Neutrino oscillations are quantum phenomena where neutrinos change flavor as they propagate through space.Neutrino oscillations are a quantum mechanical phenomenon where a neutrino initially possessing a certain lepton flavor (electron, muon, or tau) can later be detected as a neutrino of a different flavor. This is explained by the fact that flavor states are superpositions of mass states differing in mass. The interference of these mass waves during propagation leads to a periodic change in the probability of detecting different flavors.
The idea of oscillations was proposed by Bruno Pontecorvo in 1957, by analogy with kaon oscillations. The effect was first experimentally detected in 1998 at the Super-Kamiokande facility (Japan) through the deficit of muon neutrinos from atmospheric showers. Solar neutrino anomalies, previously recorded by Ray Davis's chlorine-argon experiment, were explained as oscillations. Modern data from KamLAND, Daya Bay, and others have confirmed all three mixing angles.
Neutrino propagation is described by a superposition of mass states |ν_i⟩ with definite mass mi. Flavor states |ν_α⟩ are related to mass states through the unitary mixing matrix U_αi. The Hamiltonian in vacuum is diagonal in the mass basis, so each mass state evolves with a phase exp(-i m_i² L/(2E)). The interference of these phases gives rise to an oscillating probability P(να → νβ). In matter, an effective potential for interaction with electrons is added (the Mikheyev–Smirnov–Wolfenstein effect), enhancing oscillations (e.g., in the Sun).
Understanding neutrino oscillations proves that neutrinos have mass, which means they can play a role in dark matter and influence the evolution of the Universe.
Solar neutrinos pass through the Earth completely, and only one in a hundred billion interacts along the way, so detectors are built deep underground or underwater — to filter out cosmic noise.
| P | variable | Survival probability of electron antineutrinos — probability |
| \theta_{12} | variable | Solar mixing angle — mixing angle |
| \Delta m_{12}^2 | variable | Mass-squared difference between mass eigenstates 1 and 2 — mass squared difference electronvolt squared |
| L | variable | Distance traveled by the neutrino — distance metre |
| E | variable | Neutrino energy — energy joule |
| \sin^2 | operator | Square of the sine function — sine squared |














