Time-Energy Uncertainty Relation for Neutrino Oscillations: Historical Development, Applications, and Future Prospects

The time-energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows the grasping of peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam-Tamm method, TEUR has recently been derived for neutrino oscillations by connecting the uncertainty in neutrino energy with the characteristic timescale of oscillations. Interestingly, the suggested interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects were later discussed in semiclassical gravity theory, by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations.

Automated summary

The time-energy uncertainty relation plays a crucial role in quantum mechanics, and has recently been derived for neutrino oscillations. It has been found that neutrinos can naturally emerge as unstable-like particles in this context. Further studies have explored the effects of gravity and quantum field theory on neutrino oscillations.