Bell's Theorem Assumes Classicality

There is currently a debate on whether the Wikipedia article on Toggle the table of contents Bell's theorem should say that it proves nonlocality. It does not, but people keep arguing that it does. So did Bell, in his later life. The article correctly says:

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories given some basic assumptions about the nature of measurement.

There are some hidden assumptions: no retrocausality, no parallel universes, and no superdeterminism.

A new paper addresses this issue:

Gomori, Marton and Hoefer, Carl (2023) Classicality and Bell's Theorem. [Preprint]

A widespread view among physicists is that Bell's theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view.

It explains:

Many physicists are unimpressed by Bell’s theorem. A widespread view is that Bell’s reasoning rests upon an implicit assumption of “classicality” that directly go against the fundamental principles of quantum mechanics (QM). According to such an understanding, the violation of Bell’s inequalities poses no challenge to our causal picture of the world (locality, in particular), but simply reinforces the fact that QM is not classical. One proponent of such a view is Reinhard Werner, who concisely puts it like this (Werner 2014a, p. 4):

Bell showed (maybe against his own intentions ...) that classicality and locality together lead to false empirical conclusions. Of course, all the talk about the non-locality of quantum mechanics really says [is] that any classical extension violates locality ...

In line with this picture, physicist have developed various interpretations of quantum theory that are claimed to be local and non-classical. Among recent variants are Werner’s operational quantum mechanics (Werner 2014a,b) and Robert Griffiths’s consistent histories approach (Griffiths 2020).

Others object to this view. Criticizing Werner’s position about the EPR argument and Bell’s theorem, Tim Maudlin (2014b, pp. 1-2) writes:

Werner thinks that Bell and Einstein and I have all tacitly made an assumption of which we are unaware, an assumption he labels C for ‘classicality’. ... Werner concedes that Bell proved that any classical theory that violates his inequalities must be non-local. But deny classicality and the arguments no longer go through.

That's right. Assuming a local hidden variable theory is essentially the same as assuming classicality. QM does not make that assumption, so Bell's theorem says nothing about QM. Several QM interpretations are local. QM physicists are correct that Bell's theorem has no relevance to them.

The Nobel Prize was recently given to Bell theorem tests, but the citation pointedly avoid saying that anyone proved nonlocality.

The paper goes on to make these points.

Bell does indeed assume classicality. It prefers to say that he has "standard causal-statistical assumptions", and these imply classicality. So it is correct to say Bell's theorem is about classical mechanics, not QM.

Some people define locality in a way that assumes classicality. For those people, all non-classical theories are nonlocal by definition, and this has nothing to do with Bell's theorem. It is just a wrong definition.

Philosophers and physicists are at an impasse, with physicists following QM and philosophers pursuing what they would like to believe.

It ends with:

As philosophers, we would only ask that the physicists refrain from making two sorts of statements (i) Saying that the QM treatment of EPRB is perfectly local (though they can perfectly well say that the QM treatment is not overtly non-local!). (ii) Saying that Bell did not prove what many philosophers think he proved, because he made a tacit and inappropriate presupposition of “classicality” in his argument.

This is funny. The whole paper explains that leading QM interpretations are local, and that Bell made a classicality assumption. The assumption is explicit in Bell's earlier papers, and concealed in his later ones, but it is always made.

In other words, physicists tell the truth, and it embarrasses philosophers who cling to mystical beliefs in nonlocality.