How Classical Particles Emerge From the Quantum World

TL;DR

This paper argues that classical particles emerge from quantum mechanics as entities distinct from quantum indices, challenging the traditional interpretation of symmetrization postulates and their implications for particle identity.

Contribution

It clarifies that symmetrization postulates apply to formal indices, not to classical particles, resolving the paradox of classical particles emerging from quantum indistinguishability.

Findings

Quantum symmetrization applies to indices, not particles.

Classical particles emerge as entities separate from quantum indices.

The paradox of identical classical particles is resolved by reinterpreting quantum indices.

Abstract

The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that \emph{quantum particles} of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state--in clear conflict with what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles \emph{emerge}, as new entities that do not correspond to the "particle indices" defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to \emph{particles}, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether the discussions about the status of identical quantum particles have not been misguided from the very start.