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arXiv:gr-qc/9308025

Quantum cosmology and the emergence of a classical world

Claus Kiefer

Published Aug 23, 1993• 2 citations
arXivHTMLPDF

Abstract

This paper gives an elementary introduction to some of the conceptual problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4. The direction of time
DOI
10.48550/arxiv.gr-qc/9308025

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This final chapter starts with a brief review of quantum-gravity phenomenology. It then focuses on an important conceptual issue – the relevance of quantum gravity for the general interpretation of quantum theory. A central part is devoted to the discussion of the quantum-to-classical transition, with decoherence as its crucial mechanism. It is shown that the quantum states used in cosmology can be interpreted in a sensible way. The chapter also contains a discussion of the arrow of time in the light of quantum cosmology and ends with a brief outlook and reflections.
When quantum mechanics was developed in the '20s of the last century another revolution in physics was just starting. It began with the discovery that the universe is expanding. For a long time quantum mechanics and cosmology developed independently of one another. Yet the very discovery of the expansion would eventually draw the two subjects together because it implied the big bang where quantum mechanics wasimportant for cosmology and for understanding and predicting our observations of the universe today. Textbook (Copenhagen) formulations of quantum mechanics are inadequate for cosmology for at least four reasons: 1) They predict the outcomes of measurements made by observers. But in the very early universe no measurements were being made and no observers were around to make them. 2) Observers were outside of the system being measured. But we are interested in a theory of the whole universe where everything, including observers, are inside. 3) Copenhagen quantum mechanics could not retrodict the past. But retrodicting the past to understand how the universe began is the main task of cosmology. 4) Copenhagen quantum mechanics required a fixed classical spacetime geometry not least to give meaning to the time in the Schrödinger equation. But in the very early universe spacetime is fluctuating quantum mechanically (quantum gravity) and without definite value. A formulation of quantum mechanics general enough for cosmology was started by Everett and developed by many. That effort has given us a more general framework that is adequate for cosmology --- decoherent (or consistent) histories quantum theory in the context of semiclassical quantum gravity. Copenhagen quantum theory is an approximation to this more general quantum framework that is appropriate for measurement situations. We discuss whether further generalization may still be required.
Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.