The Logic of Identity: Distinguishability and Indistinguishability in Classical and Quantum Physics

TL;DR

This paper examines the Gibbs paradox in classical and quantum physics, arguing that it stems from pragmatic distinguishability rather than fundamental particle identity, and persists even with quantum symmetrization.

Contribution

It clarifies that the Gibbs paradox is unrelated to particle identity and persists in quantum mechanics, challenging common interpretations linking it to quantum indistinguishability.

Findings

Gibbs paradox is about pragmatic distinguishability, not fundamental identity.

The paradox persists in quantum mechanics despite symmetrization.

Critiques of classical solutions to the paradox are often mistaken.

Abstract

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a quantum connection stubbornly persists in the literature, even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role (in this we develop ideas of van Kampen [10]), and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical (anti-)symmetrization postulates.