Q-spaces and the foundations of quantum mechanics

TL;DR

This paper explores a new mathematical framework using quasi-set theory to incorporate the non-individuality and indiscernibility of quantum objects from the outset, aiming for a more intuitive foundation of quantum mechanics.

Contribution

It introduces a quasi-set theoretical approach to quantum mechanics, avoiding traditional label-based formalisms and addressing foundational issues related to quantum object identity.

Findings

Provides a more intuitive formalism for quantum mechanics

Addresses non-individuality of quantum objects from the start

Proposes modifications to the underlying logic of quantum theory

Abstract

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new "closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics.