David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 53 (3):461 - 504 (1982)
Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory.
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References found in this work BETA
J. S. Bell (2004 ). On the Einstein-Podolsky-Rosen Paradox. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 14--21.
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Citations of this work BETA
Geoffrey Hellman (1992). Bell-Type Inequalities in the Nonideal Case: Proof of a Conjecture of Bell. [REVIEW] Foundations of Physics 22 (6):807-817.
Robert K. Clifton, Michael L. G. Redhead & Jeremy N. Butterfield (1991). Generalization of the Greenberger-Horne-Zeilinger Algebraic Proof of Nonlocality. Foundations of Physics 21 (2):149-184.
Arthur Fine (1984). What is Einstein's Statistical Interpretation, or, is It Einstein for Whom Bell's Theorem Tolls? Topoi 3 (1):23-36.
Miklós Rédei (1987). Reformulation of the Hidden Variable Problem Using Entropic Measure of Uncertainty. Synthese 73 (2):371 - 379.
John F. Halpin (1986). Stalnaker's Conditional and Bell's Problem. Synthese 69 (3):325 - 340.
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