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arXiv:quant-ph/0312059 · Reviews of Modern Physics

Decoherence, the measurement problem, and interpretations of quantum mechanics

Maximilian Schlosshauer

Published Feb 23, 2005• 1,441 citations
arXivHTMLPDF

Abstract

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.

DOI
10.1103/revmodphys.76.1267

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Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.
This work is a critique of the program of "environment-induced decoherence" as advocated by Zurek, Zeh and Joos, among others. In particular, the alleged relevance of decoherence for a solution of the "measurement problem" is subjected to a detailed philosophical analysis. In the first chapter, an attempt is made to unravel what exactly this "measurement problem" amounts to for the decoherence theorists. The second chapter reviews the standard decoherence literature. The third chapter starts with a brief discussion of the philosophical implications of the decoherence program, followed by a non-standard reconstruction of the decoherence argument that aims to uncover some (mostly hidden) assumptions underlying the approach. It is argued that different subsets of these assumptions result in different versions of the decoherence argument. Next, these assumptions are investigated in more detail, and a number of open problems for the decoherence approach is formulated, in addition to the well-known "problem of outcomes". These problems concern the interpretational relevance of the preferred basis, the role and status of the ignorance interpretation of mixed states, imperfect decoherence and the role of the environment and the definition of subsystems. The fourth chapter addresses the question to what extent the embedding of decoherence in an Everett-like interpretational framework, such as Zurek's "existentional interpretation" and Wallace's structural-realistic version of the many-worlds interpretation, helps to resolve these problems. The main conclusions are formulated in the fifth chapter. Namely: 1) decoherence cannot address the "preferred-basis problem" without adding new interpretational axioms to the standard formalism, 2) the the locality principle (that says that the environment is the "irrelevant" part and should therefore be ignored) is not only problematic but also interpretationally superfluous, 3) the decoherence approach, when formulated in terms of the standard interpretation of quantum mechanics, is predicated on a solution of the "problem of outcomes" and thus cannot claim to account (even partially) for the latter, and 4) that the results of the decoherence program do not increase the plausibility of a realist interpretation of the quantum state.
The decoherence approach to the measurement problem invokes dissipative interactions between a measuring apparatus and its environment to explain, within the context of ‘pure’ quantum mechanics (QM), why such devices appear to possess definite pointer readings. By ‘pure’ QM, I mean Schrödinger evolution with no wavefunction collapse. Several classes of interpretations of pure QM can rely on decoherence. One class is the ‘modal’ interpretations of van Fraassen (1979), Dieks (1989), Healey (1989), and others. Another class is the relative-state and many-world interpretations. I will argue that decoherence cannot help these interpretations address the general metaphysical challenges raised against them. But decoherence can help pick out a ‘special’ basis that determines which observables receive definite values. I'll explore to what extent decoherence rescues the modal (biorthogonal) basis-selection rule, and Zurek's (environmental interaction) basis-selection rule, from the basis degeneracy problem and the imperfect measurement problem.
Quantum mechanics has engendered some philosophical disputes surrounding its conceptual foundation.To solve these disputes,some alternative interpretations which are different from orthodox(and Copenhagen) interpretation have been engendered.In the recent twenty years,the idea of decoherence has aroused attention among physicists and physical philosophers.Decoherence effects alone cannot solve the measurement problem.But decoherence including environmental interactions not only poses new conceptual questions but also suggests solutions to fundamental problems.