Foundations of Physics Letters

, Volume 19, Issue 7, pp 633–655 | Cite as

Bell Locality and the Nonlocal Character of Nature

Article

Abstract

It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (“Bell Locality”) and the empirically well-supported predictions of quantum theory for the standard EPR-Bell set up. The demonstrated hidden variables are precisely those needed for the derivation of the Bell Inequalities. We thus refute the widespread view that empirical violations of Bell Inequalities leave open a choice of whether to reject (i) locality or (ii) hidden variables. Both principles are indeed assumed in the derivation of the inequalities, but since, as we demonstrate here, (ii) actually follows from (i), there is no choice but to blame the violation of Bell's Inequality on (i). Our main conclusion is thus no Bell Local theory can be consistent with what is known from experiment about the correlations exhibited by separated particles. Aside from our conclusion being based on a different sense of locality this conclusion resembles one that has been advocated recently by H.P. Stapp. We therefore also carefully contrast the argument presented here to that proposed by Stapp.

Key words:

EPR Bell's theorem non-locality Stapp hidden variables 

References

  1. 1.
    1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, Cambridge, 2004).Google Scholar
  2. 2.
    2. H. P. Stapp, “Bell's theorem and world process,” Nuovo Cimento 29B, 270–6 (1975).Google Scholar
  3. 3.
    3. T. Maudlin, Quantum Non-Locality and Relativity, 2nd edn. (Blackwell, Cambridge, MA, 2002).Google Scholar
  4. 4.
    4. D. Dürr, N. Zanghi, and S. Goldstein, “Quantum equilibrium and the role of operators as observables in quantum theory,” J. Stat. Phys. 116, 959–1055 (2004); see in particular Sec. 8: Hidden variables.CrossRefGoogle Scholar
  5. 5.
    5. T. Norsen, “EPR and Bell locality,” quant-ph/0408105, to appear in Are there Quantum Jumps? and On the Present Status of Quantum Mechanics, A. Bassi, D. Dürr, T. Weber, and N. Zanghi, eds. (AIP Conference Proceedings, 2006).Google Scholar
  6. 6.
    6. H. M. Wiseman, “From Eistein's theorem to Bell's theorem: A history of quantum nonlocality,” Contemp. Phys. 47, 79–88 (2006).CrossRefADSGoogle Scholar
  7. 7.
    7. E. Wigner, “Interpretation of quantum mechanics” (1976), reprinted in Quantum Theory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, 1983).Google Scholar
  8. 8.
    8. N. David Mermin, “Hidden variables and the two theorems of John Bell,” Rev. Mod. Phys. 65, 803–815 (1993).CrossRefADSGoogle Scholar
  9. 9.
    9. Einstein, Podolsky, and Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).CrossRefADSGoogle Scholar
  10. 10.
    10. S. Goldstein, “Bohmian mechanics,” The Stanford Encyclopedia of Philosophy, Edward N. Zalta, ed.; http://plato.stanford.edu/entries/qm-bohm; see also R. Tumulka, “Understanding Bohmian mechanics: A dialogue,” Am. J. Phys. 72, 1220–6 (2004).Google Scholar
  11. 11.
    11. H. P. Stapp, “Bell's theorem without hidden variables,” quant-ph/0010047.Google Scholar
  12. 12.
    12. H. P. Stapp, “Nonlocal character of quantum theory,” Am. J. Phys. 65, 300–304 (1997).CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    13. H. P. Stapp, “A Bell-type theorem without hidden variables,” Am. J. Phys. 72, 30–33 (2004).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    14. Lucien Hardy, “Quantum mechanics, local realistic theories, and Lorentz invariant realistic theories,” Phys. Rev. Lett. 68 2981–2984 (1992).CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    15. W. Unruh, “Is quantum mechanics non-local?” Phys. Rev. A 59, 126–130 (1999).CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    16. A. Shimony, “An analysis of Stapp's ‘A Bell-type theorem without hidden variables,’” quant-ph/0404121.Google Scholar
  17. 17.
    17. A. Shimony and H. Stein, “Comment on ‘Nonlocal character of quantum theory,’ …,” Am. J. Phys. 69, 848–853 (2001).CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    18. N. David Mermin, “Nonlocal character of quantum theory?” Am. J. Phys. 66, 920–4 (1998).CrossRefADSGoogle Scholar
  19. 19.
    19. N. David Mermin, “Nonlocality and Bohr's reply to EPR,” quant-ph/9712003.Google Scholar
  20. 20.
    20. H. P. Stapp, “Bell's theorem without hidden variables,” op cit.; see also P. Eberhard, “Bell's Theorem Without Hidden Variables,” Nuovo Cimento 38B, 75–80 (1977).Google Scholar
  21. 21.
    21. P. Eberhard, “Bell's Theorem and the different concepts of locality,” Nuovo Cimento 46B, 392–419 (1978).MathSciNetGoogle Scholar
  22. 22.
    22. J. A. Wheeler, “Law without law” in J. A. Wheeler and W. H. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983).Google Scholar
  23. 23.
    23. Thanks to Arthur Fine who, after reading an initial draft of the current paper, pointed out to me that similar arguments have appeared previously in the literature, e.g.: Brian Skyrms, “Counterfactual definiteness and local causation,” Phil. Sci. 49, 43–50 (1982); Patrick Suppes, “Some remarks on hidden variables and the EPR paradox,” Erkenntnis 16, 311–314 (1981), and references therein.Google Scholar
  24. 24.
    24. N. D. Mermin, “Bringing home the atomic world: Quantum mysteries for anybody,” Am. J. Phys. 49, 940–943 (1981).CrossRefADSGoogle Scholar
  25. 25.
    25. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell's inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    26. L. Ballentine and J. Jarrett, “Bell's theorem: Does quantum mechanics contradict relativity?” Am. J. Phys. 55, 696–701 (1987).CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    27. H. P. Stapp, “Response to ‘Comment on “Nonlocal character of quantum theory,’” by Abner Shimony and Howard Stein …,” Am. J. Phys. 69, 854–9 (2001).CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    28. For some additional discussion of this point, see T. Norsen, “Einstein's boxes,” Am. J. Phys. 73, 164–176 (2005).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Marlboro CollegeMarlboroUSA

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