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Philosophy of Science

Does Quantum Mechanics Disprove the Principle of the Identity of Indiscernibles?

R. L. Barnette

Published Sep 1, 1978• 35 citations
Publisher

Abstract

Alberto Cortes, in [1], attempts to show (a) that Leibniz's Principle of The Identity of Indiscernibles (L) is a principle restricted to individuals (as distinct from a class of entities Cortes takes to be non-individuals), and (b) that photons (light quanta) appear to violate L (since they don't obey Pauli's Exclusion Principle). L is stated by Leibniz as “no two substances are completely similar, or differ solo numero.” In second-order quantification theory with identity L becomes:

DOI
10.1086/288822

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Alberto Cortes, in [1], attempts to show (a) that Leibniz's Principle of The Identity of Indiscernibles (L) is a principle restricted to individuals (as distinct from a class of entities Cortes takes to be non-individuals), and (b) that photons (light quanta) appear to violate L (since they don't obey Pauli's Exclusion Principle). L is stated by Leibniz as “no two substances are completely similar, or differ solo numero.” In second-order quantification theory with identity L becomes:
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.
Elementary particles appear in different ways.Particles of the same kind (similar particles) share all state-independent properties like mass, charge, and spin quantum number; there are many similar particles, but they are indistinguishable with respect to a certain class of properties.However, the case might even be stronger: similar particles apparently share all state-dependent properties, like spatial location and spin projection.This threatens the validity of Leibniz's famous Principle of the Identity of Indiscernibles (PII; see Rodriguez-Pereyra (2014) for a historical reconstruction).As it is usually understood, quantum mechanics requires for similar particles to be in permutation invariant states.Take the following state, for example:
Leibniz’s principium identitatis indiscernibilium excludes the existence of two different objects possessing all properties identical. Although perfectly acceptable for macroscopic systems, it becomes questionable in quantum mechanics, where the concept of identical particles is quite natural and has measurable consequences. On the other hand, Leibniz’s principle seems to be indispensable when we want to individuate an item and ascribe to it particular property (e.g. value of the projection of spin on a chosen axis). We may thus abandon the principle on the quantum level, claiming it falsity here, or (better) try to find other ways of individuation of objects, possibly by adopting appropriately the very concept of it. All these problems, and many other connected with identity and indiscernibility of quantum objects, are thoroughly discussed in the book of Tomasz Bigaj, unique in the world literature due to its comprehensiveness.
The Principle of the Identity of Indiscernibles (PII) is one of the most debatably discussed subjects in the philosophy of quantum physics. Gen- erally, the discussions focus on the domain of the predicate variables involved in the standard formulation of the principle, with versions where the properties are restricted in several ways. We argue that if we restrict the domain of properties, as happens with Henkin semantics for second- order language, we have no more PII, but only a weaker form of indistin- guishability. In quantum physics, we claim that under the non-individuals interpretation, which accepts that the standard notion of identity does not apply to quantum entities, PII fails not because of the properties, but due to the lack of sense of the notion of identity involved in the principle.
The topics of identity, individuality and indiscernibility had already entered the domain of the philosophy of physics, mainly in what respects the philosophy of quantum theories. In this paper, I present the main ideas of an underlying metaphysics that considers the basic entities of quantum physics as non-individuals, that is, as entities to which the standard theory of identity of classical logic and standard mathematics (set theory) does not apply. Two things must be emphasized: the first is that we pursue Erwin Schrödinger’s ideas that the notion of identity (or sameness ) does not apply to quantum things; the second is to follow Heinz Post’s claim that the non-individuality of quantum entities ‘must be introduced right at the start’ and not by taking individuals and making them pretend to be non-individuals ‘by hand’, say by confining them to non-rigid structures. Thus, this paper should be regarded as an attempt to justify the metaphysics of non-individuals and the logical systems that cope with them, although these systems are here only referred to. We also answer some criticisms that have been directed to such a view. The paper is directed to an audience of both physicists interested in foundations and philosophers of physics. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.