|+'>, |+>|-'>, |->|+'>, and |->|-'>. Since each observer has a 50% chance of getting |+> and 50% of getting |->, and the two measurements are completely independent of each other, it would seem that each of these four worlds is equally likely."
I don't think this is how it's supposed to work for those who argue the MWI is local like Deutsch. Rather the idea is that "splitting" into worlds is local, not global; so one experimenter locally splits into copies that see |+> and |-> when they measure their particle, likewise the other experimenter splits into copies that saw |+'> and |-'>. But until their future light cones overlap there are no "worlds" containing facts about what *both* experimenters saw. And once they do overlap--say, because they both sent signals about their results to an experimenter at the midpoint between them--then they can be matched up appropriately based on information in the past light cone of the overlap region, including information about what detector setting each copy of each experimenter used. So if both experimenters used the same detector setting, then if we consider the copy of the middle observer who gets matched up with the copy of the left experimenter that got |+>, he must also be matched up with the copy of the right experimenter that got |-'>, and likewise the copy of the middle observer who gets matched up with the copy of the left experimenter who got |-> must be matched up with the copy of the right experimenter that got |+'>. You could design a cellular-automata like system that keeps track of multiple copies of each system at a given "cell" in this sort of way, and reproduces the statistics seen in Bell experiments, so the idea is at least in principle consistent (I described a simple toy model at http://www.physicsforums.com/threads/does-mwi-resolve-locality-problems-with-entanglement.206291/#post-1557143 ). Although from what I've read, the "preferred basis problem" means the current formulation of the MWI has trouble getting probabilities from the universal wavefunction in any simple frequentist way (one where you have a well-defined "fraction of copies with property X vs. fraction with property Y" for each local region of spacetime, and probability is simply interpreted in terms of this fraction), instead probabilities are usually derived in non-frequentist ways using things like decision theory. Maybe in the future a nice frequentist version of the Everett interpretation will be found though...I don't understand the details, but I think Mark Rubin has been trying to get closer to something like this in the papers at http://arxiv.org/abs/quant-ph/0204024 and http://arxiv.org/abs/quant-ph/0511188 and http://arxiv.org/abs/0909.2673 Jesse On Fri, Apr 15, 2016 at 8:33 PM, Bruce Kellett <bhkell...@optusnet.com.au> wrote: > On 16/04/2016 12:20 am, Bruno Marchal wrote: > > On 14 Apr 2016, at 14:31, Bruce Kellett wrote: > > Although all possible combinations of measurement outcomes exist in MWI, > it is not clear what limits the results of the two observers to agree with > quantum mechanics when they meet up in just one of the possible worlds. > > > Because they have separated locally, and Alice's measurement just inform > both of them (directly for Alice and indirectly for Bob once some classical > bit of information is communicated by Alice to Bob by the usual means). > > > This is the purported solution given by Deutsch and Hayden, amongst many > others. Unfortunately, it does not work, as can be demonstrated by working > through a specific example. > > Consider the usual case of a spin singlet that splits into two spin-half > components that separate and are measured by A and B at spacelike > separation. There are two possible measurement results for each observer, > call them |+> and |->. The entangled state can then be written as: > > |psi> = (|+>|-> - |->|+>). > > ignoring normalization factors for simplicity. The first ket applies to > observer A and the second to observer B. > > This is the general expression for the singlet state in any basis, such as > would be define by the orientation of the measuring magnets. We denote the > measurement results in some other direction as |+'> and |-'>. > > A and B perform their measurements at spacelike separation, but each > chooses the measurement orientation outside the light cone of the other. > There are four possible combinations of results, corresponding to four > worlds in the MWI: |+>|+'>, |+>|-'>, |->|+'>, and |->|-'>. Since each > observer has a 50% chance of getting |+> and 50% of getting |->, and the > two measurements are completely independent of each other, it would seem > that each of these four worlds is equally likely. > > But this conclusion is contradicted by quantum mechanics: if the two > observers, by chance, have their magnets aligned, then the |+>|+'> and > |->|-'> combinations are impossible. In general, the probabilities of the > four possible joint outcomes depend explicitly on the relative orientation > of the magnets of the A and B -- they are seldom all equal. How is this > taken into account in the formalism? > > In the formalism of QM, the answer is clear enough. Given the expression > for |psi> in an arbitrary basis, as above, we can choose the basis for this > expansion to be that for the orientation of magnet A. But then, in order to > get the relevant outcomes for B, we have to rotate this expansion to the > basis corresponding to the orientation of magnet B. But we have to do this > rotation before B makes his measurement! How does B know the necessary > rotation angle? Recall that both A and B make independent arbitrary > rotations at spacelike separations. > > After the measurements are complete, A and B communicate their results to > each other, so the branch of B that measured |+'> communicates this to both > copies of A, to get the combinations |+>|+'> and |->|+'>. Similarly, the > branch of B that got the result |-'> communicates this to both copies of A, > to get the remaining two combinations |+>|-'> and |->|-'>. Deutsch and > Hayden propose that non-locality is eliminated by B communicating his > orientation angle as well as his result to A. But adding the angle theta to > the information transmitted does not change the fact that one copy of B > transmits a |+'> result and one copy transmits a |-'> result. In other > words, this extra orientation information is completely irrelevant to the > outcomes of the measurements, and also irrelevant to the relatives > probabilities for the our possible worlds. > > Deutsch and Hayden have not shown that this EPR experiment is local in MWI > -- they still have to use the rotation of the wave function basis for B's > measurement *before* that measurement is made, and that information is > not locally available to B, it can only have been transmitted non-locally. > > So MWI does not give a local account of the EPR results on entanged states. > > Bruce > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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