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In Wikipedia's table of interpretations of quantum mechanics there is a column for "local dynamics" where under the Copenhagen interpretation states "yes[citation needed]". Should that be the case? I will like to understand if the Copenhagen interpretation is local in the sense of local realism, which has been shown experimentally to be false under the Bell tests.

There is a clear consensus that Bohr considered the Copenhagen view as nonrealist, both in the sense that observables do not have a predetermined value before measurement and their result is probabilistic (not deterministic). Checking Speakable and Unspeakable in Quantum Mechanics, Bell argues that Bohr is very vague and unclear on how that saves quantum mechanics from violating locality. Bell constructs a theory of beables (avoiding the 'realism assumptiom' or 'outcome determinism'), prefers to define "local causality" instead of local realism, and proves under these concepts that quantum mechanics violates local causality and is nonlocal in general.

Independently of Bell's view, it seems that Bohr would have defended locality and thus Copenhagen interpretation could be considered local or at least agnostic. As Bohr view precedes the experiments to test Bell's inequalities, maybe Copenhagen view has just never been defined under those terms.

Is the Copenhagen interpretation usually considered local in the literature or is it assumed to be nonlocal because of nonrealist local interpretations are considered untenable?

Please avoid arguing why quantum mechanics must be nonlocal in general, I am specifically looking for what is the consensus (if any) about Copenhagen interpretation (even if untenable).

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    $\begingroup$ For this question to have an unambiguous answer you'd first have to get people to agree what "the Copenhagen interpretation" actually says, when in practice "let's use Copenhagen" is often what people say when they specifically don't want to get into interpretational issues, i.e. the practical use of "Copenhagen interpretation" usually does not correspond to some clearly and carefully considered interpretation. $\endgroup$
    – ACuriousMind
    Commented Jan 22, 2023 at 11:29
  • $\begingroup$ @ACuriousMind so then there I would classify it as agnostic or no consensus. $\endgroup$
    – Mauricio
    Commented Jan 22, 2023 at 11:31
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    $\begingroup$ As far as I see, the Wiki page refers to dynamics. I do not know if it is local, it depends on how one describes interactions. Failure of local realism in the current interpretation of Bell's viewpoint instead concerns measurements. There, every interpretation must agree with the experimantal fact that non local correlations do exist. $\endgroup$ Commented Jan 22, 2023 at 12:15
  • $\begingroup$ If you write down exactly what you mean by "Copenhagen interpretation" and exactly what you mean by "local realism", it will be easy (but probably not very interesting) to answer your question. If you don't, it will be impossible. $\endgroup$
    – WillO
    Commented Jul 9 at 3:56
  • $\begingroup$ Some users are trying to reopen this question. I would like it too but I have not modify it because I think that it is not wrong. I am not trying to define "Copenhaguen interpretation" or "local realism", I want the best consensus about it or at least a discussion about its many caveats $\endgroup$
    – Mauricio
    Commented 2 days ago

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I think that the mainstream view is that the Copenhagen interpretation (actually quantum field theory, not Bohr's original QM) is local. The argument that is offered for locality is based on the non-signaling theorem.

I do not think this argument holds water since even explicitly non-local interpretations like Bohmian mechanics obey the non-signaling theorem.

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  • $\begingroup$ What is Copenhagen quantum field theory? Does that include a measurement postulate? $\endgroup$
    – Mauricio
    Commented Jan 23, 2023 at 19:31
  • $\begingroup$ The standard version of QM is not local, and nobody claims it is since it is not a relativistic theory (it assumes a Newtonian background). The field version, QED for electromagnetism, or QFT in general is supposed to be local and it is for these theories that the non-signaling theorem applies. $\endgroup$
    – Andrei
    Commented Jan 25, 2023 at 7:37
  • $\begingroup$ Take a look at this quote from "modern Quantum Mechanics" by Sakurai (page 230) - about EPR: "Consider in particular the following point: Right after observer A performs a measurement on particle 1, how does particle 2 – which may, in principle, be many light years away from particle 1 – get to “know” how to orient its spin so that the remarkable correlations apparent in Table 3.1 are realized?" "We conclude this section by showing that despite these peculiarities, we cannot use spin-correlation measurements to transmit any useful information between two macroscopically separated points." $\endgroup$
    – Andrei
    Commented Jan 25, 2023 at 9:14
  • $\begingroup$ So, we still don't have any local explanation of the EPR experiment, but since we can't send a message in this way, everything is fine. I think such an argument fails, since SR is not concerned with messages (signals that can be controlled by agents), but with any signals. Nevertheless, I think the above quotes resume very well the current mainstream view. $\endgroup$
    – Andrei
    Commented Jan 25, 2023 at 9:18
  • $\begingroup$ The change from weakly correlation to strong correlation happens non-locally. The collapse of superposition is non-local. However information cannot be determined non-locally. So it depends on your definition of local I suppose. $\endgroup$
    – Morphyl
    Commented Jul 9 at 0:59
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Bell's theorem states the following. If you have a theory in which (1) measurement results are represented by stochastic variables (random numbers) and (2) the measurement results and settings on your measurement device don't have a common cause and (3) the predictions of expectation values match those of quantum theory, then the resulting theory is non-local.

I'm going to make a brief digression before getting back to the direct subject of the question. It is not necessarily the case that any theory that agrees with quantum theory is non-local. The equations of motion of quantum theory without collapse that are commonly used to describe real systems are local. They describe physical quantities using Heisenberg picture observables that are represented by matrices not by stochastic variables. Quantum theory without collapse explains Bell correlations as a result of locally inaccessible quantum information carried in decoherent channels:

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

https://arxiv.org/abs/1109.6223

The correlations are established when the measurement results are compared, not when either system is measured separately. So there is a local theory that accounts for Bell correlations: quantum theory without collapse.

Is the Copenhagen Interpretation (CI) local? There is a problem with trying to answer this question. The CI sez that collapse happens but provides no explanation of how and why it happens. The CI also doesn't say what is happening in reality before the collapse. As such the CI's predictions are extremely vague. The measurement results after collapse are represented by stochastic variables, but since there is no specification of where that happens, advocates of the CI could say that the correlations are established when the comparison takes place and the collapse happens after that. I doubt they would say that, but since the theory is terminally vague it functions more like a religion than a scientific theory and we can't make many pronouncements on its actual implications beyond the ex cathedra proclamations of its advocates.

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