Identity in Physics: Statistics and the (Non-)Individuality of Quantum Particles

Matteo Morganti

Steven French, Décio Krause

Abstract This chapter presents the history of quantum statistics, from its beginnings in Planck’s work, through the development of Bose-Einstein and Fermi-Dirac statistics, to the more recent work on forms of parastatistics, focusing on the role played by considerations of particle identity and individuality. The new physics was taken to imply that quantum particles are non-individuals in some sense. This provides the framework for a novel account of Bohr’s view of particle individuality, which further illuminates his complementarity interpretation as well as Born and Schrödinger’s broadly structuralist approaches. Schrödinger’s view that identity does not apply to quantum particles is emphasized, as is Weyl’s incorporation of this view into his treatment of aggregates of particles.

Matteo Morganti

Tomasz Bigaj

This article follows an unorthodox approach to the individuation of quantum particles of the same type. According to this approach, individuation of the components of a composite system of identical particles is done not with the help of unphysical labels (indices) but physically meaningful projection operators. This unorthodox conception requires a modification of the standard notion of entanglement, in order to exclude states whose non-factorizability arises merely from the (anti)symmetrization of a product state. I will report several facts regarding the connections of the modified concept of entanglement with the issue of discernibility. I will also discuss recent experiments involving measurement-induced entanglement, and I will point out that they do not threaten the cogency of the new concept of entanglement. The statistical correlations observed in these experiments are explainable not by the entanglement of the initial state but by the creation of a new, genuinely entangled state by means of a pre-measurement selection. Finally, I will identify and discuss a genuine difference between non-entangled but non-factorizable states of identical particles and ordinary product states, which is that the former but not the latter admits an infinity of alternative and incompatible individuations by single-particle properties. This phenomenon can be accounted for using the concept of emergent particles proposed by Dennis Dieks. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Jonas R. Becker Arenhart, Décio Krause

Christian DE RONDE, Graciela Domenech, Federico Holik +1 more

The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual distinguishable objects. In this paper we present arguments in favor of quantum non-individuality, which -in addition to those based on quantum statistics- relate to the Kochen-Specker theorem and the principle of superposition. Then, we analyze the possibility of referring to 'possible individuals' instead of 'actual individuals', and show that the Modal-Kochen-Specker theorem precludes this interpretational move.