Advertisement

Foundations of Physics

, Volume 43, Issue 9, pp 1153–1169 | Cite as

The Scope and Generality of Bell’s Theorem

  • James Owen Weatherall
Article

Abstract

I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.

Keywords

Bell’s theorem Hidden variable theory Joy Christian 

Notes

Acknowledgements

I am grateful to Shelly Goldstein, David Malament, John Manchak, Florin Moldoveanu, Abner Shimony, Howard Stein, and an anonymous referee for helpful comments on a previous draft of this paper. Thank you, too, to Jeff Barrett, Harvey Brown, David Malament, and Tim Maudlin for discussions on these and related topics and to David Hestenes for a helpful email exchange on Clifford algebras. I am especially grateful to Joy Christian for an informative correspondence and for his kind help on this project despite our continued disagreement. Finally, this paper has benefited from audiences at the Southern California Philosophy of Physics Group and the Maryland Foundations of Physics Group, and I am grateful to Christian Wüthrich and Jeff Bub for inviting me to make these presentation.

References

  1. 1.
    Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1(3), 195–200 (1964). Also published in [4] Google Scholar
  2. 2.
    Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966). Also published in [4] ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Bell, J.S.: Bertlmann’s socks and the nature of reality. Ref.TH.2926-CERN (1980). Also published in [4] Google Scholar
  4. 4.
    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, New York (1987) zbMATHGoogle Scholar
  5. 5.
    Christian, J.: Disproof of Bell’s theorem by Clifford algebra valued local variables (2007). arXiv:quant-ph/0703179
  6. 6.
    Christian, J.: Disproof of Bell’s theorem: Further consolidations (2007). arXiv:0707.1333 [quant-ph]
  7. 7.
    Christian, J.: Disproof of Bell’s theorem: Reply to critics (2007). arXiv:quant-ph/0703244
  8. 8.
    Christian, J.: Can Bell’s prescription for physical reality be considered complete? (2008). arXiv:0806.3078 [quant-ph]
  9. 9.
    Christian, J.: Disproofs of Bell, GHZ, and Hardy type theorems and the illusion of entanglement (2009). arXiv:0904.4259 [quant-ph]
  10. 10.
    Christian, J.: Failure of Bell’s theorem and the local causality of the entangled photons (2010). arXiv:1005.4932v2 [quant-ph]
  11. 11.
    Christian, J.: Disproof of Bell’s theorem (2011). arXiv:1103.1879v1 [quant-ph]
  12. 12.
    Christian, J.: What really sets the upper bound on quantum correlations? (2011). arXiv:1101.1958v1 [quant-ph]
  13. 13.
    Christian, J.: Disproof of Bell’s Theorem: Illuminating the Illusion of Entanglement. Brown Walker Press, Boca Raton (2012) Google Scholar
  14. 14.
    Christian, J.: Whither all the scope and generality of Bell’s theorem? (2013). arXiv:2013.1653 [physics.gen-ph]
  15. 15.
    Clauser, J.F., Horne, M.A.: Experimental consequences of objective local theories. Phys. Rev. D, Part. Fields 10(2), 526–535 (1974) ADSCrossRefGoogle Scholar
  16. 16.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880–884 (1969) ADSCrossRefGoogle Scholar
  17. 17.
    Grangier, P.: “Disproof of Bell’s theorem”: more critics (2007). arXiv:0707.2223 [quant-ph]
  18. 18.
    Jarrett, J.P.: On the physical significance of the locality conditions in the Bell arguments. Noûs 18(4), 569–589 (1984) MathSciNetCrossRefGoogle Scholar
  19. 19.
    Jarrett, J.P.: Bell’s theorem: a guide to the implications. In: Cushing, J.T., McMullin, E. (eds.) Philosophical Consequences of Quantum Theory. University of Notre Dame Press, Notre Dame (1989) Google Scholar
  20. 20.
    Malament, D.B.: Notes on Bell’s theorem (2006). Available at http://www.lps.uci.edu/malament/prob-determ/PDnotesBell.pdf
  21. 21.
    Malament, D.B.: Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. University of Chicago Press, Chicago (2012) CrossRefzbMATHGoogle Scholar
  22. 22.
    Moldoveanu, F.: Disproof of Joy Christian’s “Disproof of Bell’s theorem” (2011). arXiv:1109.0535 [quant-ph]
  23. 23.
    Penrose, R., Rindler, W.: Spinors and Space-Time (2 Volumes). Cambridge University Press, New York (1987) Google Scholar
  24. 24.
    Pitowsky, I.: Quantum Probability—Quantum Logic. Springer, New York (1989) zbMATHGoogle Scholar
  25. 25.
    Shimony, A.: Bell’s theorem. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2009). Available at http://plato.stanford.edu/archives/sum2009/entries/bell-theorem/ Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Logic and Philosophy of ScienceUniversity of CaliforniaIrvineUSA

Personalised recommendations