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arXiv:quant-ph/9506020

Decoherence: Basic Concepts and Their Interpretation

H. D. Zeh

Published Jun 14, 1995• 16 citations
arXivHTMLPDF

Abstract

Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density matrix, coarse graining, and "events". 5. Conclusions.
DOI
10.48550/arxiv.quant-ph/9506020

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The Copenhagen interpretation has been remarkably successful but seems at odds with the underlying linearity of quantum mechanics. We show how it can emerge in a simple way from the underlying microscopic quantum world governed by Schrodinger's equation without the need for observers or their brains. In order to achieve this, we assemble pieces of various pre-existing ideas. Firstly, we adopt a relational approach and use the eigenvectors of the reduced density matrix of a quantum sub-system, or equivalently the Schmidt decomposition, to define the `internal state' of a sub-system. Previous work has identified serious objections to such an interpretation because it apparently leads to macroscopic superpositions and physically unacceptable instabilities near degeneracies. We show that both these problems are solved if the sub-system consists of a large number of coarse grained degrees of freedom as one expects in order to make contact with the classical world. We further argue that coarse graining is a necessary ingredient because measuring devices have both finite spatial and temporal resolutions. What results is an interpretation in which both decoherence and coarse graining play key roles and from which the rules of the Copenhagen interpretation are seen to emerge in realistic situations that include the measurement of the position of a particle and a decay process.
The Copenhagen interpretation has been remarkably successful but seems at odds with the underlying linearity of quantum mechanics. We show how it can emerge in a simple way from the underlying microscopic quantum world governed by Schrödinger’s equation without the need for observers or their brains. In order to achieve this, we assemble pieces of various pre-existing ideas. Firstly, we adopt a relational approach and use the eigenvectors of the reduced density matrix of a quantum sub-system, or equivalently the Schmidt decomposition, to define the ‘internal state’ of a sub-system. Previous work has identified serious objections to such an interpretation because it apparently leads to macroscopic superpositions and physically unacceptable instabilities near degeneracies. We show that both these problems are solved if the sub-system consists of a large number of coarse-grained degrees of freedom as one expects in order to make contact with the classical world. We further argue that coarse graining is a necessary ingredient because measuring devices have both finite spatial and temporal resolutions. What results is an interpretation in which both decoherence and coarse graining play key roles and from which the rules of the Copenhagen interpretation are seen to emerge in realistic situations that include the measurement of the position of a particle and a decay process.