Journal of Statistical Physics

, Volume 82, Issue 5–6, pp 1575–1646 | Cite as

On the consistent histories approach to quantum mechanics

  • Fay Dowker
  • Adrian Kent
Articles

Abstract

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnès, and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnès' characterization of true statements—statements which can be deduced unconditionally in his interpretation—is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction, and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yetunknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.

Key Words

Quantum mechanics quantum cosmology consistent histories decoherence 

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References

  1. 1.
    R. B. Griffiths,J. Stat. Phys. 36:219 (1984).Google Scholar
  2. 2.
    R. B. Griffiths,Found. Phys. 23:1601 (1993).Google Scholar
  3. 3.
    R. Omnès,J. Stat. Phys. 53:893, 933, 957 (1988);57:357 (1989).Google Scholar
  4. 4.
    R. Omnès,Rev. Mod. Phys. 64:339 (1992).Google Scholar
  5. 5.
    M. Gell-Mann and J. B. Hartle, InComplexity, Entropy, and the Physics of Information, W. Zurek, ed. (Addison-Wesley, Reading, Massachusetts, 1990).Google Scholar
  6. 6.
    M. Gell-Mann and J. B. Hartle, InProceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura, eds. (Physical Society of Japan, Tokyo, 1990).Google Scholar
  7. 7.
    M. Gell-Mann and J. B. Hartle, InProceedings of the 25th International Conference on High Energy Physics, Singapore, August 2–8, 1990, K. K. Phua and Y. Yamaguchi, eds. (South East Asia Theoretical Physics Association and Physical Society of Japan, distributed by World Scientific, Singapore, 1990).Google Scholar
  8. 8.
    M. Gell-Mann and J. B. Hartle, InProceedings of the NATO Workshop on the Physical Origins of Time Asymmetry, Mazagón, Spain, September 30-October 4, 1991, J. Halliwell, J. Pérez-Mercader, and W. Zurek, eds. (Cambridge University Press, Cambridge, 1994).Google Scholar
  9. 9.
    M. Gell-Mann and J. B. Hartle,Phys. Rev. D 47:3345 (1993).Google Scholar
  10. 10.
    F. Dowker and A. Kent,Phys. Rev. Lett. 75:3038 (1995).Google Scholar
  11. 11.
    B. DeWitt and R. N. Graham, eds.,The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1973).Google Scholar
  12. 12.
    J. S. Bell, The measurement theory of Everett and de Broglie's pilot wave, inQuantum Mechanics, Determinism, Causality and Particles, M. Flato et al., eds. (Reidel, Dordrecht, 1976); reprinted in J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).Google Scholar
  13. 13.
    H. Stein,Noûs 18:635 (1984).Google Scholar
  14. 14.
    A. Kent,Int. J. Mod. Phys. A 5:1745 (1990).Google Scholar
  15. 15.
    J. S. Bell, Quantum mechanics for cosmologists, inQuantum Gravity 2, C. Isham, R. Penrose, and D. Sciama, eds. (Clarendon Press, Oxford, 1981), pp. 611–637.Google Scholar
  16. 16.
    J. B. Hartle, InQuantum Cosmology and Baby Universes, S. Coleman, J. Hartle, T. Piran, and S. Weinberg, eds. (World Scientific, Singapore, 1991).Google Scholar
  17. 17.
    B. d'Espagnat,J. Stat. Phys. 56:747 (1989).Google Scholar
  18. 18.
    W. Zurek,Prog. Theor. Phys. 89:281 (1993).Google Scholar
  19. 19.
    D. Dürr, S. Goldstein, and N. Zanghi,J. Stat. Phys. 67:843 (1992).Google Scholar
  20. 20.
    A. Albrecht,Phys. Rev. D 46: 5504 (1992);48:3768 (1993).Google Scholar
  21. 21.
    J. Paz and W. Zurek,Phys. Rev. D 48:2728 (1993).Google Scholar
  22. 22.
    D. Bohm,Phys. Rev. 85:166 (1952).Google Scholar
  23. 23.
    T. M. Samols, A stochastic model of a quantum field theory, Cambridge preprint DAMTP/94-39;J. Stat. Phys. to appear.Google Scholar
  24. 24.
    J. Cushing, A. Fine, and S. Goldstein, eds.,Bohmian Mechanics and Quantum Theory: An Appraisal (Kluwer, Dordrecht, to be published).Google Scholar
