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arXiv:1910.06123

Measuring Measuring

Arne Hansen, Stefan Wolf

Published Oct 14, 2019• 1 citation
arXivHTMLPDF

Abstract

Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that our contact with the world is empirically warranted. Therefore, we study theories that satisfy the following assumption: Interactions are accounted for so that they are empirically traceable, and observations necessarily go with such an interaction with the observed system. Examining, with regard to these assumptions, an abstract representation of measurements with tools from quantum logic leads us to contextual theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement becomes problematic---also beyond quantum mechanics---if one tries to commensurate the assumption of tangible interactions with the notion of a spectator theory, i.e., with the idea that measurement results are read off without effect. The problem, thus, presents itself as the collision of different epistemological stances with repercussions beyond quantum mechanics.

DOI
10.48550/arxiv.1910.06123

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Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that our contact with the world is empirically warranted. Therefore, we study theories that satisfy the following assumption: Interactions are accounted for so that they are empirically traceable, and observations necessarily go with such an interaction with the observed system. Examining, with regard to these assumptions, an abstract representation of measurements with tools from quantum logic leads us to contextual theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement becomes problematic---also beyond quantum mechanics---if one tries to commensurate the assumption of tangible interactions with the notion of a spectator theory, i.e., with the idea that measurement results are read off without effect. The problem, thus, presents itself as the collision of different epistemological stances with repercussions beyond quantum mechanics.
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for interactions so that they are empirically traceable, and that observations necessarily go with such an interaction with the observed system. We investigate consequences of this assumption: The unfolding language game, inspired by "quantum logic," leads to a class of contextual and probabilistic theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement "problem" arises in all such theories, not only quantum mechanics: It is a consequence of the need for empirical evidence of interactions. And a consequence of the converse need for an interaction when obtaining that empirical evidence.
In quantum mechanics, the measurement problem is commonly regarded as reason for deep concern. It seems that, either, the problem can be solved and there is hope for quantum mechanics, or the theory better be left behind in search of another one. We investigate the prospect of finding a solution to the measurement problem—within quantum mechanics, as well as in theoretical frameworks beyond it. As we do so, there emerges a perspective on doing physics drawing from considerations in the philosophy of language and in epistemology. Developing this perspective for further aspects in physics reveals: The notion of a system is similarly problematic. Eventually, the question arises whether these are problems of specific physical theories, or rather of specific stances towards physics. In this regard, we examine in particular the role and understanding of assumptions.
Results of measurements give legitimacy to a physical theory: What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for interactions so that they are empirically traceable, and that observations necessarily go with such an interaction with the observed system. We investigate consequences of this assumption: The unfolding language game, inspired by logic, leads to a class of contextual and probabilistic theories. Disturbance becomes a means to render interactions, thus, also measurements, empirically tangible. The measurement problem arises in all such theories, not only quantum mechanics: It is a consequence of the need for empirical evidence of interactions.
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing physics is regarded as a creative activity to develop a meaningful description of the world, then one has to carefully discriminate between the two notions: An observer's account of experience - consitutive to meaning - is hardly expressed exhaustively by the formal framework of an interaction within one particular theory. We develop a corresponding perspective onto central terms in quantum mechanics in general, and onto the measurement problem in particular.
Abstract This chapter discusses the measurement problem in the context of modern epistemology of science, setting out an epistemological framework which will be used throughout the book. I suggest that the literature on the measurement problem typically assumes that quantum mechanics is confirmed by the empirical evidence regardless of interpretation, and I argue that this ultimately founders for reasons similar to logical positivism. I then invoke recent work in the epistemology of measurement by van Fraassen, Chang and Tal to argue that we cannot make sense of scientific epistemology without a satisfactory understanding of what is going on during the process of measurement. Finally, I propose an approach to the epistemology of science inspired by Chang’s progressive coherentism, and argue that this is the right way of thinking about epistemic situations in which our understanding of the operation of our measuring devices depends crucially on the very physics we are trying to find out about.
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.