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A discussion on particle number and quantum indistinguishability

Domenech, Graciela and Holik, Federico (2007) A discussion on particle number and quantum indistinguishability. [Preprint]


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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.

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Item Type: Preprint
Domenech, Graciela
Holik, Federico
Additional Information: Accepted for publication in Foundations fo Physics
Keywords: quasi-sets, identity, non-individuality
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Graciela Domenech
Date Deposited: 30 May 2007
Last Modified: 07 Oct 2010 15:15
Item ID: 3367
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Quantum Mechanics
Date: May 2007

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