How does the many worlds interpretation explain (away) nonlocality?

David Deutsch has an excellent paper which traces the flow of information in entangled quantum systems and shows that it is entirely local (at least in the Heisenberg picture).  What he walks through in the paper is not exactly the same thing as the experiment you're talking about, but I think it's close enough that roughly the same process applies. http://arxiv.org/pdf/quant-ph/9906007.pdf What everyone agrees on is that, regardless of the interpretation, quantum mechanics does not allow any instantaneous transmission of signals from one place to another.  Even in the Copenhagen Interpretation, it's not clear that there's anything non-local about quantum mechanics (beyond the ordinary non-locality of classical mechanics--namely, that you can sometimes have distant objects whose properties are correlated with each other).  In hidden variable theories such as David Bohm's, there is an extra non-local metaphysical structure added, but in the end any observable predictions respect locality.  Opinions differ on whether what is added there is just extra baggage or if there is some philosophical justification for adding it.  Any statistical predictions you make for what happens in one region of space would be the same whether or not you know anything about what's happening in another separated (causally disconnected) region of space, even if they are a part of the same quantum world and have been in causal contact in the past.  Objective collapse theories, such as GRW, are also non-local, but these are modifications of quantum mechanics, not just interpretations.  So when people say that experiments like the double delayed quantum erasure experiment make them think something non-local is going on, they're using a very fuzzy notion of the concept of "non-local" which (as of yet) has no scientific operational definition.  What they're basically saying is that they feel like there is something "spooky" about what's happening.  (And I wouldn't necessarily disagree with that feeling.) The many worlds interpretation is the most explicitly local of the interpretations.  Rather than walk through in detail what happens in the quantum erasure experiment, I'll give you a brief summary of what I think happens in many worlds in a more general entanglement/EPR thought experiment.  You have two different measurements that take place at different locations, and the surprising thing (since we are all more used to the classical world) is that there seems to be a spooky correlation between the two, and that this correlation depends in a non-trivial way on the decision of how to perform the measurement.  Note that in the absence of being able to compare the two measurements, there is no way for a classical observer at either location to notice that there is anything out of the ordinary going on.  Only when they walk over to each other and compare the results can they both realize there was a correlation (and that if done many times, it shows that this correlation depends on the decisions they made).  But in the many worlds interpretation, even these large classical observers are initially in giant superpositions (albeit decoherent ones) of having measured both results (not one or the other).  It's not until they come into causal contact with each other that the branches of the multiverse which involve non-correlated results fully cancel out with each other (I admit that here my understanding of what happens gets a bit fuzzy, but this is my best guess of what happens).  In other words, the information about which result they got travels through a classical channel at less than the speed of light.  One reason I suspect why many people come to the conclusion that there was something non-local going on is because they feel uncomfortable thinking about large macroscopic objects like humans as being built out of quantum mechanical structures, and also because they may be attached to religious ideas about libertarian free will which obviously contradict this picture. This isn't to say that the world is entirely local--I personally suspect that it's not.  It's just that quantum mechanics by itself--and experiments like this one--do not prove any rigorous kind of non-locality.  For that, we need things like the holographic principle and quantum gravity, both of which point toward the breakdown of Einstein's theory of relativity which is ultimately what enforces locality in physics.

You want the MWI explanation of DCQE? No problem!It is important to start by accepting that the two photons are entangled. This means that they are in a superposition: |left>|left> + |right>|right>. This is hard to understand given that Kim et al refer to a photon pair being created at random after one of the slits. But the fact is, a pair created at a single point could never give rise to any kind of interference whatsoever. I'll give a brief explanation but as your question was about the delayed choice set-up I don't want to get bogged down in the details. We really need to get to the starting point of two entangled photons, so if this helps use it otherwise take the entanglement on trust.The entangled pair is generated by "spontaneous" down conversion in a single atom (or possibly a single site in the crystal, it doesn't matter). However in MWI, there are no truly random events. Instead there is a superposition of different emission times. This goes on in all the excited atoms across both regions. This would not be much of an advance if the excitation were simply a blast of bright light. But it is not, it is a coherent pump beam. Therefore the atoms are excited coherently and the emission wavefunctions are coherent. This is quantum mechanics at its best: when we look at such a system our interaction with it creates an entanglement and thus an improper mixed state so we observe the emission at a particular, random, time. But if the state is allowed to propagate it remains a coherent state of two entangled photons emitted across both excited regions.I guarantee you'll need to chew on that. I know I did. But lets move on. We now have two photons in the state |L>|L>+|R>|R> ignoring the normalization factor as I am prone to do.The state of the first particle *alone* is therefore the improper mixed state |R> OR |L>|R> cannot create a |R> + |L> interference pattern! It is a single photon that has definitely gone through the right-hand slit. Neither can |L>. So there is never an interference pattern at D0. Never, ever, ever.To see how the interference patterns are created you can manipulate the states to change the basis from left/right  to sum/difference. For example |R> becomes (|R>+|L>) + (|R>-|L>) whilst |L> is (|L>+|R>) + (|L>-|R>). The latter can be written (|R>+|L>)-(|R>-|L>).   For brevity I'll abbreviate (|R>+|L>) to p (for plus) and (|R>-|L>) to m for minus. (I'll put the ket  back around the terms later on.) This makes the entanglement (p+m)x(p+m) +(p-m)x(p-m) =pp+mp+pm+mm +pp-mp-pm+mm The cross terms vanish leaving a simple entanglement of pp + mm. This means that if we ignore the second photon information we can treat the first term as a mixed state. It is EITHER p = |R>+|L> OR m = |R>-|L>. Thus there are two interference patterns 180 degrees out of phase. So on aggregate, the peaks and troughs cancel and there is no interference pattern at D0. Changing the basis has not affected the outcome. Thank goodness!Now the tricky bit is what happens if we do measure the second photon. The Kim apparatus resolves the second or idler photon into physical |p> and |m> states which trigger D3 and D4. (It's all done with mirrors.) |p> and |m> (second photon) therefore trigger the "no path information" detectors D3 and D4 respectively (or maybe the other way round, if I have the sign wrong). Since the entanglement was |p>|p> + |m>|m>, a "p" event at D3 implies a "p" event at D0. So, by ignoring all photons except the ones where D3 is triggered, a pattern emerges. The pattern is not *visible* at D0, it has to be "pulled out" of the general blur.   As you can see there's not much about Many Worlds in all that. However it is there if you look closely :) Collapse theories require the detection at D0 to be definite and yet the probability distribution must depend on a choice yet to be made. In the foregoing MWI description, the collapse is removed and instead there are states like |p>|p> in superposition, i.e. Many Worlds. This product state is completely unchanged when the signal photon interacts with the D0 - all that happens is the first ket then refers to the state of the detector rather than the photon. Hence the detectors themselves become entangled, i.e. there is a macroscopic superposition, the hallmark of MWI.

The short answer is that locality is interpretation dependent.  In the Copenhagen interpretation the wavefunction collapses instaneously (I.e. non locally) upon measurement.  In Bohm's hidden variables the Quantun Potential is non-local, since it responds instantaneously to changes some distance away. In Everett's Many Worlds, there is no collapse, and no quantum potential, hence it is a local theory.  Sometimes folks get confused and think that the splitting of universes or worlds or timelines is non local, but in fact the splitting is a causal process, confined to the future light cone of the event that caused the splitting.  So the universe is not split instantly by each quantum transition, but only when the effect of the transition reaches us.  Hence many worlds is a local theory.Longer answer: http://www.anthropic-principle.com/preprints/manyworlds.html