International Journal of Theoretical Physics

, Volume 54, Issue 12, pp 4410–4422 | Cite as

A Survey of the ESR Model for an Objective Reinterpretation of Quantum Mechanics

  • Claudio Garola


Contextuality and nonlocality (hence nonobjectivity of physical properties) are usually maintained to be unavoidable features of quantum mechanics (QM), following from its mathematical apparatus. Moreover they are considered as basic in quantum information processing. Nevertheless they raise still unsolved problems, as the objectification problem in the quantum theory of measurement. The extended semantic realism (ESR) model offers a way out from these difficulties by reinterpreting quantum probabilities as conditional rather than absolute and embedding the mathematical formalism of QM into a broader mathematical framework. A noncontextual hidden variables theory can then be constructed which justifies the assumptions introduced in the ESR model and proves its objectivity. Both linear and nonlinear time evolution occur in this model, depending on the physical environment, as in QM. In addition, the ESR model implies modified Bell’s inequalities that do not necessarily conflict with QM, supplies different mathematical representations of proper and improper mixtures, provides a general framework in which the local interpretations of the GHZ experiment obtained by other authors are recovered, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.


Contextuality Nonlocality Objectification problem Nonobjectivity ESR model “no-go” theorems GHZ experiment Quantum logic 


  1. 1.
    Busch, P., Lahti, P.J., Mittelstaedt, P.: The Quantum Theory of Measurement. Springer, Berlin (1991, 1996)Google Scholar
  2. 2.
    Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966)CrossRefADSMATHGoogle Scholar
  3. 3.
    Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)MathSciNetMATHGoogle Scholar
  4. 4.
    Bell, J.S.: On the Einstein-Podolski-Rosen paradox. Physics 1, 195–200 (1964)Google Scholar
  5. 5.
    Zeilinger, A.: A foundational principle for quantum mechanics. Found. Phys. 29, 631–643 (1999)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Clifton, R., Bub, J., Halvorson, H.: Characterizing quantum theory in terms of information theoretic constraints. Found. Phys. 33, 1561–1591 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolski-Rosen-Bohm gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982)CrossRefADSGoogle Scholar
  8. 8.
    Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    Genovese, M.: Research on hidden variables theories: a review on recent progresses. Phys. Rep. 413, 319–396 (2005)MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    Garola, C., Sozzo, S.: The ESR model: a proposal for a noncontextual and local Hilbert space extensions of QM. Europhys. Lett. 86, 20009–20015 (2009)CrossRefADSGoogle Scholar
  11. 11.
    Garola, C., Sozzo, S.: Embedding quantum mechanics into a broader noncontextual theory: a conciliatory result. Int. J. Theor. Phys. 49, 3101–3117 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Garola, C., Sozzo, S.: Generalized observables, Bell’s inequalities and mixtures in the ESR model. Found. Phys. 41, 424–449 (2011)MathSciNetCrossRefADSMATHGoogle Scholar
  13. 13.
    Garola, C., Sozzo, S.: The modified Bell inequality and its physical implications in the ESR model. Int. J. Theor. Phys. 50, 3787–3799 (2011)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Garola, C., Sozzo, S.: Representation and interpretation of mixtures in the ESR model. Theor. Math. Phys. 168, 912–923 (2011)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Garola, C., Sozzo, S.: Extended representations of observables and states for a noncontextual reinterpretation of QM. J. Phys. A: Math. Theor. 45, 075303–075315 (2012)MathSciNetCrossRefADSGoogle Scholar
  16. 16.
