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The Quantum Measurement Problem

Jeffrey Alan Barrett

Published Dec 26, 2019• 1 citation
Publisher

Abstract

Abstract We use the Wigner’s friend story to characterize the quantum measurement problem. On the standard formulation of quantum mechanics, whether a physical system is measured determines which of the theory's two dynamical laws obtains. For this reason, the logical consistency of the theory depends on one specifying strictly disjoint conditions for when when each law obtains, which means that one needs to say precisely what constitutes a measurement. But since the term measurement occurs in the standard theory as an undefined primitive term, the theory is at best incomplete. We see precisely how this conceptual incompleteness threatens the logical inconsistency of the theory and why, on even the most charitable reading, it entails that the theory is empirical incomplete. We end by considering why its empirically incompleteness is extremely difficult to test.

DOI
10.1093/oso/9780198844686.003.0007

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Abstract We use the Wigner’s friend story to characterize the quantum measurement problem. On the standard formulation of quantum mechanics, whether a physical system is measured determines which of the theory's two dynamical laws obtains. For this reason, the logical consistency of the theory depends on one specifying strictly disjoint conditions for when when each law obtains, which means that one needs to say precisely what constitutes a measurement. But since the term measurement occurs in the standard theory as an undefined primitive term, the theory is at best incomplete. We see precisely how this conceptual incompleteness threatens the logical inconsistency of the theory and why, on even the most charitable reading, it entails that the theory is empirical incomplete. We end by considering why its empirically incompleteness is extremely difficult to test.
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.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.
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.
In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation.I assume that (i) the quantum state is a representation of knowledge of a (real or hypothetical) observer relative to her experimental capabilities; (ii) measurements have definite outcomes in the sense that only one outcome occurs; (iii) quantum theory is universal and the irreversibility of the measurement process is only "for all practical purposes".These assumptions are analyzed within quantum theory and their consistency is tested in Deutsch's version of the Wigner's friend gedanken experiment, where the friend reveals to Wigner whether she observes a definite outcome without revealing which outcome she observes.The view that holds the coexistence of the "facts of the world" common both for Wigner and his friend runs into the problem of the hidden variable program.The solution lies in understanding that "facts" can only exist relative to the observer.
Quantum theory in its conventional formulation is notoriously subject to various measurement-related paradoxes, as exemplified by the “Schrödinger’s Cat” and “Wigner’s Friend” thought experiments. It has been shown, for example, by Frauchiger and Renner, that nested measurements such as those occurring in the Wigner’s Friend experiment can lead to inconsistencies concerning the putative outcomes of measurements. Such inconsistencies are commonly presumed to remain private and incommensurable, but this is not the case. A counterexample, in which the inconsistencies can be revealed among the observers, is reviewed. The implications for a recent attempt to shield Relational Quantum Mechanics from such inconsistencies are considered, and it is concluded that the attempt is not successful. Further implications for the state of the debate concerning the viability of quantum theory in its various formulations are discussed.
A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by ob-servers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field theory. We will conclude by considering the possibility of giving up rich dynamical explanation in the context of a many-maps formu-lation of relativistic quantum field theory. 1. Wigner’s Friend When Eugene Wigner wrote his now famous paper (1961) on the dynam-ical role of observers in quantum mechanics, quantum field theory was flour-