Foundations of Physics

, Volume 17, Issue 8, pp 813–857 | Cite as

Locality, reflection, and wave-particle duality

  • Mioara Mugur-Schächter


Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity.

In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability aredistinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability arenot incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does notestablish thatany Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is asyntactic fact.

The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—isnot factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ,thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified conceptof which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability.

The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept offolded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as aparticular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments.

Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity.


Quantum Mechanic Causal Representation Acceptable Representation Syntactic Property Quantum Mechanical Formalism 
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  1. 1.
    J. S. Bell,Physics 1, 195 (1964).Google Scholar
  2. 2.
    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969).Google Scholar
  3. 3.
    J. F. Clauser and M. A. Horne,Phys. Rev. D 10, 526 (1974).Google Scholar
  4. 4.
    S. J. Freedman and J. F. Clauser,Phys. Rev. Lett. 28, 938 (1972).Google Scholar
  5. 5.
    E. S. Fry and R. C. Thompson,Phys. Rev. Lett. 37, 465 (1976).Google Scholar
  6. 6.
    M. Lamehi-Rachti and W. Mitting,Phys. Rev. D 14, 2543 (1976).Google Scholar
  7. 7.
    R. A. Holt, Ph.D. Thesis, Harvard University, 1973.Google Scholar
  8. 8.
    A. Aspect,Phys. Rev. D 14, 1944 (1976); A. Aspectet al., Phys. Rev. Lett. 49, 1804 (1982).Google Scholar
  9. 9.
    B. d'Espagnat,Conceptions de la physique contemporaine (Hermann, Paris, 1965);A la recherche du réel (Gauthier-Villars, Paris, 1979);Une incertaine réalité (Gauthier-Villars, Paris, 1985).Google Scholar
  10. 10.
    A. Shimony, inProceedings, Ideas and New Techniques in Quantum Measurement Theory (New York, January 21–24, 1986), published inAnn. N. Y. Acad. Sc., 1986; henceforth referred to as NITQMT.Google Scholar
  11. 11.
    O. Costa de Beauregard,Found. Phys. 8, 103 (1979); NITQMT.Google Scholar
  12. 12.
    F. Selleri, “The EPR paradox fifty years later,” inFundamental Processes in Atomic Collision Physics, H. Kleinpoppen, J. S. Briggs, and H. O. Lutz, eds. (Plenum, New York, 1985); NITQMT.Google Scholar
  13. 13.
    P. Pearl, in NITQMT.Google Scholar
  14. 14.
    A. O. Barut and P. Meystre,Phys. Lett. A 105, 458 (1984).Google Scholar
  15. 15.
    N. D. Mermin,Phys. Today 38, April 1985; in NITQMT.Google Scholar
  16. 16.
    H. P. Seipp, in NITQMT.Google Scholar
  17. 17.
    G. W. Mackey,Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963).Google Scholar
  18. 18.
    P. Suppes, inLogic and Probabilities in Quantum Mechanics, P. Suppes, ed. (Reidel, Dordrecht, 1976).Google Scholar
  19. 19.
    B. C. Van Fraasen, inContemporaty Research in Quantum Theory, C. A. Hooker, ed. (Reidel, Dordrecht, 1973).Google Scholar
  20. 20.
    M. Mugur-Schächter,Found. Phys. 13, 4 (1983).Google Scholar
  21. 21.
    C. Cohen-Tannoudji, B. Diu, and F. Laloe (Hermann, Paris, 1973).Google Scholar
  22. 22.
    M. Mugur-Schächter, inQuantum Mechanics a Half Century Later, J. L. Lopes and M. Paty, eds. (Reidel, Dordrecht, 1977);Ann. Fond. Louis de Broglie,2, 94 (1976).Google Scholar
  23. 23.
