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Quantum Statistics and Non-Individuality

Steven French, Décio Krause

Published Jun 22, 2006• 1 citation
Publisher

Abstract

Abstract This chapter presents the history of quantum statistics, from its beginnings in Planck’s work, through the development of Bose-Einstein and Fermi-Dirac statistics, to the more recent work on forms of parastatistics, focusing on the role played by considerations of particle identity and individuality. The new physics was taken to imply that quantum particles are non-individuals in some sense. This provides the framework for a novel account of Bohr’s view of particle individuality, which further illuminates his complementarity interpretation as well as Born and Schrödinger’s broadly structuralist approaches. Schrödinger’s view that identity does not apply to quantum particles is emphasized, as is Weyl’s incorporation of this view into his treatment of aggregates of particles.

DOI
10.1093/0199278245.003.0003

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Abstract This chapter presents the history of quantum statistics, from its beginnings in Planck’s work, through the development of Bose-Einstein and Fermi-Dirac statistics, to the more recent work on forms of parastatistics, focusing on the role played by considerations of particle identity and individuality. The new physics was taken to imply that quantum particles are non-individuals in some sense. This provides the framework for a novel account of Bohr’s view of particle individuality, which further illuminates his complementarity interpretation as well as Born and Schrödinger’s broadly structuralist approaches. Schrödinger’s view that identity does not apply to quantum particles is emphasized, as is Weyl’s incorporation of this view into his treatment of aggregates of particles.
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One recent debate in philosophy of physics has centered whether quantum particles are individuals or not. The received view is that particles are not individuals and the standard methodology is to approach the question via the structure of quantum theory. I challenge both the received view and the standard methodology. I contend not only that the structure of quantum theory is not the right place to look for conditions of individuality that quantum particles may or may not satisfy, but also that there is an important role for traditional metaphysics to play. Consequently, my work brings together the philosophy of physics and traditional metaphysics literatures to shed new light on the debate over the individuality of quantum particles. I defend a set of conditions of individuality and argue that quantum particles satisfy these conditions thereby defending the view that particles are individuals in opposition to the received view. I also challenge a second feature of the standard methodology insofar as I challenge the significance of the Principle of the Identity of Indiscernibles in terms of which much discussion in the philosophy of physics literature is framed. My work is significant in a number of additional ways as well. My work implies that the dominant explanation for quantum statistics in terms of non-individuality is incorrect and it also undermines the ontic-structural realists metaphysical underdetermination challenge to the scientific realist.
Abstract Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.
Abstract This chapter covers the emergence of the statistical interpretation of the new quantum mechanics. After covering the earliest suggestions in this direction by Born and Pauli, it covers the statistical transformation theory of Dirac and Jordan, focusing on Jordan’s version. This version was an important part of the inspiration of Heisenberg’s uncertainty paper, which is covered next. The chapter concludes with the Como and Solvay conferences of late 1927 where Bohr revealed his complementarity principle and where the Copenhagen-Göttingen matrix-mechanics camp of Bohr, Born, Heisenberg, and Pauli squared off with Schrödinger, Einstein, De Broglie, and others in the wave-mechanics camp over the interpretation of the new quantum formalism.
Abstract In this paper, we deal with the historical origins of Fermi–Dirac statistics, focusing on the contribution by Enrico Fermi of 1926. We argue that this statistics, as opposed to that of Bose–Einstein, has been somewhat overlooked in the usual accounts of the old quantum theory. Our main objective is to offer a critical analysis of Fermi’s seminal paper and its immediate impact. Secondly, we are also interested in assessing the status of the particle concept in the years 1926–1927, especially regarding the germ of quantum indistinguishability. We will see, for example, that the first applications of the Fermi–Dirac statistics to the study of metals or stellar matter had a technical nature, and that their main instigators barely touched upon interpretative matters. Finally, we will discuss the reflections and remarks made in these respects in two famous events in physics of 1927, the Como conference and the fifth Solvay congress.