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Foundations of Physics

, Volume 42, Issue 4, pp 544–554 | Cite as

Bell Inequalities as Constraints on Unmeasurable Correlations

  • Costantino Budroni
  • Giovanni MorchioEmail author
Article

Abstract

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A i 〉, 〈B〉, 〈A i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlationA 1 A 2〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.

Keywords

Bell inequalities Unmeasurable correlations Boole algebras Extension of partial probability theories 

References

  1. 1.
    Bell, J.S.: Physics 1, 195 (1964) Google Scholar
  2. 2.
    Fine, A.: Phys. Rev. Lett. 48, 291 (1982) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Garg, A., Mermin, N.D.: Found. Phys. 14, 1 (1984) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Pitowsky, I.: Quantum Probability Quantum Logic. Springer, Berlin (1989) zbMATHGoogle Scholar
  5. 5.
    Pitowsky, I.: Br. J. Philos. Sci. 45, 95 (1994) MathSciNetCrossRefGoogle Scholar
  6. 6.
    Boole, G.: Philos. Trans. R. Soc. Lond. 152, 225 (1862) CrossRefGoogle Scholar
  7. 7.
    Griffiths, R.B.: Found. Phys. 41, 705 (2011) MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Hardy, L.: Phys. Rev. Lett. 68, 2981 (1992) MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Stapp, H.P.: Am. J. Phys. 65, 300 (1997) MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Mermin, N.D.: Am. J. Phys. 66, 920 (1998) MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    Stapp, H.P.: arXiv:quant-ph/9711060v1 (1997)
  12. 12.
    Budroni, C., Morchio, G.: J. Math. Phys. 51, 122205 (2010) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Am. J. Phys. 58, 1131 (1990) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935) ADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Mermin, N.D.: Phys. Rev. Lett. 65, 3373 (1990) MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Cohen, O.: arXiv:1004.3011v1 (2010)
  17. 17.
    Nisticò, G., Sestito, A.: Found. Phys. 41, 1263 (2011) MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de Física Aplicada IIUniversidad de SevillaSevillaSpain
  2. 2.Dipartimento di Fisica dell’Università and INFNPisaItaly

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