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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?

glS
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Manas Dogra
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2 Answers2

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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.

glS
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  • 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 – Ramiro Hum-Sah Nov 10 '20 at 18:15
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    @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 (...) – glS Nov 10 '20 at 18:48
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    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. – glS Nov 10 '20 at 18:48
  • I had this doubt for some time. Your argument is spectacularly clear and helpful. Thanks a lot for your time and consideration. – Ramiro Hum-Sah Nov 10 '20 at 20:14
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    @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. – glS Nov 11 '20 at 09:43
  • @glS In the original question I asked "how is the non-local nature of quantum entanglement explained", and you said in the above comment that non-locality is in the correlations...So how things are correlated over space-like distances without invoking hidden variables or anything classical and yet not violating relativity? – Manas Dogra Nov 14 '20 at 04:58
  • have I not addressed just that a few comments above this one? "How are things correlated over space-like distances without invoking hidden variables or classical theories?" well... with QM. You might argue this is an unintuitive aspect and/or something that is not fully understood, and I might even agree with that to some degree (though I don't think that's what most people working in the field would think), but that doesn't change the fact that the theory is perfectly consistent and that there is no controvery about this specific aspect – glS Nov 14 '20 at 09:58
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    @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. – Shashaank Mar 01 '21 at 18:46
  • @glS "there exist types of correlations that are nonlocal" so QM is nonlocal. Q.E.D. – Juan Perez Oct 10 '22 at 11:15
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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

Guy Inchbald
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  • @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 – Ramiro Hum-Sah Nov 10 '20 at 18:17
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    @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. – Manas Dogra Nov 11 '20 at 06:00
  • How does the Aspect experiment reject theories where the polarization is determined at the source? All it shows is that the correlation of the polarization of the two photons depends on the angle between the two detectors.

    If the polarization were determined at the source and both evolved in a way hidden from us (not included in the wavefunction), they would remain correlated at the detector. What am I missing?

     – Paul Feb 01 '24 at 18:09