Foundations of Physics

, Volume 44, Issue 12, pp 1302–1316

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



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 [11]), 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.


Indistinguishability Gibbs paradox Identity Identical particles 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for the History and Foundations of ScienceUtrecht UniversityUtrechtThe Netherlands

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