CHAPTER 7: The Quantum Mechanics of Closed Systems
A slightly shortened version of an article that appeared in the festschrift for C. W. Misner, eds. B. L. Hu, M. P. Ryan and C. V. Vishveshwara (Cambridge University Press, Cambridge, 1993).
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…
