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Do the Bell Inequalities Require the Existence of Joint Probability Distributions?

Published online by Cambridge University Press:  01 April 2022

George Svetlichny ,
Michael Redhead ,
Harvey Brown  and
Jeremy Butterfield
George Svetlichny
Affiliation:
Departamento de Matematica Pontificia Universidade Católica do Rio de Janeiro
Michael Redhead
Affiliation:
History and Philosophy of Science Department Cambridge University
Harvey Brown
Affiliation:
Philosophy Sub-Faculty Oxford University
Jeremy Butterfield
Affiliation:
Philosophy Faculty Cambridge University
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Abstract

Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do not impugn the common view that local realists are committed to the Bell inequality.

Type
Research Article
Information
Philosophy of Science , Volume 55 , Issue 3 , September 1988 , pp. 387 - 401
Copyright
Copyright © 1988 by the Philosophy of Science Association

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Footnotes

†

Ken Regan made extremely useful suggestions related to the mathematical issues involved in the paper, and David Wood helped us see further implications of the inequality-conforming cases discussed in Section 2. We are very grateful also to Arthur Fine, Robert Weingard, Thomas Brody and Nancy Cartwright for comments on an earlier version. One of us (G. S.) thanks CNPq and FINEP, agencies of the Brazilian government, for financial support.

References

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