Skip to main content
SpringerLink
Log in

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

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. It must be noted that the term “realistic” is used here in a very weak sense. Well known interpretations or modifications of QM, as Bohm’s theory, multi-world interpretations and GRW theory, are “realistic” in a much stronger sense and will not be considered in this paper.

  2. An intuitive explanation of this result can be given as follows: the detection probabilities change with the measurement that is performed, and the subset of individual objects that is detected generally is not a fair sample of the set of all objects that are produced. This argument resembles the argument that has been often raised to question the results of Aspect’s and similar experiments, in which fair sampling is usually assumed [20, 21]. But unfair sampling depends on the features of real measuring devices in the latter argument: hence it would not occur in the case of idealized measurements. It depends instead on the physical properties of the individual objects, hence on different physical variables, in the ESR model, so that it may occur also in the case of idealized measurements [22]. We add that the conventional interpretation of the “no-go” theorems has been questioned in particular by several authors in the framework of a statistical interpretation of QM that maintains the standard interpretation of quantum probabilities [23–27]. The criticism of this “statistical opposition” leads to avoid nonlocality of QM, while contextuality is preserved and explained, in the case of photons, by taking into account the thresholds that occur in real detectors [28, 29]. Our present view is obviously different, for it refers to a “realistic” interpretation of QM and circumvents the “no-go” theorems by modifying the standard interpretation of quantum probabilities, thus avoiding contextuality, hence nonlocality.

References

  1. Busch, P., Lahti, P.J., Mittelstaedt, P.: The Quantum Theory of Measurement. Springer, Berlin (1991, 1996)

  2. Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966)

    Article  ADS  MATH  Google Scholar 

  3. Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MathSciNet  MATH  Google Scholar 

  4. Bell, J.S.: On the Einstein-Podolski-Rosen paradox. Physics 1, 195–200 (1964)

    Google Scholar 

  5. Zeilinger, A.: A foundational principle for quantum mechanics. Found. Phys. 29, 631–643 (1999)

    Article  MathSciNet  Google Scholar 

  6. Clifton, R., Bub, J., Halvorson, H.: Characterizing quantum theory in terms of information theoretic constraints. Found. Phys. 33, 1561–1591 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  8. Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  9. Genovese, M.: Research on hidden variables theories: a review on recent progresses. Phys. Rep. 413, 319–396 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. Garola, C., Sozzo, S.: Embedding quantum mechanics into a broader noncontextual theory: a conciliatory result. Int. J. Theor. Phys. 49, 3101–3117 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garola, C., Sozzo, S.: Generalized observables, Bell’s inequalities and mixtures in the ESR model. Found. Phys. 41, 424–449 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Garola, C., Sozzo, S.: Representation and interpretation of mixtures in the ESR model. Theor. Math. Phys. 168, 912–923 (2011)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  ADS  Google Scholar 

  16. Garola, C., Persano, M., Pykacz, J., Sozzo, S.: Finite local models for the GHZ experiment. Int. J. Theor. Phys. 53, 622–644 (2014)

    Article  MATH  Google Scholar 

  17. Garola, C., Sozzo, S.: Recovering quantum logic within an extended classical framework. Erkenn 78, 399–419 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Garola, C., Persano, M.: Embedding quantum mechanics into a broader noncontextual theory. Found. Sci. 19(3), 217–239 (2014)

  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. Santos, E.: The failure to perform a loophole-free test of Bell’s inequality supports local realism. Found. Phys. 34, 1643–1673 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Santos, E.: Bell’s theorem and the experiments: increasing empirical support for local realism? Stud. Hist. Philos. Mod. Phys. 36, 544–565 (2005)

    Article  MATH  Google Scholar 

  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)

  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. Khrennikov, A.: Interpretations of Probability. De Gruyter, Berlin (1998, 2009)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  30. Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  31. Mermin, N.D.: Hidden variables and the two theorems of John Bell. Rev. Mod. Phys. 65, 803–815 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  32. Szabó, L.E., Fine, A.: A local hidden variable theory for the GHZ experiment. Phys. Lett. A 295, 229–240 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Beltrametti, E.G., Cassinelli, G.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  34. Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theor. Phys. 38, 289–358 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  35. d’Espagnat, B.: Conceptual Foundations of Quantum Mechanics. Benjamin, Reading (1976)

    Google Scholar 

  36. Timpson, C.G., Brown, H.R.: Proper and improper separability. Int. J. Quant. Inf. 3, 679–690 (2005)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, University of Salento, 73100, Lecce, Italy

    Claudio Garola

Authors
  1. Claudio Garola
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claudio Garola.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garola, C. A Survey of the ESR Model for an Objective Reinterpretation of Quantum Mechanics. Int J Theor Phys 54, 4410–4422 (2015). https://doi.org/10.1007/s10773-015-2618-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2618-y

Keywords

Search

Navigation