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Dear Physics Stack Exchange community,

I am intrigued by the concept of quantum entanglement and its implications for our understanding of the fundamental nature of reality. I have come across various explanations regarding the phenomenon of non-locality in quantum systems, where entangled particles appear to instantaneously influence each other's properties regardless of the distance between them. However, I am seeking further clarification on whether this non-local behavior is an inherent aspect of quantum mechanics or if it poses a violation of causality.

I would greatly appreciate if someone could shed light on the following questions:

1. Does quantum entanglement necessarily imply non-locality, or are there alternative interpretations that can explain entangled particle correlations without invoking non-local influences?

2. Can non-locality in quantum systems be reconciled with the principle of causality? Are there any theoretical frameworks or experimental evidence suggesting that non-locality does not violate causality?

3. What are the prevailing theories or models that attempt to explain the mechanism behind non-locality in quantum systems? Are there any ongoing research efforts aimed at further understanding this phenomenon?

I have a solid background in quantum mechanics and would welcome any insights, references to relevant research papers, or further reading materials on this topic. Thank you in advance for your expertise and guidance.

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  • $\begingroup$ Quantum mechanics is perfectly local. It is, however, non-separable. If you are interested in the topic, then you will have to understand the difference. Locality is a property of physical space, separability is a property of Hilbert space. The former describes physics of the individual system, the latter is a purely abstract construct that describes the quantum mechanical ensemble. $\endgroup$
    – FlatterMann
    Commented May 26, 2023 at 19:34
  • $\begingroup$ You should stick with local causality for everything. Ask yourself what's the difference between correlated and entangled or better yet, what is entanglement IF its not plain old correlation. If you still think they are different then explain to me how you entangle them with correlating them. I mean how do you actually do it? $\endgroup$
    – Bill Alsept
    Commented May 26, 2023 at 22:12
  • $\begingroup$ Your questions will generate widely diverging opinions, as can be seen by the comments and answers at the moderator's reference (marking as a duplicate). Despite each author claiming to be "correct", there is no generally accepted interpretation of QM and no generally accepted answers to any of your questions. See arxiv.org/abs/1301.1069 which is an informal survey by Zeilinger and others. If you search arxiv, you with find the words "Nonlocal" and "Nonlocality" in the title of nearly 5000 papers. So not everyone agrees with FlatterMan or Bill Alsept. $\endgroup$
    – DrChinese
    Commented May 27, 2023 at 18:34
  • $\begingroup$ @DrChinese my comment was more a suggestion followed by a question to help the OP sort thing out. $\endgroup$
    – Bill Alsept
    Commented May 29, 2023 at 7:15
  • $\begingroup$ @BillAlsept Understood. I will point out that you can create entangled pairs without them interacting or ever being in a common region of spacetime. Of course those will exhibit perfect correlations and violate a Bell inequality, just like any entangled photon pair. $\endgroup$
    – DrChinese
    Commented May 29, 2023 at 14:50

2 Answers 2

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It's hard to answer your first two questions without knowing precisely what definition of "locality" and "causality" you're assuming. But even without this detail, I think your key question is 3, which might be paraphrased as: 'something weird is going on; what are the main ways to explain it?'

Here are the main categories:

  1. Bohmian-style explanations: Physical things exist in space and time, and can all interact with the same non-local wavefunction which does not exist in ordinary space. Information can be mediated from one thing to another through this wavefunction, and there must be some special reference frame where that mediation is instantaneous.

  2. ER=EPR style explanations: Physical things exist in space and time, but space and time is littered with wormholes connecting different regions, wherever entangled particles exist. Information can be mediated through these wormholes.

  3. Retrocausal explanations: Physical things exist in space and time, and are connected through their worldlines, making a physical network in spacetime. Information can be mediated from one event to another through their past and/or future worldlines, following the paths where they intersect. This viewpoint is hard to make sense of without both a block-universe view of spacetime and a more subjective/traditional view of information (so that the information isn't literally "moving" through spacetime).

