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Nonlocality and Gleason's lemma. Part I. Deterministic theories

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

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker “paradox” in quantum mechanics.

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References

  1. J. Bell,Rev. Mod. Phys. 38, 447 (1966).

    Google Scholar 

  2. A. Gleason,J. Math. Mech. 6, 885 (1967).

    Google Scholar 

  3. S. Kochen and E. Specker,J. Math. Mech. 17, 59 (1967).

    Google Scholar 

  4. P. Heywood and H. Redhead,Found. Phys. 13, 481 (1983).

    Google Scholar 

  5. A. Stairs,Philos. Sci. 50, 587 (1983).

    Google Scholar 

  6. F. Belinfante,A Survey of Hidden Variables Theories (Pergamon Press, Oxford, 1973).

    Google Scholar 

  7. A. Shimony,Br. J. Philos. Sci. 35, 25 (1984).

    Google Scholar 

  8. D. Bohm and J. Bub,Rev. Mod. Phys. 38, 453 (1966).

    Google Scholar 

  9. W. Demopoulos, inStudies in the Foundations of Quantum Mechanics, P. Suppes, ed. (PSA, East Lansing, Michigan, 1980), p. 119.

    Google Scholar 

  10. G. Svetlichny and H. Brown, “Contextualist realism in quantum mechanics,” unpublished manuscript, 1990.

  11. M. Redhead,Incompleteness, Nonlocality and Realism (Clarendon Press, Oxford, 1987).

    Google Scholar 

  12. B. van Fraassen, inContemporary Research in the Foundations and Philosophy of Quantum Theory, C. Hooker, ed. (Reidel, Dordrecht, 1973), p. 80.

    Google Scholar 

  13. D. Bohm,Phys. Rev. 85, 166, 180 (1952).

    Google Scholar 

  14. D. Bohm and B. Hiley,Phys. Rep. 144, 321 (1987).

    Google Scholar 

  15. J. Bell,Found. Phys. 12, 989 (1982).

    Google Scholar 

  16. A. Elby,Found. Phys. 20, 1389 (1990).

    Google Scholar 

  17. J. Bell,Physics,1, 195 (1964).

    Google Scholar 

  18. J. Bell, inProceedings of the International School of Physics “Enrico Fermi,” Course IL: Foundations of Quantum Mechanics, B. d'Espagnat, ed. (Academic, New York, 1971), p. 171.

    Google Scholar 

  19. C. Dewdneyet al., J. Phys. A. 20, 4717 (1987).

    Google Scholar 

  20. D. Greenberger, M. Horne, and A. Zeilinger, in M. Kafatos, ed.,Bell's Theorem, Quantum Theory and Conceptions of the Universe (Kluwer Academic, Dordrecht, 1989), pp. 73–76.

    Google Scholar 

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Brown, H.R., Svetlichny, G. Nonlocality and Gleason's lemma. Part I. Deterministic theories. Found Phys 20, 1379–1387 (1990). https://doi.org/10.1007/BF01883492

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  • DOI: https://doi.org/10.1007/BF01883492

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