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Journal of Huaiyin Teachers College

A Comparison Study between Identical Particles and True-Fake Monkey Kings

Xiaohui Jiang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In the famous Chinese myth fiction Journey to the West, the story of True-Fake Monkey Kings is amazing, and the identical particles problem in quantum mechanics is puzzling; the true monkey king was found out after a series of methods, but the particles were not so lucky. They shared the topic of individuality. They all began with the indistinguishablilty; however, the monkey kings did not lose their individuality, while the particles were considered to lose theirs. We will throw light on the point that which the particles lost is the cordiality, not the cardinality, and cardinality can be premise of individualization. Thus, at least, the particles' individuality is not wholly lost.

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In the famous Chinese myth fiction Journey to the West, the story of True-Fake Monkey Kings is amazing, and the identical particles problem in quantum mechanics is puzzling; the true monkey king was found out after a series of methods, but the particles were not so lucky. They shared the topic of individuality. They all began with the indistinguishablilty; however, the monkey kings did not lose their individuality, while the particles were considered to lose theirs. We will throw light on the point that which the particles lost is the cordiality, not the cardinality, and cardinality can be premise of individualization. Thus, at least, the particles' individuality is not wholly lost.
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind ("identical particles") are completely indistinguishable from each other and lack identity. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of "particle" in ordinary language and in classical physical theory, but also with how this term is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by "particles" in the classical limit of quantum mechanics. Elaborating on earlier work, we here analyze the premises of the standard view and discuss an alternative that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information 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:
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
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'.
According to classical physics, particles are basic constituents of the physical world. Quantum theory is much less friendly to particles; in particular, relativistic quantum field theory (RQFT) creates serious obstacles for the idea that particles are fundamental. Apparently, when moving from the domain of RQFT to that of classical mechanics (CM), particles have to emerge at some stage. It is standard to assume that this emergence has been completed at the level of quantum mechanics, halfway between RQFT and CM, even though particles of the same kind in many-particle quantum mechanics have the curious feature of being ‘entities without identity’. Against this ‘Received View’ about the nature of quantum particles we outline and defend an Alternative View (AV), in which the emergent character of particles is emphasized. According to this AV, the step to a particle theory has not yet been made in quantum mechanics: conditions have still to be satisfied in order to make the particle concept applicable. If these conditions are met, the quantum particles that emerge are distinguishable individuals possessing physically defined identities, in stark contrast to what the Received View asserts. We will compare and contrast the two Views, both from a physical and a logical/conceptual point of view. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.