Advertisement

Foundations of Physics

, Volume 43, Issue 6, pp 769–791 | Cite as

Bell’s Theorem: Two Neglected Solutions

  • Louis Vervoort
Article

Abstract

Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be violated, even if they are local according to usual definitions. Violation of the Bell inequality is retraced to violation of ‘measurement independence’. These results emphasize the importance of studying the premises of the Bell inequality in realistic systems.

Keywords

Bell’s theorem Superdeterminism Supercorrelation Measurement independence Correlated spin systems Ising lattices 

Notes

Acknowledgements

I would like to thank, for many stimulating discussions, Gilles Brassard, Mario Bunge, Emmanuel M. Dissakè, Henry E. Fischer, Yvon Gauthier, Gerhard Grössing, Andrei Khrennikov, Marian Kupczynski, Jean-Pierre Marquis and Eduardo Nahmad.

References

  1. 1.
    Bell, J.S.: Physics 1, 195–200 (1964) Google Scholar
  2. 2.
    Bell, J.S.: J. Phys. (Paris) 42, C2-41–C2-62 (1981) CrossRefGoogle Scholar
  3. 3.
    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge Univ. Press, Cambridge (2004) MATHCrossRefGoogle Scholar
  4. 4.
    Jarrett, J.P.: Noûs 18, 569 (1984) MathSciNetCrossRefGoogle Scholar
  5. 5.
    Shimony, A.: In: Penrose, R. (ed.) Quantum Concepts in Space and Time, p. 182. Oxford Univ. Press, London (1986) Google Scholar
  6. 6.
    Hall, M.J.W.: Phys. Rev. A 84, 022102 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    Brans, C.: Int. J. Theor. Phys. 27, 219 (1988) CrossRefGoogle Scholar
  8. 8.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic, New York (2002) CrossRefGoogle Scholar
  9. 9.
    ‘t Hooft, G.: Entangled quantum states in a local deterministic theory (2009). arXiv:0908.3408v1 [quant-ph]
  10. 10.
    Khrennikov, A.: Interpretations of Probability. de Gruyter, Berlin (2008) Google Scholar
  11. 11.
    Hall, M.J.W.: Phys. Rev. Lett. 105, 250404 (2010) ADSCrossRefGoogle Scholar
  12. 12.
    Clauser, J., Horne, M.: Phys. Rev. D 10, 526–535 (1974) ADSCrossRefGoogle Scholar
  13. 13.
    Weihs, G., Jennewein, T., Simon, C., Weinfurter, H., Zeilinger, A.: Phys. Rev. Lett. 81, 5039–5043 (1998) MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Bell, J.S.: Epistemol. Lett. 9, 11 (1976) Google Scholar
  15. 15.
    Shimony, A., Horne, M.A., Clauser, J.S.: Epistemol. Lett. 13, 9 (1976) Google Scholar
  16. 16.
    Bell, J.S.: Epistemol. Lett. 15, 79 (1977) Google Scholar
  17. 17.
    Shimony, A.: Epistemol. Lett. 18, 1 (1978) Google Scholar
  18. 18.
    d’Espagnat, B.: Phys. Rep. 110, 201 (1984) MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Phys. Rev. Lett. 23, 880–884 (1969) ADSCrossRefGoogle Scholar
  20. 20.
    Clauser, J.F., Shimony, A.: Bell’s theorem. Rep. Prog. Phys. 41, 1881 (1978) ADSCrossRefGoogle Scholar
  21. 21.
    Stapp, H.P.: Phys. Rev. D 3, 1303 (1971) ADSCrossRefGoogle Scholar
  22. 22.
    Mermin, D.: Phys. Today 1985, 38–47 (1985) CrossRefGoogle Scholar
  23. 23.
    Eberhard, P.H.: Nuovo Cimento 38B, 75–80 (1977) ADSGoogle Scholar
  24. 24.
    Craig, E. (ed.): Routledge Encyclopedia of Philosophy. Routledge, London (1998) Google Scholar
