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- Summary
- Bell's theorem is often interpreted as a claim that either locality or realism is wrong. A recent theorem claims that realism is a consequence of the assumption of locality, so that locality must be wrong in any case.

Recently, Bricmont, Goldstein and Hemmick wrote two (quite similar) papers

1. http://de.arxiv.org/abs/1808.01648

2. http://de.arxiv.org/abs/1906.06687

in which they present a Bell-like theorem that involves only perfect correlations and does not involve any inequalities. They claim that this version proves nonlocality, i.e. that the theorem cannot be interpreted merely as a disproof of realism. (By realism one means what is often called "hidden variables" in the literature, which in the papers is mathematically precisely defined as

Paper 1, pages 21-22:

Paper 2, pages 30-31:

If they are right, then local interpretations of QM are necessarily wrong. Nevertheless, I suspect that those who are convinced that QM is a local theory are unlikely to change their mind by the arguments of those two papers. There are several attitudes that can make those people immune to this proof of nonlocality. Some of the popular attitudes of this kind are

How about you? Does the theorem convince you that one must conclude that QM is necessarily nonlocal? Or if it doesn't, which attitude do you use against that conclusion?

1. http://de.arxiv.org/abs/1808.01648

2. http://de.arxiv.org/abs/1906.06687

in which they present a Bell-like theorem that involves only perfect correlations and does not involve any inequalities. They claim that this version proves nonlocality, i.e. that the theorem cannot be interpreted merely as a disproof of realism. (By realism one means what is often called "hidden variables" in the literature, which in the papers is mathematically precisely defined as

*non-contextual value-maps*.) The following quotes from the papers illustrate their main points:Paper 1, pages 21-22:

*"The main point of our paper is to show that no choice between the rejection of “realism” or of locality has to be made, since the existence of a non-contextual value-map is a consequence of locality and the perfect correlations.*

It is also true that such a non-contextual value-map cannot exist (section 4). But, since the perfect correlations are a well-established empirical fact, the only logical conclusion is that locality is false.

So, “realism” (in the sense of the existence of a non-contextual value-map) is not an assumption in our reasoning but is a consequence of the assumption of locality (and the perfect correlations)."It is also true that such a non-contextual value-map cannot exist (section 4). But, since the perfect correlations are a well-established empirical fact, the only logical conclusion is that locality is false.

So, “realism” (in the sense of the existence of a non-contextual value-map) is not an assumption in our reasoning but is a consequence of the assumption of locality (and the perfect correlations)."

Paper 2, pages 30-31:

*"Here and in [11] we give a simpler argument, but using the maximally entangled states introduced by Schrödinger: for those states, one can, for each observable associated to one system, construct another observable associated to the second system,*

possibly far away from the first one, such that the results of the measurement of both observables are perfectly correlated. Then, assuming locality, those results must preexist their measurement. But assuming that, in general, observables have values before their measurement leads to a contradiction. Hence, the assumption of locality is false."possibly far away from the first one, such that the results of the measurement of both observables are perfectly correlated. Then, assuming locality, those results must preexist their measurement. But assuming that, in general, observables have values before their measurement leads to a contradiction. Hence, the assumption of locality is false."

If they are right, then local interpretations of QM are necessarily wrong. Nevertheless, I suspect that those who are convinced that QM is a local theory are unlikely to change their mind by the arguments of those two papers. There are several attitudes that can make those people immune to this proof of nonlocality. Some of the popular attitudes of this kind are

**a) Anti-philosophic attitude:**The theorem involves a mathematical object called non-contextual value-map which, by itself, does not help to make measurable predictions. Hence the theorem is philosophic and irrelevant for science.**b) Operational attitude:**QM is local in the operational sense and the proved nonlocality is irrelevant for physics because it cannot be used for practical instantaneous signaling.**c) Informational attitude:**Interpretations such as QBism and relational interpretation would deny that perfect correlation and locality imply the existence of the value maps. First, they would argue that values are created by measurements or interactions between the subsystems, which excludes the existence of value maps. Second, they would argue that correlations do not exist until someone or something observes or detects the correlation, which is a local physical process. For instance, they would argue that it does not make sense to talk about correlations between Alice and Bob until, for instance, Alice sends a signal to Bob so that Bob can*know*that he is correlated with Alice.How about you? Does the theorem convince you that one must conclude that QM is necessarily nonlocal? Or if it doesn't, which attitude do you use against that conclusion?