Foundations of Physics 37 (6):855-878 (2007)
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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Citations of this work BETA
Remarks on the Theory of Quasi-Sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1/2):101 - 124.
Finite Cardinals in Quasi-Set Theory.Jonas R. Becker Arenhart - 2012 - Studia Logica 100 (3):437-452.
Weak Discernibility in Quantum Mechanics: Does It Save PII?Jonas Rafael Becker Arenhart - 2013 - Axiomathes 23 (3):461-484.
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