Quantum Identity, Content, and Context: From Classical to Non-classical Logic.

Abstract

In this paper, we discuss content and context for quantum properties. We givesome examples of why quantum properties are problematic: they depend on thecontext in a non-trivial way. We then connect this difficulty with properties to theindistinguishability of elementary particles. We argue that one could be in trouble in applying the classical theory of identity to the quantum domain if we takeindiscernibility as a core and fundamental concept. Thus, in considering indistinguishability as such a fundamental notion, it implies, if taken earnestly, that oneshould not apply standard logic to quantum objects. Consequently, we end with adiscussion about novel aspects this new mathematics brings and how it relates tosome issues associated with the quantum world’s ontology and the classical limit.We emphasize that, despite several different ways of questioning classical logicin 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 fromstandard quantum logics.