    Garola, C., Persano, M., Pykacz, J., Sozzo, S.: Finite local models for the GHZ experiment. Int. J. Theor. Phys. 53, 622–644 (2014)CrossRefMATHGoogle Scholar
  17. 17.
    Garola, C., Sozzo, S.: Recovering quantum logic within an extended classical framework. Erkenn 78, 399–419 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Garola, C., Persano, M.: Embedding quantum mechanics into a broader noncontextual theory. Found. Sci. 19(3), 217–239 (2014)Google Scholar
  19. 19.
    Garola, C., Sozzo, S., Wu, J.: Outline of a generalization and reinterpretation of quantum mechanics recovering obectivity. ArXiv:1402.4394v2 [quant-ph] (2014)
  20. 20.
    Santos, E.: The failure to perform a loophole-free test of Bell’s inequality supports local realism. Found. Phys. 34, 1643–1673 (2004)MathSciNetCrossRefADSMATHGoogle Scholar
  21. 21.
    Santos, E.: Bell’s theorem and the experiments: increasing empirical support for local realism? Stud. Hist. Philos. Mod. Phys. 36, 544–565 (2005)CrossRefMATHGoogle Scholar
  22. 22.
    Garola, C.: The ESR model: reinterpreting quantum probabilities within a realistic and local framework. In: Adenier, G., Khrennikov, A., Lahti, P., Man’ko, V., Nieuwenhuizen, T (eds.) Quantum Theory: Reconsideration of Foundations-4, pp 247–252. American Institute of Physics, Ser. Conference Proceedings 962, Melville (2007)Google Scholar
  23. 23.
    Accardi, L.: Some loopholes to save quantum nonlocality. In: Adenier, G., Khrennikov, A (eds.) Foundations of Probability and Physics-3, pp 1–20. American Institute of Physics, Ser. Conference Proceedings 750, Melville (2005)Google Scholar
  24. 24.
    Khrennikov, A.: Interpretations of Probability. De Gruyter, Berlin (1998, 2009)Google Scholar
  25. 25.
    Khrennikov, A., Smolyanov, O.G., Truman, A.: Kolmogorov probability spaces describing Accardi models for quantum correlations. Open. Syst. Inf. Dyn. 12(4), 371–384 (2005)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Hess, K., Philipp, W.: Exclusion of time in Mermin’s proof of Bell-type inequalities. In: Khrennikov, A. (ed.) Quantum Theory: Reconsideration of Foundations-2. Ser. Math. Model. 10, pp 243–254. Växjö University Press, Växjö (2003)Google Scholar
  27. 27.
    Hess, K., Philipp, W.: Bell’s theorem: critique of proofs with and without inequalities. In: Adenier, G., Khrennikov, A (eds.) Foundations of Probability and Physics-3, pp 150–155. American Institute of Physics, Ser. Conference Proceedings 750, Melville (2005)Google Scholar
  28. 28.
    Khrennikov, A: Quantum probabilities and violation of CHSH-inequality from classical random signals and threshold type detection scheme. Prog. Theor. Phys. 128, 31–58 (2012)CrossRefADSMATHGoogle Scholar
  29. 29.
    Khrennikov, A.: Born’s rule from measurements of classical signals by threshold detectors which are properly calibrated. J. Mod. Opt. 59, 667–678 (2012)CrossRefADSGoogle Scholar
  30. 30.
    Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1982)MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Mermin, N.D.: Hidden variables and the two theorems of John Bell. Rev. Mod. Phys. 65, 803–815 (1993)MathSciNetCrossRefADSGoogle Scholar
  32. 32.
    Szabó, L.E., Fine, A.: A local hidden variable theory for the GHZ experiment. Phys. Lett. A 295, 229–240 (2002)MathSciNetCrossRefADSMATHGoogle Scholar
  33. 33.
    Beltrametti, E.G., Cassinelli, G.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)MATHGoogle Scholar
  34. 34.
    Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theor. Phys. 38, 289–358 (1999)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    d’Espagnat, B.: Conceptual Foundations of Quantum Mechanics. Benjamin, Reading (1976)Google Scholar
  36. 36.
    Timpson, C.G., Brown, H.R.: Proper and improper separability. Int. J. Quant. Inf. 3, 679–690 (2005)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsUniversity of SalentoLecceItaly

Personalised recommendations