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From what I understand, Einstein tried to introduce real but hidden variables to remove the apparent non-local nature of quantum entanglement, but Bell's inequality showed local realism isn't possible. I have read physicists believe in locality than hidden variables because experiments and intuition say so, thus I have no issue with the non-existence of hidden variables.

But how is then locality/causality preserved in the case of quantum entanglement, or more specifically in the case of two particles having opposite spin projections when the EPR pair is space-like separated?

Putting it in another way, quantum entanglement is local (because it doesn't allow superluminal information transfer) but it allows for non-classical correlations between space-like separated particles. How is this correlation explained without violating relativity? The particles don't influence each other but yet they are "correlated". How are these statements true at the same time without invoking hidden variables? How is the correlation made?

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Quantum mechanics is local, in the sense that it doesn't allow for superluminal interactions. This does not contradict results such as Bell inequalities or anything allowed by entanglement.

The point is that quantum mechanics allows for correlations that cannot be explained by any local classical theory. But at the same time, these correlations are such that they cannot be exploited to achieve superluminal communication. This might seem a little odd, and it arguably is, but is perfectly consistent: there exist types of correlations that are nonlocal but at the same time cannot be used to carry any kind of information.

Of course, the above is true as far as the current formalism of quantum mechanics is concerned. Theories that try to extend quantum mechanics might work differently, but there is no commonly accepted such formalism as of yet.

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  • $\begingroup$ Dear @glS. How is it possible that a non-relativistic theory, like ordinary quantum mechanics, respects the basic axiom of special relativity? namely that superluminal propagation is forbidden $\endgroup$
    – Ramiro Hum-Sah
    Nov 10, 2020 at 18:15
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    $\begingroup$ @RamiroHum-Sah that depends on what exactly you mean here with "ordinary quantum mechanics". As I'm sure you know, there are standard quantum mechanical formalism that are relativistic. But if with "ordinary" you mean here the non-relativistic formalism, then you are right, there is no intrinsic notion of "speed of light" in the framework. What the framework tells you is that nonlocal correlations cannot be exploited to achieve instantaneous communication (...) $\endgroup$
    – glS
    Nov 10, 2020 at 18:48
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    $\begingroup$ Thus any communication must happen via the natural speed dictated by the choice of Hamiltonian, that is, of physical theory that you are describing in the quantum mechanical formalism, and that is where the notion of "light" and "speed of light", and thus the impossibility of superluminal communication, come about. $\endgroup$
    – glS
    Nov 10, 2020 at 18:48
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    $\begingroup$ @ManasDogra there is exactly zero controversy. It depends on your exact definition of "local". QM is local in the sense that it doesn't allow for instantaneous information transfer. It's nonlocal in the sense that it allows for correlations that cannot be written with local hidden variable theories. The Wikipedia pages do not contradict this, you just have to read carefully what is being written. $\endgroup$
    – glS
    Nov 11, 2020 at 9:43
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    $\begingroup$ @ManasDogra just to add a bit. You are correct in your thinking that QM is non local in a way. The locality described in this answer is just no signalling ( or parameter independence since hidden variables are not mentioned. QM is non local in the sense that there are non local causal effects ( action at a distance going on ). There are 2 definitions of locality, one is no signalling or parameter independence and the other is Local causality (the kind of thing Einstein had in mind ). Local causality is violated in any theory with or without hidden variables. Whether SR prohibits it open quest. $\endgroup$
    – Shashaank
    Mar 1, 2021 at 18:46
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You are correct that Bell's theorem, in conjunction with accumulated experimental results over several decades, have demonstrated to a high degree of certainty that quantum reality is non-local.

The quantum equations can be reorganised in many ways, notably done by Bohm & Hiley to describe locally real particles accompanied by a "pilot wave". But in any such reformulation, nonlocality must manifest in the nature of the pilot wave (or similar) and its interactions with the particle. Otherwise it will not be able to predict the outcomes of all those experiments, and nor will it be an equivalent quantum formulation any more but a competing physical theory.

Suggestions that the universe is therefore locally "real", just because the particles are, beg the question as to what is meant by such "reality" if the fuller reality entails the presence of nonlocal phenomena directing them.

Perhaps ironically, Bohm got philosophical and his motivation was as much to draw out the nonlocality via what he called the "implicate order" of the Universe; cutting the locally-real particles out of his pilot wave was in a sense just a by-product of his search. But even he had no concrete proposal on how the wave interacted.

You ask about the case of two [entangled] particles having opposite spin, when separated in space. The relevant properties of the space-separated pair are described by a single quantum wave equation. Any "determined-at-source" model is an example of local realism and fails Bell's test. Thus the entanglement is intrinsically nonlocal. (This was the essential demonstration of Alain Aspect's seminal experiment). But whether the subsequent measurement events may be retrocausally related remains a matter of deep debate. For example one may seek to distinguish between quantum (measurement) causality and temporal causality, allowing the apparent (classical) causal flow of events in time to be locally subjective.

Some of the issues over what "causality", "local" and "realism" mean to different people in this context are examined by Adrian Wüthrich in Locality, Causality, and Realism in the Derivation of Bell’s Inequality

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  • $\begingroup$ @ManasDogra How is it possible that a non-relativistic theory, like ordinary quantum mechanics, respects the basic axiom of special relativity? namely that superluminal propagation is forbidden $\endgroup$
    – Ramiro Hum-Sah
    Nov 10, 2020 at 18:17
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    $\begingroup$ @RamiroHum-Sah NRQM doesn't obey STR because it doesn't have any postulate related to STR.This can also be easily seen if we compute transition amplitudes to space-like seperations which turns out to be non-zero in NRQM. $\endgroup$
    – Manas Dogra
    Nov 11, 2020 at 6:00

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