A formal framework for the study of the notion of undefined particle number in quantum mechanics

Synthese 192 (2):505-523 (2015)

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
Keywords Quantum mereology  Set theory  Undefined particle number   Quantum indistinguishability  Quantum superpositions
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DOI 10.1007/s11229-014-0583-2
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References found in this work BETA

Parts: A Study in Ontology.Peter Simons - 1987 - Oxford University Press.
Are Quantum Particles Objects?Simon Saunders - 2006 - Analysis 66 (1):52-63.
Discerning Fermions.Simon Saunders & F. A. Muller - 2008 - British Journal for the Philosophy of Science 59 (3):499 - 548.
Physics and Leibniz's Principles.Simon Saunders - 2003 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 289--307.

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The Parthood of Indiscernibles.Lidia Obojska - forthcoming - Axiomathes:1-13.

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