Quantum identity, content, and context: from classical to non-classical logic

TL;DR

This paper explores how quantum properties challenge classical logic, especially the concept of identity, and discusses the implications for quantum ontology and the development of non-classical logical frameworks.

Contribution

It introduces a novel perspective by questioning the applicability of classical identity in quantum mechanics, proposing a new mathematical approach distinct from standard quantum logics.

Findings

Quantum properties depend on context in complex ways

Indistinguishability of particles challenges classical identity

Proposes a new mathematical framework for quantum logic

Abstract

In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the indistinguishability of elementary particles. We argue that one could be in trouble in applying the classical theory of identity to the quantum domain if we take indiscernibility as a core and fundamental concept. Thus, in considering indistinguishability as such a fundamental notion, it implies, if taken earnestly, that one should not apply standard logic to quantum objects. Consequently, we end with a discussion about novel aspects this new mathematics brings and how it relates to some issues associated with the quantum world's ontology and the classical limit. We emphasize that, despite several different ways of questioning classical logic in the quantum domain, our approach is distinct. It involves one of the core concepts of classical logic, namely, identity. So, we are in a different paradigm from standard quantum logics.