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Bell and Non-Locality

  • C. K. Raju
Part of the Fundamental Theories of Physics book series (FTPH, volume 65)

Abstract

Does time have a non-trivial local structure? This question is new to physics, but central to the rest of this exposition. We explain how the notion of a structured time may be formulated. If time in reality is structured then physics cannot be based on differential equations alone, but needs to be founded on a new logic. The relation of such a new logic to quantum logic is postponed till Chapter VIB, while questions about the global structure of time are postponed till Chapter VII.

The previous chapter concluded by recommending the hypothesis of a tilt in the arrow of time. This hypothesis has two consequences: a structured time and non-locality. We outline the first consequence and indicate how most recognized new features about time in q.m. fit into the perspective of a (microphysically) structured time, whereas hidden variable theories deny the existence of this structure by supposing that ‘reality’ cannot but be definite. The rest of this chapter examines the physical acceptability of non-locality in the context of Bell’s inequalities.

We develop the background and state the inequalities. We point out the difficulty with inefficient detectors and try to correct the popular misconception that the inequalities have been conclusively violated in experiments. Without rejecting q.m., and without accepting hidden variables, we argue that the intuitive notion of locality is fuzzy and unreliable, while difficulties in the mathematical formulation of the notion of locality make ‘non-locality’ merely a disreputable tag. Finally, we point out that nothing in classical physics justifies the polemic of spookiness applied to non-locality — for several centuries, locality has remained a desirable metaphysical requirement, rarely satisfied by physical theory.

Keywords

Classical Physic Structure Time Intuitive Notion Tense Logic Spacelike Separation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes and References

