# Do non-relativistic neutrinos oscillate?

## TL;DR

This paper investigates whether non-relativistic neutrinos can oscillate, concluding that oscillations are generally not possible unless neutrino masses are nearly degenerate, with implications depending on the Lorentz frame.

## Contribution

It provides a detailed analysis showing non-relativistic neutrino oscillations are generally forbidden, clarifying conditions and frame dependencies, and aligning with Hinchliffe's rule.

## Key findings

- Non-relativistic neutrinos do not oscillate unless nearly degenerate in mass.
- Oscillations depend on the Lorentz frame choice.
- Results support Hinchliffe's rule.

## Abstract

We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe's rule.