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The Collapse of the Quantum State

Jeffrey Alan Barrett

Published Dec 26, 2019• 0 citations
Publisher

Abstract

Abstract We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.

DOI
10.1093/oso/9780198844686.003.0008

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Abstract We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.
ABSTRACT This essay aims at reviewing one of the major difficulties affecting the standard formulation of quantum mechanics, that is, the well‐known measurement problem. As it will be explained, the latter originates as a consequence of the quantum theory's postulates. Referring to this, we analyze in particular the conceptual issues implied by the projection (or collapse) rule. After having presented the measurement problem, we then illustrate three possible solutions offered by major interpretations of/alternatives to quantum theory: Bohmian mechanics, Ghirardi–Rimini–Weber theories, and the many‐worlds interpretation. As the reader will see, these theoretical frameworks solve this issue by virtue of their unambiguous ontologies and consistent dynamical laws. Finally, a synopsis of the open debates and future perspectives concerning the measurement problem in relativistic contexts concludes the paper.
Recalling the state of the art in the interpretation of quantum physics, this paper emphasizes that one cannot simply add a collapse parameter to the Schrödinger equation in order to solve the measurement problem. If one does so, one is also committed to a primitive ontology of a configuration of matter in physical space in order to have something in the ontology that constitutes the determinate measurement outcomes. The paper then argues that in the light of this consequence, the collapse postulate loses its attractiveness in comparison to an ontology of persisting particles moving on continuous trajectories according to a deterministic law.
Abstract Each formulation of quantum mechanics we consider in the book seeks to explain why we have determinate measurement records distributed according to the standard quantum statistics. The explanation we get relies on the metaphysical assumptions that underlie the particular theory. Metaphysics here does real explanatory work in accounting for our experience. While it is not at all clear what specific metaphysical commitments best explain our experience, one can distinguish between different types and degrees of empirical adequacy each formulation provides. Stronger notions of empirical adequacy might be characterized in terms of such things as the plausibility that one’s experience in fact supervenes on the sort of records a particular theory provides and the richness of the account of experience provided by the theory.
Abstract The foundations of quantum mechanics are so contested that it yields few definitive answers to metaphysical questions. So the best we can do is to lay out the various possibilities. The six possibilities considered are as follows: Bohm’s hidden variable theory, particle-only hidden variable theories, the GRW spontaneous collapse theory, spontaneous collapse theories with added three-dimensional ontology, the “flashy” spontaneous collapse theory, and the many-worlds theory. The metaphysical consequences of each of these theories are summarized. Even if quantum mechanics does not settle many ontological questions, it shifts the debate in interesting and fruitful ways. Furthermore, the metaphysical consequences may in some cases reflect back on the tenability of the theories themselves.