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

Foundations of Physics 21 (2):149-184 (1991)
  Copy   BIBTEX


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



    Upload a copy of this work     Papers currently archived: 94,623

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Non-Local Hidden Variable Theories and Bell's Inequality.Jeffrey Bub & Vandana Shiva - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:45-53.
Algebraic constraints on hidden variables.Arthur Fine & Paul Teller - 1978 - Foundations of Physics 8 (7-8):629-636.
Hidden variables and locality.Jeffrey Bub - 1976 - Foundations of Physics 6 (5):511-525.
Branching space-time analysis of the GHZ theorem.Nuel Belnap & László E. Szabó - 1996 - Foundations of Physics 26 (8):989-1002.
Multiparticle Entanglement.Daniel I. Fivel - 1999 - Foundations of Physics 29 (4):561-570.


Added to PP

95 (#180,258)

6 months
5 (#883,144)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Michael Redhead
Last affiliation: London School of Economics
Jeremy Butterfield
Cambridge University

Citations of this work

On the Significance of the Gottesman–Knill Theorem.Michael E. Cuffaro - 2017 - British Journal for the Philosophy of Science 68 (1):91-121.
Reconsidering No-Go Theorems from a Practical Perspective.Michael E. Cuffaro - 2018 - British Journal for the Philosophy of Science 69 (3):633-655.
Nonlocality and Gleason's lemma. Part 2. Stochastic theories.Andrew Elby - 1990 - Foundations of Physics 20 (11):1389-1397.

View all 8 citations / Add more citations