Foundations of Physics

, Volume 45, Issue 9, pp 1002–1018 | Cite as

Einstein’s Boxes: Incompleteness of Quantum Mechanics Without a Separation Principle

  • Carsten HeldEmail author


Einstein made several attempts to argue for the incompleteness of quantum mechanics (QM), not all of them using a separation principle. One unpublished example, the box parable, has received increased attention in the recent literature. Though the example is tailor-made for applying a separation principle and Einstein indeed applies one, he begins his discussion without it. An analysis of this first part of the parable naturally leads to an argument for incompleteness not involving a separation principle. I discuss the argument and its systematic import. Though it should be kept in mind that the argument is not the one Einstein intends, I show how it suggests itself and leads to a conflict between QM’s completeness and a physical principle more fundamental than the separation principle, i.e. a principle saying that QM should deliver probabilities for physical systems possessing properties at definite times.


Completeness of quantum mechanics Hidden variables  No-hidden-variable proofs Separability 


  1. 1.
    Fine, A.: The Shaky Game: Einstein, Realism and the Quantum Theory, Chapter 5. University of Chicago Press, Chicago (1986)Google Scholar
  2. 2.
    Einstein, A.: Quanten-Mechanik und Wirklichkeit. Dialectica 2, 320 (1948)zbMATHCrossRefGoogle Scholar
  3. 3.
    Howard, D.: Einstein on locality and separability. Stud. Hist. Philos. Sci. 16, 171 (1985)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Held, C.: Die Bohr-Einstein-Debatte. Quantenmechanik und physikalische Wirklichkeit. Schöningh, Paderborn (1998)Google Scholar
  5. 5.
    Norsen, T.: Einstein’s boxes. Am. J. Phys. 73, 164 (2005)CrossRefADSGoogle Scholar
  6. 6.
    Shimony, A.: Comment on Norsen’s defense of Einstein’s ‘box argument’. Am. J. Phys. 73, 177 (2005)CrossRefADSGoogle Scholar
  7. 7.
    Norton, J.D.: Little boxes: a simple implementation of the Greenberger, Horne, and Zeilinger result for spatial degrees of freedom. Am. J. Phys. 79, 182 (2011)CrossRefADSGoogle Scholar
  8. 8.
    Popper, K.R.: Quantum Theory and the Schism in Physics. Routledge, London (1982)Google Scholar
  9. 9.
    Butterfield, J.: Quantum theory and the mind. In: Proceedings of the Aristotelian Society (Supp.) LXIX, vol. 113 (1995)Google Scholar
  10. 10.
    Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  11. 11.
    Held, C.: Axiomatic quantum mechanics and completeness. Found. Phys. 38, 707 (2008)zbMATHMathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Held, C.: Incompatibility of standard completeness and quantum mechanics. Int. J. Theor. Phys. 51, 2974 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)zbMATHGoogle Scholar
  14. 14.
    Weinberg, S.: Lectures on Quantum Mechanics. Cambridge University Press, Cambridge (2013)zbMATHGoogle Scholar
  15. 15.
    Beltrametti, E., Cassinelli, G.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)zbMATHGoogle Scholar
  16. 16.
    Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447 (1966); reprint in [13], pp. 1–13.Google Scholar
  17. 17.
    Kochen, S., Specker, E.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59 (1967)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Peres, A.: Incompatible results of quantum measurements. Phys. Lett. A 151, 107 (1990)MathSciNetCrossRefADSGoogle Scholar
  19. 19.
    Mermin, D.: Simple unified form of the major no-hidden-variables theorems. Phys. Rev. Lett. 65, 3373 (1990)zbMATHMathSciNetCrossRefADSGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Universität ErfurtErfurtGermany

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