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Philosophia Verlag GmbH eBooks

Oppositions and Quantum Mechanics:

Jonas R. Becker Arenhart, Décio Krause

Published Jun 16, 2017• 4 citations
Publisher

Abstract

Abstract. In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechan-ics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up ” and “spin down ” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility are entangled in discussions of this problem in such a way that a proper conceptual treatment of those issues through the square seems profitable.

DOI
10.2307/j.ctv2nrzhd7.16

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Abstract. In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechan-ics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up ” and “spin down ” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility are entangled in discussions of this problem in such a way that a proper conceptual treatment of those issues through the square seems profitable.
We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger's cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist. We analyze that claim by employing the traditional square of opposition. We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them.
The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin‐statistics connection and the Symmetrization Postulate. In light of recent theories (such as q‐deformed commutators) that allow for ‘small’ violations of the spin‐statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles.1 Introduction2 Philosophical background2.1 Important terminology2.1.1 Identity2.1.2 Indistinguishability2.1.3 Indiscernibility2.2 When are particles indistinguishable?2.3 The Principle of the Identity of Indiscernibles and quantum mechanics2.4 The Principle of the Identity of Indiscernibles and logic2.5 Particle history2.6 Transcendental individuality3 Some quantum formalism3.1 The Principle of Permutation Invariance and the Symmetrization Postulate3.2 The configuration‐space approach3.3 Commutators and anticommutators, and identical particle statistics3.4 Q‐mutators4 Identical particle statistics: a holistic point of view5 Conclusions
The philosophy of physics is continuous with physics itself. Just as certain issues in the Foundations of Mathematics have been discussed by both mathematicians and by philosophers of mathematics, so certain issues in the philosophy of physics have been discussed by both physicists and by philosophers of physics. And just as there are issues of a more epistemological kind that tend to concern philosophers of mathematics more than they do working mathematicians, so there are issues that concern philosophers of physics more than they do working physicists. In this brief report I shall try to give an account of the present state of the discussion in America of both kinds of issues, starting with the problems of quantum mechanics, which concern both physicists and philosophers, and ending with general questions about necessary truth and the analytic-synthetic distinction which concern only philosophers. The problem of ‘measurement’ in quantum mechanics Quantum mechanics asserts that if A and B are any two possible ‘states’ of a physical system, then there exists at least one state (and in fact a continuous infinity of states) which can be described as ‘superpositions of A and B ’. If A and B are the sorts of states talked about in classical physics – definite states of position, or momentum, or kinetic energy, etc. – then their superpositions may not correspond to classically thinkable states.
One of the most famous metaphysical problems in the philosophy of quantum mechanics concerns the individuality status of quantum entities: are they individuals, or non-individuals? The typical approach to the problem consists in defending one of the options by appealing directly to features of quantum mechanics with the addition, eventually, of theoretical virtues the favoured proposal may have. In this paper, we argue that this strategy is inappropriate, because the problem of individuality is ill formulated in the case of quantum mechanics. In a nutshell, our point is that considerations exclusively from quantum mechanics are too general and generic to grant the level of particularity required for providing for a principle of individuality. Problems of individuality appear only at the level of particular applications of the theory in specific contexts, and in these cases, we shall argue, search for a metaphysical notion of individuality may be substituted by an epistemic notion of individuation. The approach also has the benefits of dissolving the problems created by metaphysical underdetermination on this front. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.
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.