Towards a Bell-Kochen-Specker theorem of identity

TL;DR

This paper explores how fundamental quantum theorems like Bell and Kochen-Specker relate to the concept of particle identity, suggesting that indistinguishable particles either lack individual identity or have a context-dependent one.

Contribution

It extends quantum foundational theorems to the issue of particle identity, proposing a link between ontological views and quantum contextuality or nonlocality.

Findings

Indistinguishable particles either lack individualism or have context-dependent identity.

Quantum theorems imply constraints on particle identity in quantum theory.

Arguments connect quantum symmetry with ontological perspectives on identity.

Abstract

In contrast to conventional, dynamical entanglement, in which particles with definite identity have uncertain properties, in so-called statistical entanglement, which arises between indistinguishable particles because of quantum symmetry rules, even particle identities are uncertain. The Bell and Kochen-Specker theorems imply that quantum properties either lack realism or possess it with a caveat of contextuality or nonlocality. In the matter of identity of multi-particle states of indistinguishable particles, these contrasting ontological attitudes are mirrored by the "bundle" vs. haecceity views. We offer some arguments aimed at importing the above theorems to the issue of identity in quantum theory, with the conclusion (under certain assumptions) that indistinguishable particles either lack individualism or possess a definite identity with a caveat of contextuality or nonlocality.