Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

TL;DR

This paper provides a theoretical analysis showing that particles with imaginary mass, modeled by specific wave equations, propagate at subluminal speeds, challenging the notion of superluminal particles like tachyons.

Contribution

It demonstrates that solutions to spacelike wave equations for particles with imaginary mass do not contain superluminal components, confirming subluminal behavior.

Findings

Solutions of the tachyonic Klein-Gordon equation lack superluminal components.

Spacelike wave equations describe subluminal particles with imaginary mass.

Wave packets propagate with subluminal group velocities, behaving as localized waves at low energies.

Abstract

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.