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arXiv:1306.4907

Inferential vs. Dynamical Conceptions of Physics

David Wallace

Published Jun 20, 2013• 4 citations
arXivHTMLPDF

Abstract

I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.

DOI
10.48550/arxiv.1306.4907

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I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.
Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.
The Statistics of Non-Boolean Event Structures.- Possibility and Probability.- Some Remarks on Hamiltonian Systems and Quantum Mechanics.- The Possibility Structure of Physical Systems.- Quantum Mechanical Physical Quantities as Random Variables.- On the Interference of Probabilities.- Classical and Quantum Probability and Set Theory.- Discussion.- A Generalized Measure and Probability Theory for the Physical Sciences.- Discussion.- Quantum Logic, Convexity, and a Necker-Cube Experiment.- On the Applicability of the Probability Concept to Quantum Theory.- Discussion.- A Mathematical Setting for Inductive Reasoning.- Discussion.- Classical Statistical Mechanics Versus Quantal Statistical Thermodynamics: A Study in Contrasts.- Discussion.- A Semantic Analysis of Niels Bohr's Philosophy of Quantum Theory.
Quantum physics consists of a formal core that is universally agreed upon (basically being a piece of mathematics with suggestive names for concepts matching related concepts of experimental culture) and an interpretational halo (trying to make this relation more precise) that remains highly disputed even after more than 90 years of modern quantum physics. The latter is the subject of the interpretation of quantum mechanics (see Part II), where many interpretations coexist and compete for the attention of those interested in what quantum physics really means. In this chapter, an axiomatic introduction to the undisputed formal core of quantum physics is given. The axioms described present nonrelativistic quantum statistical mechanics in the Schrödinger picture. The relativistic case is outside the scope of these axioms, as it must be treated by quantum field theory; see Chapter 7. As in any axiomatic setting (necessary for a formal discipline), there are a number of different but equivalent sets of axioms or postulates that can be used to define formal quantum physics. Since they are equivalent, their choice is a matter of convenience. The choice presented here is a formulation featuring three aspects: It emphasises the similarity of quantum mechanics and classical mechanics, gives most direct access to statistical mechanics, and is free from allusions to measurement. The reason for the first is that this similarity serves as a guide to meaning. From the axiomatic setting for quantum mechanics presented below, classical mechanics (in the Koopman setting discussed in Section 7.10) is obtained by simply restricting the operators to be diagonal, so that all operations happen pointwise on the diagonal elements. Thus, multiplication is commutative, and one can identify operators and functions. In particular, the density operator degenerates into a probability density. Therefore, the quantum case appears as a generalization of the classical case allowing for noncommutativity, so that both q-observables and the density operator are (usually infinite-dimensional) operators. The reason for the second is that statistical mechanics is the main tool for applications of quantum physics to the macroscopic systems we are familiar with. The reason for the third is that realistic measurements constitute a complex process involving macroscopic detectors, hence should be explained by quantum statistical mechanics rather than be part of the axiomatic foundations themselves. (This is in marked contrast to other foundations, and distinguishes the present system of axioms.)
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics. Furthermore, concurrent advances in experimental techniques and in the theory of quantum computation have led to a strong interest in questions of quantum information, in particular in the sense of the amount of information about unknown parameters in given observational data or accessible through various possible types of measurements. This scenery is outlined (with an audience of statisticians and probabilists in mind).
Even though quantum mechanics has existed for almost 100 years, questions concerning the foundation and interpretation of the theory still remain. These issues have gathered more attention in recent years, but does this mean that physicists are more aware of foundational issues concerning quantum mechanics? A survey was sent out to 1234 physicists affiliated to 8 different universities. 149 responded to the questions, which both concerned foundational issues related to quantum mechanics, specifically, as well as questions concerning interpretations of physical theories in general. The answers to the survey revealed that foundational concepts in quantum mechanics are still a topic that only a minority of physicists are familiar with, although a clear majority of physicists find that interpretations of physical theories are important. The various questions, as well as how the respondents answered, are presented. The survey intends to give an overview of what the opinion of the physics community, in general, is concerning issues related to quantum mechanics.
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