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Bell’s Inequality and Its Elementary Background

  • Alexander Afriat
  • Franco Selleri

Abstract

Now that the history of the EPR paradox has been considered, its conceptual background will be examined. The underlying philosophy is that of local realism, which, in addition to realism and locality, includes time’s arrow. From these natural and intuitive elements Bell’s inequality, briefly encountered in Chapter 1, is rigorously deduced. Of course it is grossly violated by quantum mechanics, which is therefore inconsistent with the principles represented in the inequality.

Keywords

Quantum Theory Physical Reality Spin Component Local Realism Reality Criterion 
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References

  1. 1.
    D. Bohm, Phys. Rev. 85, 166–193 and 180–193 (1952).MathSciNetADSCrossRefMATHGoogle Scholar
  2. 2.
    L. De Broglie, Une tentative d’interpretation causale et non-lineaire de la mecanique ondula-toire, Paris, Gauthier-Villars (1956).Google Scholar
  3. 3.
    A. Einstein, in: Albert Einstein: Philosopher-Scientist (P. A. Schilpe ed.), Open Court, La Salle (1970), p. 3.Google Scholar
  4. 4.
    Quoted by Max Born, Physics in My Generation, Springer, New York (1969), p. 162.CrossRefGoogle Scholar
  5. 5.
    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777–780 (1935).ADSCrossRefMATHGoogle Scholar
  6. 6.
    E. P. Wigner, Z. Phys. 133, 101–108 (1952).MathSciNetADSMATHGoogle Scholar
  7. 7.
    H. A. Araki and M. M. Yanase, Phys. Rev. 20, 622–626 (1960).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    M. M. Yanase, Phys. Rev. 123, 666–668 (1961).ADSCrossRefGoogle Scholar
  9. 9.
    L. W. Alvarez, in: Proc. 1975 Int. Symp. Lepton and Photon Interactions at High Energies, Stanford (1975), p. 967.Google Scholar
  10. 10.
    A. Einstein, in: Louis de Broglie, Physicien et Penseur (A. George, ed.), Albin Michel, Paris (1953), p. 7.Google Scholar
  11. 11.
    The above derivation of Bell’s inequality is a reformulation of N. D. Mermin’s. Phys. Today April 1985, pp. 38–47.Google Scholar
  12. 12.
    J. S. Bell, in; Foundations of Quantum Mechanics (B. d’Espagnat, ed.), Italian Physical Society, Course IL, Academic Press, New York (1971), pp. 171–181.Google Scholar
  13. 13.
    B. D’Espagnat, Conceptions de la physique contemporaine, Hermann, Paris (1965).Google Scholar
  14. 14.
    F. Selleri, in; Symposium on the Foundations of Modern Physics (K. V Laurikainen et al, eds.), Ed. Frontieres, Paris (1994), pp. 255–272.Google Scholar
  15. 15.
    W. Heisenberg, The Physical Principles of the Quantum Theory, University of Chicago Press (1930), p. 20.MATHGoogle Scholar
  16. 16.
    J. P. Wesley, Classical Quantum Theory, Benjamin Wesley, Blumberg (1996), especially Chap. 6.Google Scholar
  17. 17.
    J. R. Croca, in: Causality and Locality in Modern Physics (S. Jeffers et al, eds.), Kluwer, Dordrecht (1997).Google Scholar
  18. 18.
    G. Binnig and H. Rohrer, Rev. Mod. Phys. 59, 615–625 (1987).ADSCrossRefGoogle Scholar
  19. 19.
    R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. 3, Addison-Wesley, Reading (1965), pp. 1–11.MATHGoogle Scholar
  20. 20.
    J. Von Neumann, in: Les nouvelles theories de la physique; Conference Proceedings, Warsaw 1938, International Institute of Intellectual Cooperation, Paris (1939), pp. 32–40.Google Scholar
  21. 21.
    N. Bohr, in: Les nouvelles theories de la physique; Conference Proceedings, Warsaw 1938, International Institute of Intellectual Cooperation, Paris (1939), pp. 40–41.Google Scholar
  22. 22.
    N. Bohr, Phys. Rev. 48, 696–702 (1935).ADSCrossRefMATHGoogle Scholar
  23. 23.
    J. Von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).MATHGoogle Scholar
  24. 24.
    Quoted in A. Lande, New Foundations of Quantum Mechanics, Cambridge University Press, Cambridge (1965), pp. 147–148.MATHGoogle Scholar
  25. 25.
    G. Lukäks, La distruzione della ragione, Einaudi, Torino (1959), p. 271.Google Scholar
  26. 26.
    For a review see F. Selleri, Quantum Paradoxes and Physical Reality, Kluwer, Dordrecht (1990), especially Chap. 3.CrossRefGoogle Scholar
  27. 27.
    M. Jammer, The Conceptual Development of Quantum Mechanics, Tomash Publishers, New York (1989), p. 179.Google Scholar
  28. 28.
    N. Svartholm, Søren Kierkegaard und die Moderne Physik, University of Gøteborg, preprint (1967). As far as we know the only published version of this paper is N. Svartholm, in: Che cos ‘e la realtá (F. Selleri, ed.), Jaca Book, Milano (1990), p. 113.Google Scholar
  29. 29.
    D. Favrholdt, Riv. Storia Scienza, 2, 445–461 (1985).Google Scholar
  30. 30.
    J. Faye, Niels Bohr: His Heritage and Legacy. An Anti-Realist View of Quantum Mechanics, Kluwer, Dordrecht (1991).CrossRefGoogle Scholar
  31. 31.
    R. N. Moreira, in: Waves and Particles in Light and Matter (A. Van der Merwe et al., eds.), Plenum, New York (1994), p. 395.CrossRefGoogle Scholar
  32. 32.
    Quoted by R. N. Moreira, in: Waves and Particles in Light and Matter (A. Van der Merwe et al., eds.), Plenum, New York (1994), p. 397.Google Scholar
  33. 33.
    L. De Brogue, Une tentative d’interpretation causale et non-lineaire de la mecanique ondula-toire, Paris, Gauthier-Villars (1956).Google Scholar
  34. 34.
    C. Dewdney and B. J. Hiley, Found. Phys. 12, 27–48 (1982).ADSCrossRefGoogle Scholar
  35. 35.
    C. Philippidis, C. Dewdney, and B. J. Hiley, Nuovo dm. 52B, 15–28 (1979).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Alexander Afriat
    • 1
  • Franco Selleri
    • 2
  1. 1.London School of EconomicsLondonEngland
  2. 2.University of BariBariItaly

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