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arXiv:2303.03465

The measurement problem in the light of the theory of decoherence

Antoine Soulas

Published Mar 6, 2023• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2303.03465

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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.
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.
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.
Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis
The quantum measurement problem remains a central unresolved issue in theoretical physics, arising from the incompatibility between unitary quantum dynamics and the emergence of definite measurement outcomes. Closely related is the question of the physical status of the wavefunction within contemporary quantum theory. This review critically surveys leading approaches to the measurement problem, focusing on their formal consistency, physical assumptions, and empirical implications. We examine the standard measurement framework, the role of environment-induced decoherence and quantum Darwinism, and the restrictions imposed by no-go theorems such as Bell, Kochen–Specker, and Pusey–Barrett–Rudolph. Interpretations including Everettian many-worlds, Bohmian mechanics, spontaneous collapse models, relational quantum mechanics, QBist approaches, and Copenhagen-type frameworks are assessed in terms of their ability to account for classical definiteness without sacrificing empirical adequacy. We also review experimental efforts probing macroscopic superpositions and collapse dynamics. The analysis indicates that, despite its predictive success, quantum theory lacks a complete physical account of outcome selection. This suggests that the measurement problem reflects a fundamental structural limitation of current theory, motivating either new physical principles or a redefinition of the wavefunction’s ontological role.