  25. 25.
    Bunge, M.: Chasing Reality: Strife over Realism. Univ. Toronto Press, Toronto (2006) Google Scholar
  26. 26.
    Jammer, M.: The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective. Wiley-Interscience, New York (1974) Google Scholar
  27. 27.
    Bohr, N.: Nature 136, 1025–1026 (1935) CrossRefGoogle Scholar
  28. 28.
    Aspect, A.: Nature 398, 189–190 (1999) ADSCrossRefGoogle Scholar
  29. 29.
    Fine, A.: Phys. Rev. Lett. 48(5), 291–295 (1982) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    Forman, P.: In: McCormach, R. (ed.) Historical Studies in the Physical Sciences, vol. 3, pp. 1–115. University of Pennsylvania Press, Philadelphia (1971) Google Scholar
  31. 31.
    Bohm, D.: Phys. Rev. 85, 180–193 (1952) MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Vervoort, L.: Europhys. Lett. 50(2), 142–147 (2000) ADSCrossRefGoogle Scholar
  33. 33.
    Spinoza: Ethics. In: Curley, E., Translator, The Collected Writings of Spinoza, vol. 1. Princeton Univ. Press, Princeton (1985) Google Scholar
  34. 34.
    Della Rocca, M.: Spinoza. Routledge, London (2008) Google Scholar
  35. 35.
    Graumann, C.F., Moscovici, S. (eds.): Changing Conceptions of Conspiracy. Springer, New York (1987) Google Scholar
  36. 36.
    De la Peña, L., Cetto, A.: The Quantum Dice: An Introduction to Stochastic Electrodynamics. Kluwer Academic, Dordrecht (1996) Google Scholar
  37. 37.
    Grössing, G., et al.: Ann. Phys. 327, 421 (2012) ADSMATHCrossRefGoogle Scholar
  38. 38.
    Khrennikov, A.: J. Phys. Conf. Ser. 306, 012021 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    Couder, Y., Protière, S., Fort, E., Boudaoud, A.: Nature 437, 208 (2005) ADSCrossRefGoogle Scholar
  40. 40.
    Couder, Y., Fort, E.: Phys. Rev. Lett. 97, 154101 (2006) ADSCrossRefGoogle Scholar
  41. 41.
    Vervoort, L.: In: D’Ariano, M., et al. (eds.), Am. Inst. Phys. Conf. Proceedings, FPP6, p. 348 (2012) Google Scholar
  42. 42.
    Vervoort, L.: The Interpretation of Quantum Mechanics and of Probability: Identical Role of the ‘Observer’ (2011). arXiv:1106.3584
  43. 43.
    Nieuwenhuizen, T.: In: Accardi, L. (ed.) AIP Conf. Proc., vol. 1101, Melville, New-York, pp. 127–133 (2009). CrossRefGoogle Scholar
  44. 44.
    Kupczynski, M.: Phys. Lett. A 116, 417–422 (1986) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Yeomans, J.M.: Statistical Mechanics of Phase Transitions. Oxford Science Publ., Oxford (1992) Google Scholar
  46. 46.
    Feynman, R.P.: Statistical Mechanics, 11th edn. Addison-Wesley, Redwood City (1988) Google Scholar
  47. 47.
    Vervoort, L.:. Bell’s theorem and highly correlated systems. arXiv:1211.1411 [quant-ph]
  48. 48.
    Sachdev, S.: Quantum Phase Transitions, 2nd edn. Cambridge Univ. Press, Cambridge (2011) MATHCrossRefGoogle Scholar
  49. 49.
    Einstein, A.: Dialectica 320 (1948) Google Scholar
  50. 50.
    Hoefer, C.: Causal Determinism. In: Zalta, E.N. (ed.), The Stanford Enc. of Philosophy (2010). http://plato.stanford.edu/archives/spr2010/entries/determinism-causal Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of MontrealMontrealCanada

Personalised recommendations