Review of Local Hidden Variable Theories

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Main Question or Discussion Point

Marco Genovese has put out a review that fairly well summarizes where things are at in tests of Bell's Theorem. He has done similar papers previously, and the references are quite comprehensive (there are 505, and they cover the spectrum).

Research on Hidden Variable Theories: a review of recent progresses

An except:

The transition from the XIX century point of view of a perfectly deterministic nature described by classical mechanics to the actual quantum mechanical point of view of a probabilistic world has been difficult and largely debated and still many points at the very foundations of quantum mechanics need a clarification. It should also be noticed that whilst this new paradigm has been largely accepted by physicists community, its assimilation in diffused culture is still rather limited.

Furthermore, as we have seen, a conclusive experiment falsifying in an absolutely uncontroversial way local realism is still missing.

More in details, for what concerns local hidden variable theories, since Bell theorem it is known that a general answer about their validity can be given by an experiment. In the last 40 years various experiments have addressed this problem: strong indications favouring standard quantum mechanics have been obtained, but no conclusive experiment has yet been performed, mainly due to low detection efficiencies that demand for additional assumptions.

Nevertheless, relevant progresses toward this goal have been made in the last ten years and in my opinion an ultimate experiment could not be far in the future.

However, we have to acknowledge that this personal opinion is not generally shared: on one side some authors deem that the large amount of experimental data disfavouring Local Hidden Variable Theories is already largely sufficient for excluding them, on the other side other authors (see for example [505]) claim that the lack of a conclusive experiment after 40 years and in particular the ”resistance” of detection loophole to be eliminated could point out a practical impossibility of falsifying local realism. These discussion largely involve methodological questions [475,476,477,478] which are amply beyond the purposes of this paper.

Even if Local Realistic Theorem will be excluded by an ultimate Bell inequalities experiment, non-local hidden variable theory will still remain a possible alternative to standard quantum mechanics. Following the discussion of last sections, in our opinion a large space still remains for relevant contributions to study this possibility both from a theoretical and an experimental point of view.
 

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Even if Local Realistic Theorem will be excluded by an ultimate Bell inequalities experiment, non-local hidden variable theory will still remain a possible alternative to standard quantum mechanics. Following the discussion of last sections, in our opinion a large space still remains for relevant contributions to study this possibility both from a theoretical and an experimental point of view.
You should have said non-locally causal hidden variable theories ...
The diffusion equation is perfectly local, albeit ``signals'' can go faster than the speed of light in vacuum.
 

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