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

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

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Identity and Individuality in Quantum Theory.Steven French - 2008 - Stanford Encyclopedia of Philosophy.
The Parthood of Indiscernibles.Lidia Obojska - 2019 - Axiomathes 29 (5):427-439.

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References found in this work

Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Oxford University Press.
Parts : a Study in Ontology.Peter Simons - 1987 - Revue de Métaphysique et de Morale 2:277-279.
Are Quantum Particles Objects?Simon Saunders - 2006 - Analysis 66 (1):52-63.
Relational Holism and Quantum Mechanics1.Paul Teller - 1986 - British Journal for the Philosophy of Science 37 (1):71-81.

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