Abstract
The theme of this paper is the multiplicity ofthe consistent sets of histories emerging in theconsistent-histories approach to quantum mechanics. Wepropose one criterion for choosing preferred families among them: that the physically realizablequasiclassical domain ought to be one corresponding toclassical histories. We examine the way classicalmechanics arises as a particular window, and theimportant role played by the canonical group and theHamiltonian. We finally discuss a possible implicationof our selection criterion: that only a class of Hilbertspace operators corresponds to physical quantities, and hence the full nondistributivity of thelattice of quantum propositions is redundant.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Anastopoulos, C. (1997). Physical Review D, 56, 1009.
Dowker, H. F., and Halliwell, J. J. (1992). Physical Review D, 46, 1580.
Dowker, H. F., and Kent, A. (1996). Journal of Statistical Physics, 82, 1575.
Gell-Mann, M., and Hartle, J. B. (1990). In Complexity, Entropy and the Physics of Information, W. Zurek, ed., Addison-Wesley, Reading, Massachusetts.
Gell-Mann, M., and Hartle, J. B. (1993). Physical Review D, 47, 3345.
Ghirardi, G. C., Rimini, A., and Weber, T. (1986). Physical Review D, 34, 470.
Griffiths, R. B. (1984). Journal of Statistical Physics, 36, 219.
Hartle, J. B. (1993). Spacetime quantum mechanics and the quantum mechanics of spacetime, in Proceedings of the 1992 Les Houches School, Gravitation and Quantization.
Hartle, J. B., and Griffiths, R. B. (1997). Preprint gr-qc 9710025.
Isham, C. J. (1994). Journal of Mathematical Physics, 35, 2157.
Isham, C. J. (1997). International Journal of Theoretical Physics, 36, 785.
Isham, C. J., and Linden, N. (1994). Journal of Mathematical Physics, 35, 5452.
Isham, C. J., and Linden, N. (1996). Preprint quant-ph 9612035.
Isham, C. J., Linden, N., and Schreckenberg, S. (1994). Journal of Mathematical Physics, 35, 6360.
Kent, A. (1996a). Physical Review A, 54, 4670.
Kent, A. (1996b). Preprint gr-qc 9607073.
Kent, A. (1997). Physical Review Letters, 78, 2874.
Kent, A., and McElwaine, J. (1997). Physical Review A, 55, 1703.
Margenau, x., and Park, x. (1968). International Journal of Theoretical Physics, 1, 212.
Omnès, R. (1988a). Journal of Statistical Physics, 53, 893.
Omnès, R. (1988b). Journal of Statistical Physics, 53, 957.
Omnès, R. (1989). Journal of Statistical Physics, 57, 357.
Omnès, R. (1992). Reviews of Modern Physics, 64, 339.
Omnès, R. (1996). The Interpretation of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.
Penrose, R. (1986). In Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds., Clarendon, Oxford.
Perelomov, A. M. (1986). Generalized Coherent States and Their Applications, Springer-Verlag, Berlin.
Sorkin, R. D. (1994). Modern Physics Letters A, 9, 3119.
Sorkin, R. D. (1996). In Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability: Quantum Classical Correspondence, D. H. Feng and B. L. Hu, eds., International Press.
Rights and permissions
About this article
Cite this article
Anastopoulos, C. Preferred Consistent History Sets. International Journal of Theoretical Physics 37, 2261–2272 (1998). https://doi.org/10.1023/A:1026658523246
Issue Date:
DOI: https://doi.org/10.1023/A:1026658523246