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I'm not sure I understand what distinction you are making. Bohmian mechanics is deterministic, just as Newtonian mechanics is. Each particle affects every other particle, just as with Newtonian mechanics.Yes, this does answer my concern better. But I still have a question left. My point was that in Newtonian gravity I can by only observing one particle deduce something about the behavior of the other, without the need of me knowing the initial state of the universe, just local observations of one particle. That is not possible in quantum mechanics. Is it possible in Bohmian mechanics? If not, then the claim that the nonlicality of Bohmian mechanics is the same as that in Newton's gravity is simply incorrect. This was the only point that I wanted to make. If on the other hand it is possible, then it seems that Bohmian mechanics is substantially different from QM, not just an interpretation. So different that it is already ruled out.

That is, in principle, different from standard QM, which is nondeterministic, but in practice they make the same predictions. If you don't know the exact positions of every particle, but only a probability distribution, then Bohmian mechanics only allows you to make probabilistic predictions.