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Philosophy of Science

The Principle of the Identity of Indiscernibles and Quantum Mechanics

James Ladyman, Tomasz Bigaj

Published Jan 1, 2010• 73 citations
Publisher

Abstract

It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the ‘received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.

DOI
10.1086/650211

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It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the ‘received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.
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.
It has often been suggested that similar quantum particles may be a counterexample to the principle of the Identity of Indiscernibles. In this article, I discuss the status of indiscernibility in a perspectival approach to quantum mechanics. I argue that adopting an internal physical perspective can have the effect of making entities discernible even if they are not discernible relative to external reference frames, and thus perspectivalism offers a new way to understand the physical meaning of weak discernibility. I discuss whether this approach is circular, and I consider whether the reference frames involved are physically meaningful. I conclude that the Identify of Indiscernibles can probably be maintained in this context, though there are outstanding questions pertaining to the meaning of the quantum state and the way in which a system should be represented in its own reference frame.
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.