[jostylr]

In EPR, the setup is that there are two labs doing measurements outside of each other's lights cone. The outcome in one lab allows a perfect prediction of what happens in the other. This means that it is not possible that something random is going on in unless there is some nonlocal coordination between the two. This suggests that there is some actual fact of the matter as to how the experiment will turn out. That is, they argued that QM+locality = extra information beyond the wave function to determine outcomes. Bell then saw Bohm's theory and wondered about getting rid of the nonlocality. Bell showed that QM+extra info determining outcomes = nonlocal. In short, EPR + Bell shows that if QM predictions are correct (the predictions, not the theory), then there is something nonlocal going on. The lab experiments confirmed this and nature is indeed nonlocal.

Thus, there is no local theory that has definite experimental results compatible with what is actually demonstrated in labs. Many worlds, to the extent that one can apply any notion of locality to it, avoids this by not having singular, definitive experimental results (all results happen).

[griffzhowl]

> The outcome in one lab allows a perfect prediction of what happens in the other.

I guess you know this, but just to clarify, that's only if the same measurement is performed in the other lab. If the other lab measures an orthogonal spin component, that result can't be predicted at all (I'm assuming entangled spin-1/2 particles for simplicity). It's more precise to say that measurement in the first lab tells you the state in the second lab, and with that information the probabilities for the various possible measurement results in the other lab can be predicted. In particular, if the other lab measures the spin along the same axis, the results can be perfectly correlated, as you say.

So there's some kind of nonlocality, but it's not the kind of nonlocality that makes problems with relativity, because the correlations can't be used to signal or cause any difference in the distant lab, only to predict, in general probabilistically, what would happen in the other lab if some measurements are performed. So entanglement allows this interesting middle ground between a local theory and a theory that's nonlocal in the sense that it would allow nonlocal causation, which is the kind of nonlocality that would worry Einstein. There should be different words for the different kinds of nonlocality, but maybe nonlocal correlation versus nonlocal causation serves the purpose

[jostylr]

In EPR, it is critical that it is the same measurement. Bell explores doing different measurements. For EPR, they assumed that if you can predict with certainty what happens in a space-like separated region, then there must be a fact of the matter about it. Not being probabilistic was very important for that. Bell then showed that there cannot be a fact of the matter without there also being some nonlocal means going on in order to account for the QM predictions. It is critical to appreciate the two separate pieces of arguments, how they differ, and how jointly they do lead to some kind of nonlocality. Tim Maudlin has a, now old, book exploring these different levels of nonlocality in quantum mechanics.

I recently heard a talk from Tim Maudlin where he mentioned that foliations are the easiest and most natural structures to use to provide nonlocality and, if there is such a thing, maybe there is a clever way of using it to actually communicate and discover the foliation in some sense. He mentioned there is current research on using arrival times which are experimental results outside of the operator formalism, as far as I know. I found an article describing the research:

https://www.altpropulsion.com/ftl-quantum-communication-reth...

[GoblinSlayer]

If MWI is true, then nature is local without extra information beyond wave function.