Indistinguishable particles

In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, indistinguishable particles (also called identical or indiscernible particles) are <a href="/facts/Particle/JHKr2w6h">particles</a> that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, <a href="/facts/Elementary_particle/CTFDM97U">elementary particles</a> (such as <a href="/facts/Electron/L0KBo5cW">electrons</a>), composite <a href="/facts/Subatomic_particle/tMEzcTWQ">subatomic particles</a> (such as <a href="/facts/Atomic_nuclei/orpIm5Xl">atomic nuclei</a>), as well as <a href="/facts/Atom/FoQ4kGN5">atoms</a> and <a href="/facts/Molecule/N9ljSfFq">molecules</a>. 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 <a href="/facts/Particle_statistics/hJaSBe1l">quantum statistics</a>. They were first discussed by <a href="/facts/Werner_Heisenberg/n4qzYvj4">Werner Heisenberg</a> and <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a> in 1926.
There are two main categories of identical particles: <a href="/facts/Boson/XtPFcjb5">bosons</a>, which can share <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a>, and <a href="/facts/Fermion/LEckdDsR">fermions</a>, which cannot (as described by the <a href="/facts/Pauli_exclusion_principle/lsBKGeHD">Pauli exclusion principle</a>). Examples of bosons are <a href="/facts/Photon/mFNhAEzA">photons</a>, <a href="/facts/Gluon/t6YH8I21">gluons</a>, <a href="/facts/Phonon/tflWW6vw">phonons</a>, <a href="/facts/Helium-4/vNsL5qhC">helium-4</a> nuclei and all <a href="/facts/Meson/9R0kIc1q">mesons</a>. Examples of fermions are <a href="/facts/Electron/L0KBo5cW">electrons</a>, <a href="/facts/Neutrino/yGWVfSg2">neutrinos</a>, <a href="/facts/Quark/hwuuVkV5">quarks</a>, <a href="/facts/Proton/clCjepXP">protons</a>, <a href="/facts/Neutron/oRCM1geb">neutrons</a>, and <a href="/facts/Helium-3/SmPC5oT3">helium-3</a> nuclei.
The fact that particles can be identical has important consequences in <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a>, where calculations rely on <a href="/facts/Probability_theory/mFBn51rE">probabilistic</a> 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' <a href="/facts/Gibbs_paradox/bxFk0U5p">mixing paradox</a>.

Indistinguishable particles open-in-new

Indistinguishable particles