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The Quantum Mechanics of Closed Systems

Published online by Cambridge University Press:  03 February 2010

J. B. Hartle
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106-9530
B. L. Hu
Affiliation:
University of Maryland, College Park
M. P. Ryan, Jr
Affiliation:
Universidad Nacional Autónoma de México
C. V. Vishveshwara
Affiliation:
Indian Institute of Astrophysics, India
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Summary

ABSTRACT

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In “Copenhagen” quantum mechanics, probabilities can be assigned to histories of a subsystem that have been “measured”. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system's initial condition and dynamics. Such sets of histories are said to decohere. We define decoherence for closed systems in the simplified case when quantum gravity can be neglected and the initial state is pure. Typical mechanisms of decoherence that are widespread in our universe are illustrated.

Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact.

Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained.

Type
Chapter
Information
Directions in General Relativity
Proceedings of the 1993 International Symposium, Maryland: Papers in Honor of Charles Misner
, pp. 104 - 124
Publisher: Cambridge University Press
Print publication year: 1993

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