Abstract
We reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptions which, in our opinion, are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories. We prove that such assumptions, unless one limits the set of the decoherent families which can be taken into account, lead to a logical contradiction. The line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent histories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.
Similar content being viewed by others
REFERENCES
J. S. Bell, in Proceedings of the Nobel Symposium 65: Possible Worlds in Arts and Sciences (Stockholm, 1986).
J. S. Bell, in Sixty-Two Years of Uncertainty, A. Miller ed. (Plenum, New York, 1990).
S. Goldstein, Physics Today (March 1998), p. 42.
R. B. Griffiths, J. Stat. Phys. 36:219 (1984).
R. B. Griffiths, Am. J. Phys. 55:11 (1987).
R. B. Griffiths, Found. Phys. 23:1601 (1993).
R. B. Griffiths, Phys. Rev. A 54:2759 (1996).
R. B. Griffiths, Phys. Rev. A 57:1604 (1998).
R. Omnès, J. Stat. Phys. 53:893 (1988); 53:933 (1988); 53:957 (1988); 57:357 (1989).
R. Omnès, Rev. Mod. Phys. 64:339 (1992).
R. Omnès, The Interpretation of Quantum Mechanics (Princeton University Press, 1994).
M. Gell-Mann and J. B. Hartle, in Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, S. Kobayashi et al., eds. (Physical society of Japan, Tokio, 1990); in Complexity, Entropy and the Physics of Information, SFI Studies in the Sciences of Complexity, Vol VIII, W. Zurek, ed. (Addison Wesley, Reading, 1990).
M. Gell-Mann and J. B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, K. K. Phua et al., eds. (World scientific, Singapore, 1991).
M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47:3345 (1993).
H. F. Dowker and A. Kent, Phys. Rev. Lett. 75:3038 (1995); J. Stat. Phys. 82:1575 (1996).
B. d'Espagnat, Phys. Lett. A 124:204 (1987); J. Stat. Phys. 56:747 (1989); Found. Phys. 20:1147 (1990).
S. Goldstein and D. N. Page, Phys. Rev. Lett. 74:3715 (1995).
R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures on Physics, Vol. III, Quantum Mechanics (Addison-Wesley, 1963-1965).
Y. Aharonov and L. Vaidman, J. Phys. A 24:2315 (1991).
R. Griffiths and J. B. Hartle, Phys. Rev. Lett. 81:1981 (1998).
A. Kent, Phys. Rev. Lett. 78:2874 (1997).
A. Kent, Phys. Rev. Lett. 81:1982 (1998).
I. Giardina and A. Rimini, Found. Phys. 26:973 (1996).
M. Gell-Mann and J. B. Hartle, preprint gr-qc/9404013, v.3, May 5, 1996.
S. Kochen and E. P. Specker, J. Math and Mech. 17:59 (1967).
J. S. Bell, Found. Phys. 12:989 (1982).
D. Dürr, S. Goldstein, and N. Zanghí, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A. Fine, and S. Goldstein, eds. (Kluwer Academic Press, 1996); M. Daumer, D. Dürr, S. Goldstein, and N. Zanghí, Erkenntnis 45:379 (1997).
A. Bassi and G. C. Ghirardi, Phys. Lett. A 257:247 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bassi, A., Ghirardi, G. Decoherent Histories and Realism. Journal of Statistical Physics 98, 457–494 (2000). https://doi.org/10.1023/A:1018647510799
Issue Date:
DOI: https://doi.org/10.1023/A:1018647510799