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Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality

  • Part V. Invited Papers Dedicated To John Stewart Bell
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Abstract

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument be modified in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.

“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”

J. S. Bell

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Authors and Affiliations

  1. Department of History and Philosophy of Science, Cambridge University, Free School Lane, CB2 3RH, Cambridge, United Kingdom

    Robert K. Clifton & Michael L. G. Redhead

  2. Faculty of Philosophy, Cambridge University, Sidgwick Site, Sidgwick Ave., CB3 9DA, Cambridge, United Kingdom

    Jeremy N. Butterfield

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  1. Robert K. Clifton
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  2. Michael L. G. Redhead
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  3. Jeremy N. Butterfield
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This paper is dedicated to the memory of John Bell whose brilliant work has done so much to clarify the foundations of quantum mechanics.

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Clifton, R.K., Redhead, M.L.G. & Butterfield, J.N. Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality. Found Phys 21, 149–184 (1991). https://doi.org/10.1007/BF01889530

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