Fine ways to fail to secure local realism
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 , 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:
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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.
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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.
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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.
References (43)
Einstein on locality and separability
Studies in History and Philosophy of Science
(1985)Modeling the singlet state with local variables
Physics Letters
(1999)- et al.
A local hidden variable theory for the GHZ experiment
Physics Letters
(2002) Worlds in the Everett interpretation
Studies in History and Philosophy of Modern Physics
(2002)Everett and structure
Studies in History and Philosophy of Modern Physics
(2003)- et al.
Measurement of quantum mechanical operators
Physical Review
(1960) - Bell, J. S. (1964). On the Einstein–Podolski–Rosen paradox. In Bell, J. S. (1987). Speakable and unspeakable in quantum...
- Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. In Bell, J. S. (1987). Speakable and...
- Bell, J. S. (1971). Introduction to the hidden-variable question. In Bell, J. S. (1987). Speakable and unspeakable in...
- Bell, J. S. (1976). The theory of local beables. In Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics...