This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends on what exactly the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization
This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends on what exactly the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization
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:
We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrödinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. 1. Introduction: The Currently Dominant View1.1. Weyl on Leibniz's principle1.2. Intermezzo: Terminology and Leibnizian principles1.3. The rise of the currently dominant view1.4. Overview2. Elements of Quantum Mechanics2.1. Physical states and physical magnitudes2.2. Composite physical systems of similar particles2.3. Fermions and bosons2.4. Physical properties2.5. Varieties of quantum mechanics3. Analysis of Arguments3.1. Analysis of the Standard Argument3.2. Van Fraassen's analysis3.3. Massimi's analysis4. The Logic of Identity and Discernibility4.1. The language of quantum mechanics4.2. Identity of physical systems4.3. Indiscernibility of physical systems4.4. Some kinds of discernibility5. Discerning Elementary Particles5.1. Preamble5.2. Fermions5.3. Bosons6. Concluding Discussion
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.
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.
The notions of identity and indistinguishability are a frequent source of misunderstanding, even among researchers working within the same field. The present text is primarily didactic in intent: it aims to show that a large part of such disagreements concerns the association of different meanings with one and the same word. Six notions are introduced and articulated – qualitative identity and numerical identity, haecceity, operational distinguishability, genidentity and permutational indistinguishability – and their content is clarified by examining two paradigmatic examples in parallel: two quantum particles and two occurrences of a word in a text. It is argued that the monadic version of Leibniz’s principle of the identity of indiscernibles is violated both by bosons, which can occupy one and the same state, and by fermions, for which indistinguishability operates in spite of Pauli’s exclusion principle, as the statistical counts make evident; the status of weaker relational versions of the principle remains contested. In the concluding part, the linguistic example is reread in the light of the conceptuality interpretation of quantum mechanics, for which it ceases to be merely an analogy and becomes a genuine explanation: on this interpretation, absent information can signify an absence of reality rather than mere ignorance.
Introduction In sections 6 and 7 of their paper in this volume, French and Rickles raise the question of the logical relations between the indistinguishability postulate (IP) and the various senses in which particles might fail to be individuals. In section 6 they refer to the convincing arguments of French and Redhead (1988) and of Butterfield (1993) that IP does not logically entail non-individuality, understood several ways – even though, as all seem to concede, there is something perverse about taking bosons and fermions to be individuals. Going the other way, the possibility of IP violating ‘quons’ (Greenberg, 1991) shows that if non-individuality is taken to mean the absence of continuous distinguishing trajectories, characteristic of standard quantum mechanics (QM), then non-individuality does not entail IP. Nor, as French and Rickles point out, do substance or haecceity views of individuality. But what if we conceive of individuality in terms of the Principle of the Identity of Indiscernibles (PII)? First, French and Redhead (1988) and Butterfield (1993) have given theorems showing that bosons and fermions violate PII, while the former have also demonstrated violations of PII in the case of a certain paraparticle state. But these cases, as I will explain (and as French and Rickles point out), cover just a very few of the possible kinds of quantum particles, and so for each kind the question arises as to whether it violates PII.