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arXiv:gr-qc/9512023 · Physical Review A

Quasiclassical dynamics in a closed quantum system

Adrian Kent

Published Dec 1, 1996• 107 citations
arXivHTMLPDF

Abstract

We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realized from each consistent set. We show that in this interpretation, if one assumes that an observed quasiclassical structure will continue to be quasiclassical, one cannot infer that it will obey the predictions of classical or Copenhagen quantum mechanics. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4670

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We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realized from each consistent set. We show that in this interpretation, if one assumes that an observed quasiclassical structure will continue to be quasiclassical, one cannot infer that it will obey the predictions of classical or Copenhagen quantum mechanics. \textcopyright{} 1996 The American Physical Society.
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An observer (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its initial condition, and a study of the problem of quasiclassical domains.
There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These formalisms have a natural interpretation, according to which nature somehow chooses one set of histories from among those allowed, and then randomly chooses to realise one history from that set; other interpretations are possible, but their scientific implications are essentially the same. The selection criteria proposed to date are reasonably natural, and certainly raise new questions. For example, the validity of ordering inferences which we normally take for granted – such as that a particle in one region is necessarily in a larger region containing it – depends on whether or not our history respects the criterion of ordered consistency, or merely consistency. However, the known selection criteria, including consistency and medium decoherence, are very weak. It is not possible to derive the predictions of classical mechanics or Copenhagen quantum mechanics from the theories they define, even given observational data in an extended time interval. Attempts to refine the consistent histories approach so as to solve this problem by finding a definition of quasiclassicality have so far not succeeded. On the other hand, it is shown that dynamical collapse models, of the type originally proposed by Ghirardi-Rimini-Weber, can be re-interpreted as set selection criteria within a quantum histories framework, in which context they appear as candidate solutions to the set selection problem. This suggests a new route to relativistic generalisation of these models, since covariant definitions of a quantum event are known.
I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may predict the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is closed related to the quantum state diffusion approach of Gisin and Percival.
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 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. 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. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.