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If there was a non-local theory that explained quantum entanglement correlations, does it follow that it would violate special relativity?

gandalf61
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Hume
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2 Answers2

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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:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

alanf
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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.

freecharly
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