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Philosophy of Science

Two Paradoxes in Quantum Mechanics

Henry Krips

Published Jun 1, 1969• 21 citations
Publisher

Abstract

The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density operator.

DOI
10.1086/288242

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arXiv:1910.08591•Oct 18, 2019•0 citations
The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density operator.
Despite the spectacular success of quantum mechanics (QM) over the last 80 years in explaining phenomena observed at the atomic and subatomic level, the conceptual status of the theory is still a topic of lively controversy. Most of the discussion centers around two famous paradoxes (or, as some would have it, pseudoparadoxes) associated, respectively, with the names of Einstein, Podolsky, and Rosen (EPR) and with Schrodinger's cat. In this Viewpoint, I will concentrate on the paradox of Schrodinger's cat or, as it is often known (to my mind somewhat misleadingly), the quantum measurement paradox.
Once upon a time the well-known paradoxes of quantum mechanics (one might even say the “traditional” paradoxes of quantum mechanics!—I refer here to paradoxes such as the Schrödinger cat and the Einstein-Podolsky-Rosen Paradox) seemed especially difficult because of the rather bizarre behavior of the wave packet under the von Neumann theory of measurement, to which behavior these paradoxical situations seemed to draw especial attention. Quite recently quantum theoretical accounts of the measurement process have been appearing which sidestep direct reference to such things as “contraction” of the wave packet (see, for example, Krips and Jauch). With this development it has become increasingly popular to take a “cool” approach to these paradoxes, arguing that the new approach to measurement provides a consistent, nonbizarre account of the physical situations and that the paradoxicality was due largely to intuitive blunders—even plausible intuitive blunders—accentuated (but also disguised) by the unfortunate features of the von Neumann approach to measurement. Both Krips and Jauch, for example, adopt this approach.
The interplay between non-relativistic quantum theory and metaphysics has generated radically opposed interpretations for quantum theory: Niels Bohr's 'orthodox' interpretation, and Einstein's 'realist' one. Out of this debate emerged the classical first-generation paradoxes of quantum theory: Schrodinger's Cat and the Einstein-Podolsky-Rosen paradoxes. And more recently a range of new paradoxes has emerged from the work of J.S. Bell which questions the `local' nature of quantum theory, prefiguring a return either to an action-at-a-distance metaphysics or to a radically holistic conception of matter. This book outlines the contours of these debates, and presents an interpretation of quantum theory which, while metaphysically realist, resolves most of the paradoxes. This interpretation takes quantum systems to be fuzzy particles, piloted by fields of propensities which are represented by density operators on Hilbert space; and constitutes, in part, a return to an earlier view of quantum systems advanced by De Broglie, Schrodinger, Born, and Einstein. A book for philosophers and physicists who are interested in the philo sophy o f science.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.