How Classical Particles Emerge From the Quantum World

Abstract

The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state-in clear conflict with what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the "particle indices" defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided.

On Some Troubles with the Metaphysics of Fermionic Compositions

“…Firstly, the assumption of factorism produces incorrect predictions concerning the behavior of physical systems in the classical limit, as well as the behavior of quanta within the realm of quantum field theory. As [6] first observed, factorism cannot account for the emergence of well-defined classical trajectories of indistinguishable particles, since under this interpretation such particles always occupy the exact same (mixed) states regardless of their interactions with the environment. To that Caulton adds that the transition from QM to QFT is similarly threatened by factorism, since according to the latter theory quanta always occupy pure states.…”

“…We interpret operators σ s r (P) as representing the following intuitive statements: 6 (INT)"Exactly r out of s particles possess propertyP .…”

“…One may disagree with this stipulation, but as a consequence of Footnote 5 Continued assumption of distinctness is an unnecessary addition to the general characterization of haecceitism that Caulton has in mind. 6 Operators σ s r (P) are natural generalizations of symmetric operators of the form P ⊗ P ⊥ + P ⊥ ⊗ P in the case of two particles. These two-particle projectors are commonly interpreted as expressing the fact that exactly one particle possesses property P (see [14], p. 74; [2], p. 194).…”

“…See e.g. [2,[4][5][6]12,14,15,22,26]. Caulton [4] deserves to be singled out here as containing the most technically and conceptually advanced analysis of the permutation-invariant method of individuating quantum particles.…”

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

“…For example, in the initial unmixed Gibbs situation, with the partition in place and with atoms of the same kind on both sides, N should refer to the total number of atoms on both sides of the partition: it clearly does not make any physical difference when we exchange labels across the partition. 3 But this implies that we correct the multiplicity of states by the same numerical factor, both before and after the removal of the partition. All entropy changes will therefore be exactly the same as when we do not make these corrections at all.…”