Time-energy uncertainty relations for neutrino oscillations and the Mossbauer 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 (Mossbauer) 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 Mossbauer neutrinos would indicate a stationary phenomenon where the evolution of the neutrino state occurs in space rather than in time. A Mossbauer neutrino experiment could provide a unique possibility to reveal the true nature of neutrino oscillations.