  1. 1.
    N. Rescher and A. Urquhart, Temporal Logic ( Wien: Springer, 1971 ).zbMATHCrossRefGoogle Scholar
  2. 2.
    W. H. Newton-Smith, The Structure of Time, Routledge and Kegan Paul, London, 1974.Google Scholar
  3. 3.
    Rescher, Ref. 1, tries to relate the U-calculus to the measurement of time by beginning with a set T of ‘instants’ and a metric (or pseudo-metric) on it. This induces a U-relation that is irreflexive, asymmetric, and transitive, provided one can fmd two ‘instants’ to, ti, such that Utoti. Such a U-relation, obtained by globalizing the past and future at one instant of time, turns out to be counter-intuitive and also counter-physical when the local (physical) earlier-later relationships are not globally consistent.Google Scholar
  4. 4.
    For instance, in the one-dimensional case of two like charges without radiation damping or any other external forces, people have attempted to prove the uniqueness of solutions provided the charges stay separated by a distance which is ‘a large multiple of the radius of the universe’. We recall that the higher-dimensional case is qualitatively different. See, e.g., R. D. Driver, Phys. Rev., 19, 1098–1107 (1979).Google Scholar
  5. 5.
    The paradigm is an observable with non-degenerate discrete (preferably finite) spectrum. The difficulty is that von Neumann’s collapse postulate does not trivially generalise to the continuous spectrum case, as he had thought.Google Scholar
  6. 6.
    Strictly, the terminology of spin detection or spin-meters may be preferable.Google Scholar
  7. 7.
    EPR and other papers on measurement theory are reproduced in J.A. Wheeler and W.H. Zurek (eds), Quantum Theory and Measurement (Princeton: Univ. Press, 1983). The original reference is: A. Einstein, B Podolsky, N. Rosen, Phys. Rev., 47, 777 (1935).Google Scholar
  8. 8.
    D. Bohm, Quantum Theory, Prentice-Hall, New Jersey, 1951.Google Scholar
  9. 9.
    S. Kochen and E. Specker, J. Math. Mech., 17, 59 (1967). Reprinted along with other relevant papers, such as Gleason’s in C. A. Hooker (ed) The Logico-Algebraic Approach to Quantum Mechanics, D. Reidel, Dordrecht, 1983.Google Scholar
  10. 10.
    J. M. Jauch and C. Piron, Helv. Phys. Acta 36, 827 (1963).MathSciNetzbMATHGoogle Scholar
  11. 11.
    G.W. Mackey, Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.Google Scholar
  12. 12.
    A. M. Gleason [1956] reproduced in Hooker, Ref. 9.Google Scholar
  13. 13.
    A detailed account of these no-hidden-variable theorems and the resulting constraints on hidden variable theories may be found in F. J. Belinfante, A Survey of Hidden Variable Theories,Pergamon Press, Oxford, 1973. See also Bell’s 1966 paper, Ref. 15 or 16 below.Google Scholar
  14. 14.
    D. Bohm, ‘Quantum theory in terms of “hidden” variables I,’ Phys. Rev., 85, 166–179 (1952); ‘A suggested interpretation of the quantum theory in terms of “hidden” variables II,’ Phys. Rev., 85, 180–93 (1952).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    J. S. Bell, Rev. Mod. Phys., 38, 458–62 (1966). This paper was prepared prior to the more famous paper in Physics, 1, 195 (1964).Google Scholar
  16. 16.
    J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Univ. Press 1987) pp 45–46. The book contains a collection of all the papers of Bell on the philosophy of quantum mechanics.Google Scholar
  17. 17.
    e.g. J. F. Clauser and A. Shimony, Rep. Prog. Phys., 41, 1881 (1978); A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett., 47, 460 1981); 49, 91 (1982); A. Aspect, J. Dalibard, and G. Roger Phys. Rev. Lett., 49, 1804 (1982). W. Perrie et al, Phys. Rev. Lett., 54, 1790 (1985).CrossRefGoogle Scholar
  18. 18.
    G. Zukav, The Dancing Wu-Li Masters (N.Y.: Flamingo, 1981 ). The book is, otherwise, a well-written popular introduction.There have been more serious attempts at generalization to telepathy, telekinesis etc., by some physicists such as O. Costa de Beauregard.Google Scholar
  19. 19.
    O. Penrose and I.C. Percival, Proc. Phys. Soc., 79, 605 (1962).MathSciNetADSzbMATHCrossRefGoogle Scholar
  20. 20.
    Bell 1966, Ref. 15, or chapter 1 of Ref. 16.Google Scholar
  21. 21.
    J. Bub, The Interpretation of Quantum Mechanics ( N.Y.: Benjamin, 1974 ).CrossRefGoogle Scholar
  22. 22.
    E. P. Wigner, Amer. J. Phys., 33, 1005–9 (1970).ADSCrossRefGoogle Scholar
  23. 23.
    S. Freedman and E. P. Wigner, Found. Phys., 3, 457 (1973).ADSCrossRefGoogle Scholar
  24. 24.
    J. S. Bell, Ref. 16.Google Scholar
  25. 25.
    Some of the issues are considered, for instance, in R.K. Clifton, M.L.G. Redhead, and J. N. Butterfield, Found Phys., 21,149–183 (1991). An easier exposition maybe found in Michael Redhead, Incompleteness, Nonlocality and Realism, Clarendon, Oxford, 1987.Google Scholar
  26. 26.
    According to Barut (personal communication), Bell disagreed, though I do not know the nature of the disagreement. Bell had considered a very similar example to motivate his proof.Google Scholar
  27. 27.
    A. O. Barut and P. Meystre, Phys. Lett., 105-A, 458–62, 1984; A. O. Barut, Hadronic J. Suppl., 1, (1986).Google Scholar
  28. 28.
    A. Garg and D. Mermin, Phys. Rev., D35, 383 (1987).CrossRefGoogle Scholar
  29. 29.
    local realism’, as defined by Garg and Mermin, Ref. 28, refers to the averaging procedure for a hidden variable theory.Google Scholar
  30. 30.
    e.g., A. Fine, Found. Phys., 21, 365 (1991).ADSCrossRefGoogle Scholar
  31. 31.
    e.g., E. Santos, Found. Phys., 21, 221 (1991).MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    G.C. Hegerfeldt, Phys. Rev., D10, 3320 (1974); G. C. Hegerfeldt and S.N.M. Ruijsenaars, Phys. Rev., D22, 377 (1980). This has been made almost a starting point for stochastic quantization by E. Prugovecki and members of his school. See also, G.C. Hegerfeldt, Phys. Rev. Lett., 72, 596 (1994).Google Scholar
  33. 33.
    C. K. Raju, J. Phys. A: Math. Gen., 16, 3739–53 (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. 34.
    See, e.g., R. D. Richtmeyer, Principles of Mathematical Physics, Vol. 1. Springer, Berlin (1982), or M. Taylor, Pseudo-Differential Operators, N.Y., Academic (1974).Google Scholar
  35. 35.
    As a leading expert, Dafermos, remarked in private conversation, the right way to define hyperbolicity is to put in more and more physics!Google Scholar
  36. 36.
    See, e.g., P.C.W. Davies, The Physics of Time Asymmetry, Surrey Univ. Press, London, 1974.Google Scholar
  37. 37.
    J. B. Hartle, in: Proceedings of the Fifth Marcel Grossman Meeting, D. Blair et al (eds), R. Ruffmi (series ed.), Wiley Eastern, Singapore, 1989, pp 107–24.Google Scholar
  38. 38.
    e.g., D. T. Pegg, J. Phys. A: Math., Gen., 24, 3031–40 (1991).ADSCrossRefGoogle Scholar
  39. 39.
    A.J. Leggett and A. Garg, Phys. Rev. Lett., 55, 857 (1985). A.J. Leggett, ‘Quantum mechanics at the macroscopic level.’ In: J. de Boer, E. Dal and O. Ulfbed (eds), The Lessons of Quantum Theory: Niels Bohr Centenary Symposium, Elsevier, Amsterdam, 1986, pp 35–58, and in: G. Grinstein, and G. Mezenko (eds), Directions in Condensed Matter Physics: Memorial Volume in Honor of Shang-keng Ma, World Scientific, Singapore, 1986, pp 185–248.Google Scholar
  40. 40.
    S. Foster and A. Elby, Found. Phys., 21, 773–80 (1991).ADSCrossRefGoogle Scholar
  41. 41.
    First noted by W. Ehrenberg and R.W. Siday, Proc. Phys. Soc. (Lond.) B62, 8 (1949), and by Y. Aharonov and D. Bohm, Phys. Rev., 115, 485 (1959). An exhaustive review may be found in M. Peshkin and A. Tonomura, The Aharonov-Bohm Effect, Lecture Notes in Physics No. 340, Springer, Berlin, 1989.Google Scholar
  42. 42.
    Article by M. Peshkin, p 4, in the book cited in Ref. 41.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • C. K. Raju
    • 1
    • 2
  1. 1.Indian Institute of Advanced StudyRashtrapati NivasShimlaIndia
  2. 2.Centre for Development of Advanced ComputingNew DelhiIndia

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