  25. 25.
    Y. Aharonov, P. Bergmann, and J. Lebovitz,Phys. Rev. B 134:1410 (1964).Google Scholar
  26. 26.
    J. B. Hartle,Phys. Rev. D 44:3173 (1991).Google Scholar
  27. 27.
    C. J. Isham, InIntegrable Systems, Quantum Groups and Quantum Field Theories, L. A. Ibort and M. A. Rodriguez (eds.) (Kluwer, London 1993); C. J. Isham,J. Math. Phys.23:2157 (1994); C. J. Isham and N. Linden,J. Math. Phys. 35:5452 (1994).Google Scholar
  28. 28.
    M. Gell-Mann and J. B. Hartle, Equivalent sets of histories and multiple quasiclassical domains, Preprint UCSBTH-94-09, gr-qc/9404013, submitted to gr-qc 8 April 1994.Google Scholar
  29. 29.
    S. Goldstein and D. Page,Phys. Rev. Lett. 74:3715 (1995).Google Scholar
  30. 30.
    J. S. Bell,Physics 1:195 (1964);Rev. Mod. Phys. 38:447 (1966).Google Scholar
  31. 31.
    D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1951), Chapter 22.Google Scholar
  32. 32.
    E. Joos and H. D. Zeh,Z. Phys. B. 59:2 (1985).Google Scholar
  33. 33.
    W. Zurek,Phys. Rev. D 24:1516 (1981);26:1862 (1982).Google Scholar
  34. 34.
    A. Caldeira and A. Leggett,Physica 121A:587 (1983).Google Scholar
  35. 35.
    J. McElwaine, Approximate and exact consistency of histories, University of Cambridge preprint DAMTP/95-32, grant-ph/9506034, Submitted toPhys. Rev. A. Google Scholar
  36. 36.
    P. H. Gosse,Omphalos: An Attempt to Untie the Geological Knot (1857).Google Scholar
  37. 37.
    R. Omnès, Private communication.Google Scholar
  38. 38.
    R. Griffiths, Private communication.Google Scholar
  39. 39.
    S. Saunders, The quantum block universe, Harvard Department of Philosophy preprint (1992); Decoherence, relative states, and evolutionary adaptation, Harvard Department of Philosophy preprint (1993).Google Scholar
  40. 40.
    H. Everett,Rev. Mod. Phys. 29:454 (1957).Google Scholar
  41. 41.
    M. Gell-Mann and J. B. Hartle, Equivalent sets of histories and multiple quasiclassical domains, preprint UCSBTH-94-09, revised version as of 26 April 1995.Google Scholar
  42. 42.
    M. Gell-Mann,The Quark and the Jaguar (Little, Brown and Co., London, 1994).Google Scholar
  43. 43.
    J. B. Hartle, Private communication.Google Scholar
  44. 44.
    A. Whitaker,Einstein, Bohr and the quantum world, to be published.Google Scholar
  45. 45.
    J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955).Google Scholar
  46. 46.
    E. P. Wigner, Remarks on the mind-body question, inThe Scientist Speculates, I. J. Good ed. (Heinemann, London, 1961). pp. 284–302.Google Scholar
  47. 47.
    R. Penrose, The nature of space and time, Isaac Newton Institute debate with S. W. Hawking (May 1994).Google Scholar
  48. 48.
    D. Page,Phys. Rev. Lett. 70:4034 (1993).Google Scholar
  49. 49.
    S. Goldstein, Private communication.Google Scholar
  50. 50.
    R. D. Sorkin, Quantum mechanics as quantum measure theory, Syracuse preprint SU-GP-93-12-1, gr-qc/9401003.Google Scholar
  51. 51.
    G. Ghirardi, A. Rimini, and T. Weber,Phys. Rev. D 34:470 (1986).Google Scholar
  52. 52.
    R. Omnès,Phys. Lett. A 187:26 (1994).Google Scholar
  53. 53.
    N. Gisin,Helv. Phys. Act. 62:363 (1989).Google Scholar
  54. 54.
    I. Percival,Proc. Roy. Soc. Lond. Ser. A 447:189 (1994).Google Scholar
  55. 55.
    R. Penrose,Shadows of the Mind (Oxford University Press, Oxford, 1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Fay Dowker
    • 1
    • 2
  • Adrian Kent
    • 3
  1. 1.Physics DepartmentUniversity of California Santa BarbaraSanta Barbara
  2. 2.Isaac Newton Institute for Mathematical SciencesCambridgeUK
  3. 3.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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