A Discussion on Particle Number and Quantum Indistinguishability

Foundations of Physics 37 (6):855-878 (2007)
Abstract
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept
Keywords quasisets  particle number  quasicardinality  quantum indistinguishability
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DOI 10.1007/s10701-007-9129-5
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Remarks on the Theory of Quasi-Sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1/2):101 - 124.
No Two Entities Without Identity.Benjamin C. Jantzen - 2011 - Synthese 181 (3):433-450.
Many Entities, No Identity.Jonas R. Becker Arenhart - 2012 - Synthese 187 (2):801-812.

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