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Time-energy uncertainty relation (TEUR) plays a fundamental role in quantummechanics, as it allows to grasp peculiar aspects of a variety of phenomenabased on very general principles and symmetries of the theory. Using theMandelstam-Tamm method, TEUR has been recently derived for neutrinooscillations by connecting the uncertainty on neutrino energy with thecharacteristic time-scale of oscillations. Interestingly enough, the suggestiveinterpretation of neutrinos as unstable-like particles has proved to naturallyemerge in this context. Further aspects have been later discussed insemiclassical gravity by computing corrections to the neutrino energyuncertainty in a generic stationary curved spacetime, and in quantum fieldtheory, where the clock observable turns out to be identified with thenon-conserved flavor charge operator. In the present work, we give an overviewon the above achievements. In particular, we analyze the implications of TEURand explore the impact of gravitational and non-relativistic effects on thestandard condition for neutrino oscillations.

Time-energy uncertainty relation for neutrino oscillations: historical development, applications and future prospects