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Oxford University Press eBooks

Probability in Physics: Stochastic, Statistical, Quantum

Published Sep 4, 2014• 0 citations
Publisher

Abstract

Abstract This chapter defends an overtly pragmatic version of a Best System account of laws. David Albert and Barry Loewer’s version of such an account is critically examined, and it is argued that the account’s pragmatic dimension is in tension with the foundationalism to which Albert and Loewer also subscribe.
DOI
10.1093/acprof:oso/9780199673421.003.0010

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This paper is a discussion of David Albert's approach to the foundations of classical statistical menchanics. I point out a respect in which his account makes a stronger claim about the statistical mechanical probabilities than is usually made, and I suggest what might be motivation for this. I outline a less radical approach, which I attribute to Boltzmann, and I give some reasons for thinking that this approach is all we need, and also the most we are likely to get. The issue between the two accounts turns out to be one about the explanatory role probabilities play in statistical mechanics.
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 previous chapter addressed the challenge of making sense of the notion of a quantum state assignment being performed correctly without thereby acknowledging the notion of a quantum state a quantum system ‘is in’. The present chapter discusses what interpretation of quantum probabilities goes best with the account that I have called the ‘Rule Perspective’ and started to develop in the previous chapter. The first section considers what quantum probabilities should be taken to be probabilities of in the Rule Perspective; the second investigates what philosophical interpretation of probabilities applies best to quantum probabilities thus conceived. The third section considers two objections to the resulting account of quantum probabilities. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This chapter first discusses statistical techniques and concepts — including probability, probability distribution, average and expectation value, and uncertainty — that are relevant to quantum mechanics. The physical interpretation of probability in quantum mechanics is then discussed. It is argued that by adopting the statistical interpretation, one can think clearly about quantum mechanics without committing to any of the various physical interpretations, and without tackling the conceptual hurdles that they present. The history and substance of interpretational issues in quantum mechanics is then briefly discussed, the point being to introduce these profound, unresolved questions without taking sides in ongoing scientific debates. The chapter closes with a personal reflection on Albert Einstein, the most revered and fascinating figure in physics, and the one most famously at odds with the conventional interpretation of quantum mechanics.
Abstract Tim Maudlin has influentially argued that Humeanism about laws of nature stands in conflict with quantum mechanics. Specifically Humeanism implies the principle Separability: the complete physical state of a world is determined by the intrinsic physical state of each space‐time point. Maudlin argues Separability is violated by the entangled states posited by QM. We argue that Maudlin only establishes that a stronger principle, which we call Strong Separability, is in tension with QM. Separability is not in tension with QM. Moreover, while the Humean requires Separability to capture the core tenets of her view, there's no Humean‐specific motivation for accepting Strong Separability. We go on to give a Humean account of entangled states which satisfies Separability. The core idea is that certain quantum states depend upon the Humean mosaic in much the same way as the laws do. In fact, we offer a variant of the Best System account on which the systemization procedure that generates the laws also serves to ground these states. We show how this account works by applying it to the example of Bohmian Mechanics. The 3N‐dimensional configuration space, the world particle in it and the wave function on it are part of the best system of the Humean mosaic, which consists of N particles moving in 3‐dimensional space. We argue that this account is superior to the Humean account of Bohmian Mechanics defended by Loewer and Albert, which takes the 3N‐dimensional space, and its inhabitants, as fundamental.
The purpose of the present chapter is to respond to a thread of recent criticism against one candidate framework for interpreting quantum theories, a framework introduced and defended by David Albert and Barry Loewer: wave function realism, a framework for interpreting the ontology of quantum theories according to which what appears to be a nonseparable metaphysics ofentangled objects acting instantaneously across spatial distances is a manifestation of a more fundamental separable and local metaphysics in higher dimensions. Thechapterconsiders strategies for extending the wave function realist interpretation of quantum mechanics to the case of relativistic quantum theories, responding to arguments that this cannot be done.