Where is the problem? by J.M. Levy-Leblond Experiment and quantum measurement theory by A. Zeilinger A consistent interpretation of quantum mechanics. The measurement process in the individual interpretation of quantum mechanics by H. Primas Principle of stationarity in the action functional and the theory of measurement by R. Fukuda Quantum (statistical) mechanics, measurement and information by R. Balian State vector collapse as a classical statistical effect of measurement by M. Cini and M. Serva Consecutive quantum measurements by A. Peres No-collapse versions of quantum mechanics by Y. Ben-Dov An attempt to understand the many-worlds interpretation of quantum theory by E.J. Squires Uncertainty and measurement by P.T. Landsberg Author Index
Where is the problem? by J.M. Levy-Leblond Experiment and quantum measurement theory by A. Zeilinger A consistent interpretation of quantum mechanics. The measurement process in the individual interpretation of quantum mechanics by H. Primas Principle of stationarity in the action functional and the theory of measurement by R. Fukuda Quantum (statistical) mechanics, measurement and information by R. Balian State vector collapse as a classical statistical effect of measurement by M. Cini and M. Serva Consecutive quantum measurements by A. Peres No-collapse versions of quantum mechanics by Y. Ben-Dov An attempt to understand the many-worlds interpretation of quantum theory by E.J. Squires Uncertainty and measurement by P.T. Landsberg Author Index
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.
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.
Endeavoring to formulate an exhaustive solution to the measurement problem in view of the theory of decoherence leads to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise definition of the measurement and some new vocabulary to speak about quantum mechanics. Considering the latter as a probabilistic theory all along allows us to avoid the usual probability problem of the many-worlds interpretations. A thorough verification of the consistency of quantum mechanics at all scales is proposed, as well as a discussion of what can be deemed an observer.
Standard quantum theory is highly successful in all its applications, from photons and atoms, to semiconductors, superconductors, quarks, and so on. Yet the need to understand what the theory is really trying to tell us about the nature of the world beyond specific predictions forces us into the realm of philosophy, or, as some have dubbed it, quantum metaphysics: the study of the interpretation of quantum mechanics. There is a wide range of opinions regarding the philosophical foundations of quantum mechanics. This chapter focuses on two of the most prominent interpretations: the Copenhagen interpretation, and one alternative interpretation that has been gaining some support in recent years, the many-worlds interpretation (MWI), also known as the many universes interpretation. The central issues of contention are: firstly, that the measurement of some attribute of a quantum system generally involves the probabilistic collapse, or reduction, of the state vector where the probabilistic nature of the process is inherent—that is, not reducible to a more fundamental, deterministic explanation; and, secondly, the problem of bringing a measurement to a completion—a problem generally known as the measurement paradox.
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.
Theory of measurement is presented which is based on the statistical interpretation of quantum mechanics. The reduction of wave packet is ascribed to undue comparison of the state of an ensemble before measurement and the state of an individual system after measurement. By studying the evolution of statistical operators for subsystems and composite systems comprising an object, a measuring apparatus and an observer, one can definitely locate where the measurement is done, thus negating the principle of psycho-physical parallelism due to von Neumann. Time needed for measurement is also discussed. The Einstein-Podolsky-Rosen state is described as an eigenstate of correlation. The argument lends support to the standpoint that the physical state of a system is to be represented by the statistical operator, not by the wave function, in the conceptual foundation of quantum mechanics.