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Probabilities in Physics

Claus Beisbart, Stephan Hartmann

Published Sep 1, 2011• 130 citations

Abstract

Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.

DOI: 10.1093/acprof:oso/9780199577439.001.0001

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Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.

The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned.I argue that this understanding of chances in quantum mechanics, despite being a part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers.

The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned.I argue that this understanding of chances in quantum mechanics, despite being a part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers.

Some of our best physical theories, notably quantum mechanics and statistical physics, are probabilistic. A question thus is what the probabilities from the theories mean. Since the theories provide a very successful account of the world, it is attractive to say that their probabilities mirror real-world (“ontic”) probabilities independent of human observers. The aim of this talk is to assess a view of such probabilities that has lately attracted much attention under the label “Humean chances”. The talk first clarifies what a philosophical view, or interpretation, of probabilities is supposed to achieve and lists the most important views of ontic probabilities. I then explain the Humean account as championed by David Lewis and Barry Loewer, among others, and discuss it critically in view of applications to physics, in particular to statistical physics. The main question is whether the account succeeds as a view about ontic probabilities. The talk is also meant to give an in-depth introduction into important issues in the metaphysics of probability.

Abstract This chapter states the aims of this volume and provides an introduction to the material to follow. In the first section, various interpretations of probabilities are surveyed and discussed with an eye to physics and its probabilities. It is stressed that the axioms of the probability calculus do not suffice to understand probabilities from physics. Objectivist interpretations take it that probabilistic statements reflect mind-independent facts. However, as a discussion of frequentism, propensity views, and other objectivist interpretations shows, it is difficult to say what exactly these facts are. According to subjectivist views, probabilities are used to express degrees of belief. These views have problems to explain why physicists reasonably agree on the values of many probabilities. The second section of this introduction summarizes the chapters of this volume.

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths.

Abstract Some of the most compelling examples of the existence of truly objective probabilities come from physics, in particular quantum physics and statistical mechanics. So it is crucial to the overall success of HOC that it be compatible with the objective probabilities found in these theories. First, objective probabilities in classical (Boltzmannian) statistical mechanics (SM) are discussed. It is shown that HOC does capture the central probabilistic postulates of SM, and indeed that it may do so in two distinct ways. Second, objective probabilities in standard, non-relativistic quantum mechanics (QM), the context in which the notion that fundamental physics is at bottom chancy first became widely accepted, are discussed. It is shown that HOC is especially apt for capturing the probabilities of QM; other accounts may do equally well (though some clearly do not), but none can do the job better.