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arXiv:0712.0149

The Quantum Measurement Problem: State of Play

David Wallace

Published Dec 3, 2007• 51 citations
arXivHTMLPDF

Abstract

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation.

DOI
10.48550/arxiv.0712.0149

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This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation.
Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the 'measurement problem', as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (§§1-2), to present an account of how quantum measurements are actually dealt with in modern physics (hint: it does not involve a collapse of the wave function) and to state the measurement problem from the perspective of that account; and secondly (§§3-4), to clarify what role decoherence plays in modern measurement theory and what effect it has on the various strategies that have been proposed to solve the measurement problem.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment.
In this article, I shall focus on two of the main problems raising interpre-tational issues in quantum mechanics, namely the notorious measurement problem (discussed together with the theory of measurement in section 4) and the equally important but not quite as widely discussed problem of the classical regime (discussed together with decoherence in section 3). The two problems are distinct, but they are both intimately related to some of the is-sues arising from entanglement and density operators, which are thus briefly reviewed in section 2. A few fundamentals are rehearsed in section 1. The article will aim to be fairly non-technical in language, but modern in out-look and covering the chosen topics in more depth than most introductory treatments. The philosophy and foundations of quantum mechanics offer many more examples of live research issues, and much progress has been achieved re-cently in such traditional approaches as collapse theories, pilot-wave the-ories and Everett interpretations, and in the (time-honoured but recently revived) area of axiomatic reconstructions of the theory. Recent years have
In their article, Chandralekha Singh, Mario Belloni, and Wolfgang Christian focus exclusively on “functional understanding of quantum mechanics,” which they claim “is quite distinct from the foundational issues alluded to by Feynman.”But are the foundational and the functional really so distinct? The work of other physics education researchers suggests not. For example, in a classic article, Alan Van Heuvelen discusses students’ prevalent and frustrating use of “primitive formula-centered problem-solving strategies” 1 1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 and suggests that physical, intuitive understanding developed through qualitative diagrams and models “must come before students start using math in problem solving. The equations become crutches that short-circuit attempts at understanding.” Van Heuvelen also urges that “instead of thinking of [problems] as an effort to determine some unknown quantity, [teachers] might … encourage students to think of the problem statement as describing a physical process—a movie of a region of space during a short time interval or of an event at one instant of time.” I suspect Singh, Belloni, and Christian would agree with this advice. They comment that such “qualitative understanding of quantum mechanics is much more challenging than facility with the technical aspects.”But isn't the main barrier to such intuitive, qualitative understanding the nature of quantum mechanics itself—at least, the version of the theory advocated by Niels Bohr, Werner Heisenberg, and virtually every textbook writer since? Why should we expect students to invest the time and energy necessary to, say, visualize the time-dependence of |ψ|2 when we also preach the ambiguous and contradictory Copenhagen dogma that ψ does not represent anything physically real, yet still provides a complete description of physical reality? Why are we surprised that students are confused about, and don't take seriously, something that we assure them is, at best, some kind of algorithmic fantasy? Is there really any difference between “shut up and calculate” and “plug and chug”?Why not teach them Bohmian mechanics—an alternative (deterministic) version of quantum theory in which particles are particles (and really exist, all the time) and the same dynamical laws apply whether anyone is looking or not? 2 2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. About this alternative theory John S. Bell asked, “Why is [it] ignored in text books? Should it not be taught … as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced upon us by experimental facts, but by deliberate theoretical choice?” 3 3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 If we really want to help students understand quantum mechanics, the first step is to reject the confusion-spawning foundational vagueness, ambiguity, and philosophical absurdity of Copenhagen quantum theory, and adopt a clearer, more scientific, less fuzzy version. (See Sheldon Goldstein's two-part article “Quantum Theory Without Observers,” Physics Today, March 1998, page 42, and Physics Today, April 1998, page 38) The first step, in short, is to present them with a theory that can be understood.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 , Google ScholarCrossref2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. Google Scholar3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 , Google ScholarCrossref© 2007 American Institute of Physics.