If there was a non-local theory that explained quantum entanglement correlations, does it follow that it would violate special relativity?
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$\begingroup$ Not necessarily, imagine if the particles were connected through a wormhole like structure. It would violate the postulate that the space is minkowski though, so you could say it violates special relativity but not in the sense that it would involve faster than light local speeds. $\endgroup$– Pato GalmariniCommented Apr 22 at 0:53
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$\begingroup$ Tachyon particles, for example, would introduce non-locality but still be consistent with SR. $\endgroup$– Maximal IdealCommented Apr 22 at 6:51
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2 Answers
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Bell's theorem states that a theory that is local and describes observable quantities in terms of stochastic variables that have a single value at the time of measurement picked with the relevant probability can't reproduce some predictions of quantum theory such as Bell correlations.
As pointed out by Lucien Hardy in Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories, such a theory also can't be Lorentz invariant and so is incompatible with special relativity. See also his phd thesis:
http://etheses.dur.ac.uk/6079/1/6079_3430.PDF
Pilot wave theories and all theories featuring collapse including spontaneous collapse and possibly the Copenhagen interpretation must also be both non-local and non-Lorentz invariant. As a result they are incompatible with special relativity and also with quantum field theory and so are currently unable to reproduce almost all of the successful predictions of quantum theory:
https://arxiv.org/abs/2205.00568
Quantum theory without collapse (QTWC) describes systems in terms of quantum observables represented by Hermitian operators, not by stochastic variables. In such theories when information about an observable is copied out of a quantum system, this suppresses interference, this process is called decoherence:
https://arxiv.org/abs/2208.09019
QTWC explains Bell correlations in terms of quantum information carried in decoherent channels that allows the correlations to arise when measurement results are compared instead of at the time of measurement:
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There is at least one such non-local theory. It is standard quantum mechanics. The non-local correlation between entangled particles does not violate special relativity because the correlation of the random measurement results on the two particles cannot be used to send a signal. There is no causal connection between results of the measurements. The correlation can only be seen when comparing the results afterwards. Also the Bohm theory, which is explicitly non-local, gives the same results as standard quantum mechanics.
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$\begingroup$ Why does not being able to send a signal for messaging purposes imply no causal influences between the particles? And the Bohm theory is explicitly non local yes but it does violate relativity no? Can it be constructed in such a way that it doesn’t? $\endgroup$– HumeCommented Apr 22 at 3:45
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$\begingroup$ physics.stackexchange.com/questions/811135/… $\endgroup$– alanfCommented Apr 22 at 8:11
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$\begingroup$ To me this is a sleight of hand, because you have no explanation about why you cannot simulate separated away spin experiment in two separate computers. The only way to obtain the non classical correlations it is to transfer information between the two computers. If you know what the other party is measuring (I mean the orientation detector, not the result), then you can reproduce the correlations. $\endgroup$ Commented Apr 22 at 23:41