Foundations of Physics

, Volume 45, Issue 5, pp 471–482 | Cite as

Bell’s Theorem and the Issue of Determinism and Indeterminism

  • Michael EsfeldEmail author


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.


Bell’s theorem Determinism Indeterminism Locality  Free choice of measurement settings Bohmian mechanics GRW theory 



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.

Conflict of interest

The author declares that he has no conflict of interest.


  1. 1.
    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bell, J.S., Shimony, A., Horne, M.A., Clauser, J.F.: An exchange on local beables. Dialectica 39, 85–110 (1985)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bohm, D.: A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. Phys. Rev. 85, 166–193 (1952)CrossRefADSzbMATHGoogle Scholar
  4. 4.
    Colbeck, R., Renner, R.: No extension of quantum theory can have improved predictive power. Nat. Commun. (2011). doi: 10.1038/ncomms1416
  5. 5.
    Conway, J.H., Kochen, S.: The strong free will theorem. Not. Am. Math. Soc. 56, 226–232 (2009)zbMATHMathSciNetGoogle Scholar
  6. 6.
    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)]Google Scholar
  7. 7.
    Dorato, M., Esfeld, M.: GRW as an ontology of dispositions. Stud. Hist. Philos. Mod. Phys. 41, 41–49 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Dürr, D., Goldstein, S., Zanghì, N.: Quantum Physics Without Quantum Philosophy. Springer, Berlin (2013)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)CrossRefADSzbMATHMathSciNetGoogle Scholar
  11. 11.
    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)CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Ghirardi, Gian Carlo, Rimini, Alberto, Weber, Tullio: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470–491 (1986)CrossRefADSzbMATHMathSciNetGoogle Scholar
  13. 13.
    Gisin, N.: Stochastic quantum dynamics and relativity. Helv. Phys. Acta 62, 363–371 (1989)MathSciNetGoogle Scholar
  14. 14.
    Gisin, N.: Propensities in a non-deterministic physics. Synthese 89, 287–297 (1991)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Goldstein, S., Norsen, T., Tausk, D.V., Zanghì, N.: Bell’s theorem.’s_theorem (2011)
  16. 16.
    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)zbMATHGoogle Scholar
  17. 17.
    Hofer-Szabó, G., Rédei, M., Szabó, L.E.: The Principle of the Common Cause. Cambridge University Press, Cambridge (2013)CrossRefGoogle Scholar
  18. 18.
    Maudlin, T.: Quantum Non-locality and Relativity, 3rd edn. Wiley-Blackwell, Chichester (2011)CrossRefGoogle Scholar
  19. 19.
    Norsen, T.: Local causality and completeness: Bell vs. Jarrett. Found. Phys. 39, 273–294 (2009)CrossRefADSzbMATHMathSciNetGoogle Scholar
  20. 20.
    Norsen, T.: J. S. Bell’s concept of local causality. Am. J. Phys. 79, 1261–1275 (2011)CrossRefADSGoogle Scholar
  21. 21.
    Price, H.: Time’s Arrow and Archimedes’ Point. New Directions for the Physics of Time. Oxford University Press, Oxford (1996)Google Scholar
  22. 22.
    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. (2010)
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Tumulka, R.: A relativistic version of the Ghirardi–Rimini–Weber model. J. Stat. Phys. 125, 825–844 (2006)CrossRefADSzbMATHMathSciNetGoogle Scholar
  25. 25.
    Tumulka, R.: Comment on the free will theorem. Found. Phys. 34, 186–197 (2007)CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    Tumulka, R.: The point processes of the GRW theory of wave function collapse. Rev. Math. Phys. 21, 155–227 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of LausanneLausanneSwitzerland

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