It's explained in the footnote of the article. Bell's experiment rules out local hidden variable theories but it's still possible to formulate non-local hidden variable theories that work.
> "Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables, such as De Broglie–Bohm theory, etc)"
Local hidden variable theories are not possible, but any local theory is not possible, assuming definite outcomes of experiments (many worlds might be considered local, but there is no definite outcome).
Non-local hidden variable theories are quite possible, do quite well in explaining a number of facets of QM, and, in fact, inspired Bell's work.
Nevertheless, Einstein certainly was no fan of the non-locality though he did not know of Bell's argument, of course.
Local hidden variable theories are ruled out by Bell's Theorem. Not hidden variable theories in general. I realise GP was describing a local HVT, but it's still an important distinction.
Sure it can. Bell's theorem implies you can have locality or hidden variables, but not both. de Broglie-Bohm is an example of a non-local hidden-variable theory.
They test a CHSH Bell inequality in this paper. This rules out local hidden variable theories. Non-local hidden variable (NLHV) theories are another matter entirely. Indeed, some NLHV theories may reproduce the predictions of quantum theory exactly.
Not sure how broadly you're willing to draw the borders around "non-local" but I'd argue most quantum physicists take Bell's inequality to suggest that hidden variable theories are impossible because something non-local isn't happening.
That's not quite accurate. Local hidden variable theories have been proven wrong, but pilot wave theory is a nonlocal hidden variable theory. Bell himself was a proponent of pilot wave theory.
> Bell's theorem states that any physical theory that incorporates local realism cannot reproduce all the predictions of quantum mechanical theory. Because numerous experiments agree with the predictions of quantum mechanical theory, and show differences between correlations that could not be explained by local hidden variables, the experimental results have been taken by many as refuting the concept of local realism as an explanation of the physical phenomena under test. For a hidden variable theory, if Bell's conditions are correct, the results that agree with quantum mechanical theory appear to indicate superluminal effects, in contradiction to the principle of locality.
As I understand it, Bell showed that, if quantum mechanics is correct, then any deterministic hidden variable theory would either have to be non-local or non-causal.
Aspect et al demonstrated experimentally that quantum mechanics is correct in the Bell sense.
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