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.
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References
1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, Cambridge, 2004).
2. H. P. Stapp, “Bell's theorem and world process,” Nuovo Cimento 29B, 270–6 (1975).
3. T. Maudlin, Quantum Non-Locality and Relativity, 2nd edn. (Blackwell, Cambridge, MA, 2002).
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.
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).
6. H. M. Wiseman, “From Eistein's theorem to Bell's theorem: A history of quantum nonlocality,” Contemp. Phys. 47, 79–88 (2006).
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).
8. N. David Mermin, “Hidden variables and the two theorems of John Bell,” Rev. Mod. Phys. 65, 803–815 (1993).
9. Einstein, Podolsky, and Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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).
11. H. P. Stapp, “Bell's theorem without hidden variables,” quant-ph/0010047.
12. H. P. Stapp, “Nonlocal character of quantum theory,” Am. J. Phys. 65, 300–304 (1997).
13. H. P. Stapp, “A Bell-type theorem without hidden variables,” Am. J. Phys. 72, 30–33 (2004).
14. Lucien Hardy, “Quantum mechanics, local realistic theories, and Lorentz invariant realistic theories,” Phys. Rev. Lett. 68 2981–2984 (1992).
15. W. Unruh, “Is quantum mechanics non-local?” Phys. Rev. A 59, 126–130 (1999).
16. A. Shimony, “An analysis of Stapp's ‘A Bell-type theorem without hidden variables,’” quant-ph/0404121.
17. A. Shimony and H. Stein, “Comment on ‘Nonlocal character of quantum theory,’ …,” Am. J. Phys. 69, 848–853 (2001).
18. N. David Mermin, “Nonlocal character of quantum theory?” Am. J. Phys. 66, 920–4 (1998).
19. N. David Mermin, “Nonlocality and Bohr's reply to EPR,” quant-ph/9712003.
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).
21. P. Eberhard, “Bell's Theorem and the different concepts of locality,” Nuovo Cimento 46B, 392–419 (1978).
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).
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.
24. N. D. Mermin, “Bringing home the atomic world: Quantum mysteries for anybody,” Am. J. Phys. 49, 940–943 (1981).
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).
26. L. Ballentine and J. Jarrett, “Bell's theorem: Does quantum mechanics contradict relativity?” Am. J. Phys. 55, 696–701 (1987).
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).
28. For some additional discussion of this point, see T. Norsen, “Einstein's boxes,” Am. J. Phys. 73, 164–176 (2005).
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Norsen, T. Bell Locality and the Nonlocal Character of Nature. Found Phys Lett 19, 633–655 (2006). https://doi.org/10.1007/s10702-006-1055-9
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DOI: https://doi.org/10.1007/s10702-006-1055-9