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Humean Chance in Physics

Carl Hoefer

Published Oct 24, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1093/oso/9780190907419.003.0007

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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.
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.
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.
The thesis of this article is simple: even if it is accepted that quantum mechanics is a fundamentally probabilistic theory, this provides us with no special reason to believe in "chances" in the sense of objectively existing factors that are responsible for the relative frequencies we encounter in experiments.More in general, quantum mechanics gives us no special reason to believe in the actual existence of modalities.We may intuitively be inclined to believe in chances as a kind of causes, just as in classical mechanics we are inclined to think of forces as causal powers that produce accelerations.It might even be the case that intuitions of this kind can be developed into a coherent metaphysical scheme (something which has yet to be done, I think).But as I shall argue, a sober Humean perspective on quantum mechanics is certainly possible as well, and has much to recommend it.In short, the thesis of the present paper is that for a Humean, quantum mechanics introduces no reasons to abandon his position.
In trying to develop a theory of chance, I have so far drawn largely on a metaphysical picture inspired by classical physics, and have used statistical mechanics as my central example of chance arising in physical theories. It has proven difficult to develop an adequate theory of chance. But perhaps things will look different if we turn to quantum mechanics. The theory of quantum mechanics is extremely well confirmed. It is doubtful whether it is strictly true in its current form, due to the well-known conflict between quantum mechanics and the general theory of relativity, but it is an outstandingly good example of a successful physical theory, and it represents a stark break from earlier models of the physical world. Perhaps by tapping into these resources, we can develop an adequate metaphysics of chance. The quantum mechanical world It is widely believed that quantum mechanics is starkly opposed to classical physics, because quantum mechanics claims that the world is governed by fundamentally indeterministic laws. As it happens, this common belief oversimplifies somewhat. Quantum mechanics is a theory that is formulated in relatively mathematical terms, quite removed from concepts of directly observable physical entities. Consequently, there is a great deal of room for interpretation of the meaning of the mathematics. Indeed, there are at least three interpretations of quantum mechanics which are serious candidates for giving an adequate account of how the mathematics relates to reality.
Abstract This chapter considers three ways in which probabilities may be derived from a physical theory without adverting to subjective considerations. The first derives from a fundamentally stochastic dynamics that implies transition chances at the level of natural law. The second is a Humean approach, in which probabilities are deployed as part of a compact system for conveying information about the structure of the Humean mosaic, i.e. the distribution of local physical quantities in space-time. The last employs either deterministic or stochastic dynamics together with a measure of typicality, i.e. a measure of sets of initial conditions that count as extremely large. Probabilities emerge in this setting as typical frequencies, that is, frequencies exhibited by most initial conditions.
On a very intuitive way of thinking, if it is already determined that some event will happen, then there is no non-trivial chance of it failing to happen, and if it is already determined that some event will not happen, then there is no non-trivial chance of it happening. A different sort of worry that arises for an actual frequentist analysis of deterministic chance is that such an analysis seems unsuited to theories like Boltzmannian statistical mechanics or Bohmian mechanics insofar as those theories are supposed to describe the evolution of the Universe as a whole. It should be clear, then, that there are options available for understanding deterministic chance that are in keeping with several of the leading metaphysical analyses of chance. It is widely accepted that whatever chances are, they are to be contrasted with individual credences . According to classical statistical mechanics, the fundamental laws are Newtonian and thus deterministic.