This is a systematic review of the concept of indistinguishability, in both classical and quantum mechanics, with particular attention to Gibbs paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of classical indistinguishability, notwithstanding the widely-held view, that classical particles can always be distinguished by their trajectories. The last section is about the notion of object more generally, and on whether indistinguishables should be thought of as objects at all.

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory, some to classical theory. The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability. Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of (...) the tensor product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction. (shrink)

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, (...) classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical partition (...) functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics. (shrink)

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 Gibbs’ concept ‘generic phase’, save that it is defined for state spaces with only finitely-many states of bounded volume and energy. 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. (shrink)

Classical particles of the same kind are distinguishable: they can be labeled by their positions and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated as (...) indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox. (shrink)

Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should be revised, either on the basis of quantum mechanics or on the basis of general and fundamental considerations about the distinguishability of particles. In this article we argue against this response. We show that both the extensive thermodynamic and the non-extensive statistical entropy are (...) perfectly alright within their own fields of application. Changes in the statistical formulas that remove the discrepancy must be seen as motivated by pragmatic reasons rather than as justified by basic arguments about particle statistics. (shrink)