What does 'indistinguishability' mean in an ontology without individuals?

OLIMPIA LOMBARDI

Buenos Aires

Workshop; Workshop Identity, Individuality and Indistinguishability in Physics and Mathematics; 2021

Laboratoire SPHERE - Sciences, Philosophie, Histoire, Université Paris Diderot-CNRS

By contrast to the Hilbert space formalism ofquantum mechanics, in the algebraic formalism a quantum system is representedby an algebra of observables, and states are functionals on that algebra. Ifthis mathematical priority of observables on states is transposed to theontological domain, the result is an ontology whose primary items are propertiesand relations, and systems are bundles of properties. This kind of ontology hasbeen proposed, underlining the advantages ofthis picture to deal with the main ontological challenges of quantum mechanics:contextuality, non-locality, and indistinguishability.In this talk I will focus onlyon indistinguishability in order to show that, in an ontology withoutindividuals, indistinguishability is not a relation betweenparticles, but an internal symmetry of a single composite system. Moreover, insuch an ontology, theIndistinguishability Principle is not an ad hoc postulate of the theory, butturns out to be a consequence of the ontologically motivated symmetry of theobservables of the composite system.