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Bell's theorem proves that local hidden variables theories cannot reproduce quantum mechanics (with the exception of superdeterministic theories). Are there any local theories that do not involve hidden variables? How do such theories explain the observed correlations?

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    $\begingroup$ The theory you’re asking about is just standard QM! $\endgroup$
    – knzhou
    Jul 24 '19 at 4:59
  • $\begingroup$ Keep in mind that Bell uses "real" in a way that is now considered idiosyncratic. He means "counterfactually definite", not "realism." The most popular local, counterfactually indefinite interpretation is Everettian. If you really mean "antirealist" then the Copenhagen view of Bohr/Heisenberg is the famous example, but you're not going to get a concrete "explanation" in the traditional sense (by definition of "antirealist"), and correspondingly the writings of Bohr/Heisenberg are famously unclear. $\endgroup$
    – user1247
    Jul 24 '19 at 5:40
  • $\begingroup$ knzhou, standard QM just predicts the correlations, does not explain them in any way. You prepare the experiment, perform the measurements and you get some correlations. An explanation requires a chain of reasoning connecting the initial preparation to the measurements results. $\endgroup$
    – Andrei
    Jul 24 '19 at 5:56
  • $\begingroup$ user1247, Copenhagen, with its state collapse appears non-local. Bohr denied this. But he did not actually present that local explanation either. He said "a closer examination reveals that the procedure of measurement has an essential influence on the conditions on which the very definition of the physical quantities in question rests" . He does not say what this influence is. $\endgroup$
    – Andrei
    Jul 24 '19 at 6:04
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In the context of discussing quantum mechanics, realism means that the evolution of a system can be represented by a number or set of numbers, each of which represents the value of some measurable quantity. Note that this has nothing at all to do with the philosophical idea that reality is objective. It could easily be the case that reality is objective and that the evolution of physical systems can't be described by a set of numbers each of which is measurable.

Quantum mechanics with out modifications like the collapse postulate, can describe the evolution of systems in terms of sets of Hermitian operators, each of whose eigenvalues represents a possible outcome of a measurement. The evolution of those observables is local under the laws of motion that occur in the real world:

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

https://arxiv.org/abs/1109.6223

The correlations are explained by quantum information being transported in decoherent systems such that the observables of those systems depend on the information being transmitted, but the expectation values of measurements on those observables doesn't depend on that information - locally inaccessible information.

If you include a collapse postulate, or modify quantum mechanics to include collapse, then there is no explanation of how information gets transmitted in measurements of entangled systems.

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  • $\begingroup$ alanf, I would disagree with your definition of realism. Many worlds (MWI) is a realist interpretation (the wavefunction is a real field "out there"). I agree that such an interpretation can, in principle, explain EPR. On the other hand, the collapse postulate is part of QM (not added to QM) and represents the connection between the theory and experiment. As far as I know there is no way to account for the observed probabilities in the context of MWI. I know Deutsch claimed to have deduced the Born rule from decision theory, but I see such a deduction as circular. to be cont: $\endgroup$
    – Andrei
    Jul 24 '19 at 10:41
  • $\begingroup$ cont: In order for a rational agent to exist you need a specific type of physical laws, therefore the decision theory implicitly assumes the Born rule. Had QM been different we would have defined differently a "rational agent". It is also unclear to me how a measurement is defined in MWI. $\endgroup$
    – Andrei
    Jul 24 '19 at 10:49
  • $\begingroup$ In the MWI a measurement is an interaction that copies information from one system to another. The information that get copied is information about some mutually orthogonal set of states arxiv.org/abs/1212.3245. Your criticism of the decision theory paper is unclear. A decision theoretic agent would need to be able to keep records of the state it's going to measure and of the results of the measurement, both of which are possible in the MWI. You haven't explained any other constraint, so I don't know what your objection is. $\endgroup$
    – alanf
    Jul 24 '19 at 21:16
  • $\begingroup$ I would suggest we discuss this by e-mail instead of comments. My e-mail address is alanmichaelforrester@googlemail.com. $\endgroup$
    – alanf
    Jul 24 '19 at 21:17

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