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- Title
A formal framework for the study of the notion of undefined particle number in quantum mechanics.
- Authors
Costa, Newton; Holik, Federico
- Abstract
It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position-supported by E. Schrödinger-asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions.
- Subjects
QUANTUM mechanics; WHOLE &; parts (Philosophy); QUANTUM numbers; QUANTUM logic; SET theory
- Publication
Synthese, 2015, Vol 192, Issue 2, p505
- ISSN
0039-7857
- Publication type
Article
- DOI
10.1007/s11229-014-0583-2