The Concept 'Indistinguishable'

TL;DR

This paper offers a deflationary interpretation of the concept of indistinguishable particles in quantum theory, linking it to the Gibbs concept of generic phase and clarifying its historical and conceptual significance.

Contribution

It introduces a simplified, finite-state perspective on indistinguishability, challenging traditional views and shedding new light on the history of quantum theory.

Findings

Reinterprets indistinguishability as akin to Gibbs' generic phase

Highlights differences between quantum and Gibbs concepts of indistinguishability

Provides a historical analysis of the concept's development

Abstract

The concept of indistinguishable particles in quantum theory is fundamental to questions of ontology. All ordinary matter is made of electrons, protons, neutrons, and photons and they are all indistinguishable particles. Yet the concept itself has proved elusive, in part because of the interpretational difficulties that afflict quantum theory quite generally, and in part because the concept was so central to the discovery of the quantum itself, by Planck in 1900; it came encumbered with revolution. I offer a deflationary reading of the concept "indistinguishable" that is identical to the Gibbs concept of "generic phase", save that it is defined for state spaces with only finitely-many states of bounded volume and energy (finitely-many orthogonal states, in quantum mechanics). That, and that alone, makes for the difference between the quantum and Gibbs concepts of indistinguishability. This claim is heretical on several counts, but here we consider only the content of the claim itself, and its bearing on the early history of quantum theory rather than in relation to contemporary debates about particle indistinguishability and permutation symmetry. It powerfully illuminates that history.