Time-energy Uncertainty Relations for Neutrino Oscillations and the Mössbauer Neutrino Experiment

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.