Time-Energy Uncertainty Relations for Neutrino Oscillation and M\"Ossbauer Neutrino Experiment

TL;DR

This paper derives time-energy uncertainty relations for neutrino oscillations and discusses how M"ossbauer neutrino experiments could test these fundamental quantum principles and the nature of neutrino oscillations.

Contribution

It introduces a new application of the Mandelstam-Tamm method to neutrino oscillations and proposes M"ossbauer experiments as a test for the energy uncertainty requirement.

Findings

Small energy uncertainty in M"ossbauer neutrinos conflicts with the uncertainty needed for oscillations.

M"ossbauer neutrino experiments can test the applicability of time-energy uncertainty relations.

Potential to reveal the true quantum nature of neutrino oscillations.

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 (M\"ossbauer) 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. A M\"ossbauer neutrino experiment could provide a unique possibility to test the applicability of the time-energy uncertainty relation to neutrino oscillations and to reveal the true nature of neutrino oscillations.