Time–energy uncertainty relations for neutrino oscillations and the Mössbauer neutrino experiment

Abstract

Using the Mandelstam–Tamm method we derive time–energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant (Mössbauer) production and absorption of tritium antineutrinos is in conflict with the energy uncertainty which, according to the time–energy uncertainty relation, is necessary for neutrino oscillations to happen. Oscillations of Mössbauer neutrinos would indicate a stationary phenomenon where the evolution of the neutrino state occurs in space rather than in time. A Mössbauer neutrino experiment could provide a unique possibility to reveal the true nature of neutrino oscillations.