And finally, there's dodging the need for an explanation via either:

  1. No Reality / Many-Worlds Viewpoint: There's nothing actually existing anywhere in space-time, everything real resides in a Hilbert or Fock space. Worrying about something "over here" affecting something "over there" is therefore not a worry; there's no conventional sense of "here" or "there" in a huge-dimensional Hilbert space. (So called "Copenhagen" accounts tend to shift back and forth between this and something closer to #1.)

or

  1. Superdeterminism: The universe was set up such that what we see locally and causality follows from that setup; this explains everything except for the setup itself. There is no need to in turn explain how it was set up in such a special way; that's just how it was.
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  • $\begingroup$ None of these is correct. The most simple explanation that covers all known phenomena is that "objects don't exist other than as emergent phenomena". The physical vacuum can exchange energy among different volume elements (which we call "systems"). These energy exchanges can be reversible (if they are involving only finite volumes of the physical vacuum) and irreversible (involving sufficiently large emergent objects or infinite amounts of the physical vacuum). The remainder of the theory (Hilbert/Fock space etc.) is merely the solution theory for how these energy exchanges happen on average. $\endgroup$
    – FlatterMann
    Commented May 27, 2023 at 0:55
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To understand the concept of entanglement, it may be helpful to look at the history of the development of the concept. J.S. Bell used two simple assumptions to derive what is now called Bell's inequality. One of his assumptions is locality. The other one is that there is only one unique reality. Later, it was shown by using entangled states that nature violates Bell's inequality, which shows that at least one of his assumptions must be wrong.

Which one? Well, special relativity tells us that his assumption about locality must be correct. So the violation of the Bell's inequality, which leads to the concept of entanglement does not violate locality, or causality for that matter. Therefore, the assumption that must be wrong is the assumption that there is a unique reality. It is on this basis that QM is formulated.

You can see this notion of multiple realities in the expressions that are used for entangled states. They always consist of superpositions of multiple terms. Each term represents a reality. When an observation produces a result that is consistent with one of these terms then any other observations will produce result from the same term.

Now, one must be care not to confuse the notion of such multiple realities with the idea of a multiverse. That is not the case, because one can always change the state with a unitary transformation that would combine some the terms in the state to produce a new representation of the state. The entanglement would remain the same but the nature of the observations associated with each term would be different.

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  • $\begingroup$ Your comment "special relativity tells us that his assumption about locality must be correct" is not generally accepted in the literature. Ditto your assertion that causality holds; this too is an open question. In fact, there is substantial experimental evidence that it does not hold. For example: you can entangle photons AFTER they have been detected - certainly that shouldn't be possible if we live in a causal universe. And you can entangle photons that have never existed in a common light cone. According to the usual view of special relativity, that shouldn't be possible either. $\endgroup$
    – DrChinese
    Commented May 27, 2023 at 18:51
  • $\begingroup$ @DrChinese: Sometimes the results of experiments are sensationalised to the point of being misleading. Be careful and don't just believe everything you read. For example, I don't believe the nonsense about entangling photons after they have been detected. Yes you can entangle photon that did not come from the same source, (with entanglement swapping) but that does not violate causality. It has to do with the understanding of what entanglement means. $\endgroup$
    – flippiefanus
    Commented May 28, 2023 at 3:51
  • $\begingroup$ Of course you can entangle photons after they have been detected... what, do you just reject experimental evidence that conflicts with your opinions? Zeilinger et al: arxiv.org/abs/quant-ph/0201134 (bottom 1/3 of page 5, explicit test of delayed swap) Entanglement Between Photons that have Never Coexisted arxiv.org/abs/1209.4191 (photon 1 is detected and ceases to exist prior to being entangled with photon 4) The swap can be done at anytime you like relative to the detection of the entangled photons: before and/or after. Got a reference otherwise? $\endgroup$
    – DrChinese
    Commented May 28, 2023 at 16:51
  • $\begingroup$ @DrChinese: both your references refer to entanglement swapping, which I have not problem with. (I was even involved with experimental work on entanglement swapping.) However, one should be careful how one phrases the conclusions from such experiments to avoid misleading interpretations. These experiments do NOT violate causality. $\endgroup$
    – flippiefanus
    Commented May 29, 2023 at 3:58
  • $\begingroup$ "These experiments do NOT violate causality." Since you are well familiar with swapping, how can you say this? I appreciate that all interpretations of QM do not agree on this point. But surely entangling photons after their detection - which looks on the surface to violate causality - should leave one with some pretty serious doubts. Of course, this paradox is fully in keeping with QM. Changing the time (causal) ordering changes nothing in the statistical predictions whatsoever. $\endgroup$
    – DrChinese
    Commented May 29, 2023 at 14:57

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