    A. Einstein, inAlbert Einstein: Philosopher and Scientist, P. A. Schilpp, ed. (Open Court, La Salle, 1949).Google Scholar
  24. 24.
    L. de Broglie,Thèse, Paris, 1924.Google Scholar
  25. 25.
    L. de Broglie,J. Phys. Radiat. (Paris) 6, 8, 225 (1927);Tentative d'Interprétation causale et nonlinéaire de la mécanique ondulatoire (Gauthier-Villars, Paris, 1956).Google Scholar
  26. 26.
    M. Mugur-Schächter, D. Evrard, and F. Thieffine,Phys. Rev. D 6, 3397 (1972).Google Scholar
  27. 27.
    D. Evrard,Nuovo Cimento 76, 2, 139 (1983).Google Scholar
  28. 28.
    L. Cohenet al., J. Math. Phys. 21, 794 (1979); L. Cohen,J. Chem. Phys. 80, 4277 (1984);25, 2402 (1984); inNon-Equilibrium Quantum Statistical Physics, G. Moore and M. O. Scully, eds. (Plenum, New York, 1986); in NITQMT.Google Scholar
  29. 29.
    J. Leggett, in NITQMT.Google Scholar
  30. 30.
    S. Chakravarty, in NITQMT.Google Scholar
  31. 31.
    S. Washburn and R. A. Webb, in NITQMT.Google Scholar
  32. 32.
    C. Tesche, in NITQMT.Google Scholar
  33. 33.
    G. J. Dolan, in NITQMT.Google Scholar
  34. 34.
    A. Zajonc, in NITQMT.Google Scholar
  35. 35.
    J. D. Franson, in NITQMT.Google Scholar
  36. 36.
    S. A. Werner, in NITQMT.Google Scholar
  37. 37.
    P. Grangier and A. Aspect, in NITQMT.Google Scholar
  38. 38.
    H. Rauch, in NITQMT.Google Scholar
  39. 39.
    A. Zeilinger, in NITQMT.Google Scholar
  40. 40.
    J. M. Levy-Leblond,La Recherche 17(175), 394 (1986).Google Scholar
  41. 41.
    E. P. Wigner,Am. J. Phys. 31, 6 (1963).Google Scholar
  42. 42.
    D. Bohm and B. J. Hiley,Found. Phys. 11, 179 (1981);11, 529 (1981).Google Scholar
  43. 43.
    J. P. Vigier,Nuovo Cimento Lett. 24, 258 (1979); in NITQMT.Google Scholar
  44. 44.
    G. Lochak,Epist. Lett., May 1976, p. 1;Found. Phys. 6, 173 (1976).Google Scholar
  45. 45.
    M. Mugur-Schächter,Epist. Lett., March 1976, p. 1 (1976); inEinstein 1879–1955, Colloque du Centenaire (Collège de France, CNRS, 1979).Google Scholar
  46. 46.
    H. P. Stapp,Nuovo Cimento B 40, 191 (1977).Google Scholar
  47. 47.
    C. F. von Weizsacker, inFoundations of Modern Physics, P. Lahti and P. Mittelstaedt, eds. (World Scientific, Singapore, 1986); henceforth referred to as FMP.Google Scholar
  48. 48.
    J. A. Wheeler, in FMP.Google Scholar
  49. 49.
    E. Beltrametti, in FMP.Google Scholar
  50. 50.
    H. Neumann, in FMP.Google Scholar
  51. 51.
    P. Mittelstaedt, in FMP.Google Scholar
  52. 52.
    C. Randall, in FMP.Google Scholar
  53. 53.
    F. E. Schroeck, in FMP.Google Scholar
  54. 54.
    R. Peierls, in FMP.Google Scholar
  55. 55.
    M. Jammer, in FMP.Google Scholar
  56. 56.
    O. Piccioni, in FMP.Google Scholar
  57. 57.
    H. P. Noyes, in FMP.Google Scholar
  58. 58.
    D. Aerts, in FMP.Google Scholar
  59. 59.
    D. W. Wood, in FMP.Google Scholar
  60. 60.
    N. Rosen, in FMP.Google Scholar
  61. 61.
    F. Rohlrich, in FMP.Google Scholar
  62. 62.
    B. C. Van Fraassen, in FMP.Google Scholar
  63. 63.
    M. Kupczynski, in FMP.Google Scholar
  64. 64.
    Y. Shadmi, in FMP.Google Scholar
  65. 65.
    K. Y. Laurikainen, in FMP.Google Scholar
  66. 66.
    J. Rayski, in FMP.Google Scholar
  67. 67.
    G. W. Series, in FMP.Google Scholar
  68. 68.
    C. P. Enz, in FMP.Google Scholar
  69. 69.
    F. Bonsack, Colloquium on hidden variables and locality, running for more than 10 years inEpist. Lett. and animated by personal contributions.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Mioara Mugur-Schächter
    • 1
  1. 1.Mécanique Quantique et Structures de L'InformationUniversité de ReimsReims CedexFrance

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