Individuality, quasi-sets and the double-slit experiment

TL;DR

This paper explores how quasi-set theory can model quantum non-individuality, focusing on the double-slit experiment, and suggests potential revisions to better capture indistinguishability in quantum physics.

Contribution

It analyzes the applicability of quasi-set theory to quantum phenomena, especially the double-slit experiment, and proposes ways to enhance its capacity to represent indistinguishability.

Findings

Quasi-set theory partially models quantum non-individuality.

The double-slit experiment highlights the need for degrees of indistinguishability.

Revisions to quasi-set axioms may improve modeling of quantum indistinguishability.

Abstract

Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is on the double-slit experiment, a major physical phenomenon which was never modeled from a quasi-set-theoretic point of view. The double-slit experiment strongly motivates the concept of degrees of indistinguishability within a field-theoretic approach, and that notion is simply missing in $\cal Q$. Nevertheless, other physical situations may eventually demand a revision on quasi-set theory axioms, if someone intends to use it in the quantum realm for the purpose of a clear discussion about non-individuality. I use this opportunity to suggest another way to cope with identity in quantum theories.