Neutrinos and $v<c$

TL;DR

This paper presents a covariant classical and quantum framework for neutrino oscillations, consistent with field equations, and explores implications for CP violation and potential early neutrino arrival times in experiments.

Contribution

It introduces a semiclassical model for neutrino oscillations within the Stueckelberg covariant formalism, linking it to non-Abelian gauge interactions and CP violation mechanisms.

Findings

Model consistent with field equations and Lorentz force

Predicts possible early neutrino arrival ('pull back')

Provides a basis for future high-precision neutrino transit experiments

Abstract

The Stueckelberg formulation of a manifestly covariant relativistic classical and quantum mechanics is briefly reviewed and it is shown that in this framework a simple (semiclassical) model exists for the description of neutrino oscillations. The model is shown to be consistent with the field equations and the Lorentz force (developed here without and with spin by canonical methods) for Glashow-Salam-Weinberg type non-Abelian fields interacting with the leptons. We discuss a possible fundamental mechanism, in the context of a relativistic theory of spin for (first quantized) quantum mechanical systems, for CP violation. The model also predicts a possibly small "pull back", i.e., early arrival of a neutrino beam, for which the neutrino motion is almost everywhere within the light cone, a result which may emerge from future long baseline experiments designed to investigate neutrino transit times with significantly higher accuracy than presently available.