Fine ways to fail to secure local realism

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Abstract

Since he proved his theorem in 1982, Fine has been challenging the traditional interpretation of the experimental violation of the Bell Inequalities (BI). A natural interpretation of Fine's theorem is that it provides us with an alternative set of assumptions on which to place blame for the failure of the BI, and opens to a new interpretation of the violation of the BI. Fine has a stronger interpretation for his theorem. He claims that his result undermines the traditional interpretation in terms of local realism. The aim of this paper is to understand and to assess Fine's claim. We distinguish three different strategies that Fine uses in order to support his view. We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena.

Section snippets

Bell-type theorems and experiments

Bell-type theorems come in various versions1, but most of them follow the following scheme: some inequalities (the Bell inequalities—henceforth the BI) are derived from a set of assumptions S, and then shown to be violated by some quantum statistical predictions. It is concluded that no model which satisfies all the

A hidden assumption in the traditional derivation?

One way to construct h.v. models is to construe observables as random variables defined over a common classical probability space. Such construction is usually referred to as an “ensemble representation”. It is a formal consequence of an ensemble representation that the joint distributions are well-defined for all pairs of observables, commuting or not. Further, these joint distributions are compatible with the singles as marginals. Hence, by Fine's theorem, some BI hold for such models. Fine

A de facto argument: Fine's prism models

Fine has constructed local realistic models for the Bell experiments, the so-called prism models.16 Fine seems to believe that the existence of his prism models implies that the traditional interpretation of the violation of the BI, according to which no local determinate

Beyond the alternative? Fine's strong claim

Fine's last line of argumentation in favor of his strong claim, i.e. that it is not local realism but rather the definition of the PJPD which is at stake in the violation of the BI, uses the converse of his derivation of the BI, that is, that any model in which the BI hold is equivalent to a model in which the PJPD are well-defined. From this, Fine wants to deduce that any set of assumptions from which the BI are derivable has, in Fine's terms, the “existence of well defined joint

Conclusion

We have argued that:

  • Fine's argument that the definition of joint probabilities is a hidden assumption in the traditional derivations of the BI holds only for a restricted class of h.v. theories, which were ruled out by previous theorems.

  • Fine's argument, to the effect that the existence of his prism models is a de facto argument against the traditional interpretation of Bell-type results, does not hold, because prism models are incompatible with some quantum statistical predictions.

  • Fine's

Acknowledgments

I wish to express my gratitude Guido Bacciagaluppi and Armond Duwell for insightful comments on earlier drafts of this paper. I also wish to thank an anonymous referee for helpful clarifications.

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