Abstract
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell’s theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.
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References
Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)
Bell, J.S., Shimony, A., Horne, M.A., Clauser, J.F.: An exchange on local beables. Dialectica 39, 85–110 (1985)
Bohm, D.: A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. Phys. Rev. 85, 166–193 (1952)
Colbeck, R., Renner, R.: No extension of quantum theory can have improved predictive power. Nat. Commun. (2011). doi:10.1038/ncomms1416
Conway, J.H., Kochen, S.: The strong free will theorem. Not. Am. Math. Soc. 56, 226–232 (2009)
de Broglie, L.: La nouvelle dynamique des quanta. In: Electrons et photons. Rapports et discussions du cinquième Conseil de physique tenu à Bruxelles du 24 au 29 octobre 1927 sous les auspices de l’Institut international de physique Solvay, pp. 105–132. Gauthier-Villars, Paris (1928). [English translation in Bacciagaluppi, G., Valentini, A.: Quantum Theory at the Crossroads. Reconsidering the 1927 Solvay Conference, pp. 341–371. Cambridge University Press, Cambridge (2009)]
Dorato, M., Esfeld, M.: GRW as an ontology of dispositions. Stud. Hist. Philos. Mod. Phys. 41, 41–49 (2010)
Dürr, D., Goldstein, S., Zanghì, N.: Quantum Physics Without Quantum Philosophy. Springer, Berlin (2013)
Frankfurt, H.G.: Freedom of the will and the concept of a person. J. Philos. 68, 5–20 (1971). Reprinted in Frankfurt, H.G.: The Importance of What We care About. Philosophical Essays. Cambridge: Cambridge University Press. Chapter 2, (1988)
Ghirardi, G.C., Grassi, R., Benatti, F.: Describing the macroscopic world: closing the circle within the dynamical reduction program. Found. Phys. 25, 5–38 (1995)
Ghirardi, G.C., Pearle, P., Rimini, A.: Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Phys. Rev. A 42, 78–89 (1990)
Ghirardi, Gian Carlo, Rimini, Alberto, Weber, Tullio: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986)
Gisin, N.: Stochastic quantum dynamics and relativity. Helv. Phys. Acta 62, 363–371 (1989)
Gisin, N.: Propensities in a non-deterministic physics. Synthese 89, 287–297 (1991)
Goldstein, S., Norsen, T., Tausk, D.V., Zanghì, N.: Bell’s theorem. http://www.scholarpedia.org/article/Bell’s_theorem (2011)
Goldstein, S., Tausk, D.V., Tumulka, R., Zanghì, N.: What does the free will theorem actually prove? Not. Am. Math. Soc. 57, 1451–1453 (2010)
Hofer-Szabó, G., Rédei, M., Szabó, L.E.: The Principle of the Common Cause. Cambridge University Press, Cambridge (2013)
Maudlin, T.: Quantum Non-locality and Relativity, 3rd edn. Wiley-Blackwell, Chichester (2011)
Norsen, T.: Local causality and completeness: Bell vs. Jarrett. Found. Phys. 39, 273–294 (2009)
Norsen, T.: J. S. Bell’s concept of local causality. Am. J. Phys. 79, 1261–1275 (2011)
Price, H.: Time’s Arrow and Archimedes’ Point. New Directions for the Physics of Time. Oxford University Press, Oxford (1996)
Seevinck, M.P.: Can quantum theory and special relativity peacefully coexist? Invited white paper for Quantum Physics and the Nature of Reality, John Polkinghorne 80th Birthday Conference. St Annes College, Oxford. 26–29 September 2010. http://arxiv.org/abs/1010.3714 (2010)
Seevinck, M.P., Uffink, J.: Not throwing out the baby with the bathwater: Bell’s condition of local causality mathematically ‘sharp and clean’. In: Dieks, D., Gonzalez, W., Hartmann, S., Uebel, T., Weber, M. (eds.) Explanation, Prediction and Confirmation. New Trends and Old Ones Reconsidered, pp. 425–450. Springer, Dordrecht (2011)
Tumulka, R.: A relativistic version of the Ghirardi–Rimini–Weber model. J. Stat. Phys. 125, 825–844 (2006)
Tumulka, R.: Comment on the free will theorem. Found. Phys. 34, 186–197 (2007)
Tumulka, R.: The point processes of the GRW theory of wave function collapse. Rev. Math. Phys. 21, 155–227 (2009)
Wüthrich, C.: Can the world be shown to be indeterministic after all? In: Beisbart, C., Hartmann, S. (eds.) Probabilities in Physics, pp. 365–390. Oxford University Press, Oxford (2011)
Acknowledgments
I’m grateful to Nicolas Gisin and Travis Norsen for discussions of the topic of this paper and to an anonymous referee for very helpful comments on the original submission.
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Esfeld, M. Bell’s Theorem and the Issue of Determinism and Indeterminism. Found Phys 45, 471–482 (2015). https://doi.org/10.1007/s10701-015-9883-8
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DOI: https://doi.org/10.1007/s10701-015-9883-8