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Thus, we see that local causality condition (1) is mathematically equivalent to the assumption of joint probabilities, $p(A_1,A_2,B_1,B_2)$. The latter is a form of realism: complementary observables are treated as mere numbers [...].

This quote is taken from "Quantum non-locality - it ain't necessarily so" by Zukowski and Brukner. In this paper they primarily argue (as far as I understood) that the assumptions "locality" (in terms of factorizability) and "realism" (in the form depicted in the quote above) in Bell's Theorem are on equal footing [In contrast to views described in papers such as this one written by Norsen]. My question concerns the following scenario: If one adopts the view that both assumptions ("reality" and "locality") are indeed on equal footing, and then one decides to reject "realism"(existence of the joint probability $p(A_1,A_2,B_1,B_2)$) in order to restore locality - does this really suffice to rule out all possible forms of realism?

The existence of $p(A_1,A_2,B_1,B_2)$ requires that the possible measurement values exist, no matter which observables are measured on either side and more importantly the values exist prior to the measurements. But I can imagine that other forms of realism, e.g. nonlocal real hidden variables, do not require the existence of this joint probability $p(A_1,A_2,B_1,B_2)$, since the values of system $B$ can change depending on what outcomes are obtained on $A$ and vice versa. Additionally I wonder if another way of bypassing Zukowski's reality condition would be contextual hidden variables (since joint probabilites such as $p(A_1,A_2,B_1,B_2)$ look like a noncontextual state assignment, which is ruled out by the Kochen-Specker-Theorem anyway.)

I do not doubt the derived equality between their notions of "locality" (factorization condition) and "realism" (existence of joint probability) in Zukowski's and Brukner's paper cited above, but I'm certainly unsure if rejecting this "form of realism" would rule out all forms of hidden variables. I'm aware that this is a quite subtle topic, but nevertheless I hope I could convey my issue - can anyone help to clarify?

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I'm not sure what you mean by 'reality and locality on an equal footing.

The EPR experiment, tests both

  1. locality
  1. quantum state realism.

The first, locality, means that influences cannot travel faster than the speed of light.

The second, quantum state realism, means that a quantum state has a definite value at all times. This is generally an unstated assumption in classical mechanics, including electromagnetism. For example, it goes without saying that a particle has a defnite position at all times. It's only with the advent with QM that this came under question. It's this that I take what you mean by 'realism'.

It's for this reason Einstein declared the QM to be incomplete. Given he was responsible for reintroducing locality into gravity, it's not surprising that he would think so.

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  • $\begingroup$ I did not express clearly what I mean with "both assumptions are on equal footing", sorry - it is often claimed that "realism" can be derived from "locality" (as in the paper by Norsen I've cited above) and according to this reasoning "locality" should be abandoned instead of "realism". In the paper by Zukowski and Brukner they argue differently; they state that "realism" and "locality" are equivalent assumptions and that there's no clue which of them should be denied. And my question concerns explicitly their notion of "realism" and if this realism condition is general enough@Mozibur Ullah $\endgroup$
    – Juri V
    Apr 5, 2021 at 12:40
  • $\begingroup$ @Juri V:Well, I've just glanced at the paper. One thing to note is what they call 'counter-factual definiteness' is what I call 'value definiteness'. And its this aspect, as I've signalled above, is what people implicitly think of as real or realism. $\endgroup$
    – Mozibur Ullah
    Apr 5, 2021 at 12:47
  • $\begingroup$ @Juri V: The point about Bells experiment is that they show that value definiteness or counter-factual definiteness does not hold in QM. It then follows from the EPR experiment that QM must be non-local. This is the phenomena of entanglement. $\endgroup$
    – Mozibur Ullah
    Apr 5, 2021 at 12:52
  • $\begingroup$ @juri V: The non-locality of entanglement hasn't been widely tested by experiment and has been under-reported - but there was one reported in Nature, that reported to be at least $10,000c$, that is, ten at least ten thousand times the speed of light. $\endgroup$
    – Mozibur Ullah
    Apr 5, 2021 at 12:54
  • $\begingroup$ @Juri V: In fact, they report it to be 100,000 x faster!!! $\endgroup$
    – Mozibur Ullah
    Apr 5, 2021 at 12:59
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It is not clear to me what ground a generalized notion of 'realism' covers in your view.

From the very conclusion of the paper you cite, one can read "Individual events may have spontaneous, acausal nature." Wouldn't that be a form of realism?

In other words, if 'realism' is not to be taken as the exact same thing as 'hidden variables', then the paper explicitely gives room for other forms of realism. On the other hand if 'realism' does mean 'hidden variables', then those have to be non-local anyway, and so must also be acausal (as per relativity). So we find again the escape door given in the conclusion, that "Individual events may have spontaneous, acausal nature."

Maybe the problem here is that for many of us, realism implies determinism. But it is not so. Realism in philosophy is the standpoint that a given thing [...] exists independently of knowledge, thought, or understanding. This is not invalidated by the violation of Bell's inequalities (a violation which is, as an experimental result, very real itself).

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  • $\begingroup$ Maybe my question is rather: Does abandoning "reality" in Zukowski's sense (existence of this joint probability) exclude hidden variables and is doing so a possibility to restore locality? More generally I read these papers because I want to understand how one can argue for a local and "anti-realist" (by that I mean the wave function is not considered as an element of reality) worldview, since there are a lot of interpretations that do so (e.g. QBism). $\endgroup$
    – Juri V
    Apr 5, 2021 at 13:12
  • $\begingroup$ I'm aware that realism is a broad notion with a lot of different meanings. in this context here I considered "realism" to be the same as the existence of hidden variables - especially because I want to make sense to the view that Bell's theorem might be considered as no go theorem of hidden variables. $\endgroup$
    – Juri V
    Apr 5, 2021 at 13:16

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