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Oxford University Press eBooks

Phenomenology, decoherence, and the arrow of time

Claus Kiefer

Published Apr 19, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1093/acprof:oso/9780199585205.003.0010

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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.
Abstract This chapter starts with discussing possible observations that are independent of a concrete quantum-gravity approach. Then decoherence, that is, the quantum-to-classical transition, is discussed in detail. This is important for understanding the classical appearance of our world and the evolution of primordial quantum fluctuations into galaxies and clusters of galaxies. The chapter also presents an introduction to the arrow of time and its possible explanation from quantum gravity. It ends with general reflections and an outlook.
The development of quantum cosmology, in which Stephen Hawking played a crucial role, has frequently encountered substantial conceptual and technical difficulties related to the problem of time in quantum gravity and to general issues concerning the foundations of quantum theory. In this contribution to Stephen's 60th Birthday Conference, I describe some recent work in which the decoherent histories approach to quantum theory is used to quantize simple cosmological models and perhaps shed some light on some of these difficulties.
Abstract We discuss how the classical notions of time and causal structure may emerge together with quantum-mechanical probabilities from a universal quantum state. For this, the process of decoherence between semiclassical branches is important. Our discussion is based on quantum geometrodynamics, a canonical approach to quantum gravity. In this framework, a particular boundary condition may illuminate the issue of the arrow of (classical) time in connection to the growth of entanglement entropy.
In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.
This chapter focuses on canonical quantum gravity and discusses how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. It shows that a significant progress can be made by considering the canonical quantization of gravity from the Bohmian point of view. The chapter highlights some important properties that will also be used in the context of quantum gravity. It explores the conceptual problems that appear when trying to interpret the theory in the context of orthodox quantum theory. The chapter describes Bohmian quantum gravity and explains how it solves the conceptual problems and minisuperspace models. It also shows how the problem of the quantum-to-classical limit in inflationary and bouncing models is solved. The chapter provides a new approach to semiclassical gravity, which treats gravity classically and matter quantum mechanically, based on Bohmian mechanics.