Identical Particles in Quantum Mechanics

TL;DR

The paper argues that particle indistinguishability in quantum mechanics is not fundamental but depends on the definition of particle states, proposing a definition aligned with practical usage and classical limits.

Contribution

It introduces a new perspective on particle indistinguishability, showing it depends on state definitions and proposing a definition consistent with classical intuition.

Findings

Classical mechanics can exhibit indistinguishable particles under certain state definitions.

Indistinguishability is not an inherent quantum property but depends on how particle states are defined.

A proposed particle definition aligns quantum and classical descriptions of particles.

Abstract

If, in a system of identical particles, the one particle state is defined by the partial trace to one of the component spaces of the total Hilbert space, then all one particle states are identical. The particles are indistinguishable. This is often thought to be a typical quantum mechanical phenomenon. I will show however that an analogous procedure to define particle states exists in classical mechanics, which results in classical indistinguishable identical particles. From this analogy it follows that the indistinguishability of identical particles depends on how we define particle states. It is not an inevitable result of the symmetry postulate. Indeed, if particles are defined by partial traces, consistent use of the symmetry postulate leads to the conclusion that all identical particles in the universe are indistinguishable, so that particles can never be pointed at, not even in the classical limit. This does not correspond to the way the term particle is actually used in practice. I will argue that a particle should be defined in such a way that in the classical limit the quantum particle state becomes the state of a classical particle. This will lead us to a definition of particles which is in line with the way the term particle is actually used by physicists.