Editing Indistinguishable particles (section)

{{Short description|Concept in quantum mechanics of perfectly substitutable particles}}
{{Use American English|date=January 2019}}
{{more citations needed|date=September 2008}}
{{Statistical mechanics|cTopic=[[Particle statistics|Particle Statistics]]}}

In [[quantum mechanics]], '''indistinguishable particles''' (also called '''identical''' or '''indiscernible particles''') are [[particle]]s that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, [[elementary particle]]s (such as [[electron]]s), composite [[subatomic particle]]s (such as [[atomic nuclei]]), as well as [[atom]]s and [[molecule]]s. Although all known indistinguishable particles only exist at the quantum scale, there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability, as explored in [[particle statistics#Quantum statistics|quantum statistics]]. They were first discussed by [[Werner Heisenberg]] and [[Paul Dirac]] in 1926.<ref>{{Cite journal |last=Gottfried |first=Kurt |date=2011 |title=P. A. M. Dirac and the discovery of quantum mechanics |url=https://pubs.aip.org/aapt/ajp/article-abstract/79/3/261/398648/P-A-M-Dirac-and-the-discovery-of-quantum-mechanics?redirectedFrom=fulltext |journal=American Journal of Physics |volume=79 |issue=3 |pages=2, 10 |arxiv=1006.4610 |doi=10.1119/1.3536639 |bibcode=2011AmJPh..79..261G |s2cid=18229595}}</ref>

There are two main categories of identical particles: [[boson]]s, which can share [[quantum state]]s, and [[fermion]]s, which cannot (as described by the [[Pauli exclusion principle]]). Examples of bosons are [[photon]]s, [[gluon]]s, [[phonon]]s, [[helium-4]] nuclei and all [[meson]]s. Examples of fermions are [[electron]]s, [[neutrino]]s, [[quark]]s, [[proton]]s, [[neutron]]s, and [[helium-3]] nuclei.

The fact that particles can be identical has important consequences in [[statistical mechanics]], where calculations rely on [[probability theory|probabilistic]] arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' [[Gibbs paradox#The mixing paradox|mixing paradox]].