Parity Violation and a Preferred Frame

Abstract

Based on parity violation in the weak interaction and evidences from neutrino oscillation, a natural choice is that neutrinos may be spacelike particles with a tiny mass. To keep causality for spacelike particles, a kinematic time under a non-standard form of the Lorentz transformation is introduced, which is related to a preferred frame. A Dirac-type equation for spacelike neutrinos is further investigated and its solutions are discussed. This equation can be written in two spinor equations coupled together via nonzero mass while respecting maximum parity violation. As a consequence, parity violation implies that the principle of relativity is violated in the weak interaction.