The emergent longitudinal wave from space and time derivatives transformations

TL;DR

This paper demonstrates that longitudinal waves naturally emerge from space and time derivative transformations, linking gauge transformations to wave phenomena and suggesting electrons behave as massless particles with a longitudinal wave component.

Contribution

It introduces a novel connection between gauge-like transformations and longitudinal wave emergence, providing a new perspective on particle wave behavior and invariance of the Dirac equation.

Findings

Longitudinal waves arise from space and time derivative transformations.

De Broglie waves are identified as longitudinal waves associated with particle motion.

Dirac equation invariance implies electrons behave as massless particles with a longitudinal wave component.

Abstract

We have shown that a longitudinal wave emerges as a result of general transformations similar to gauge transformations of electrodynamics. The time derivative and the gradient of the gauge function and their alike yield the longitudinal wave. The de Broglie wave associated with the particle motion is a longitudinal one. This wave accompanied the motion of all massive objects. It has a zero magnetic field (or vorticity). The invariance of Dirac equation under these transformations makes the electron to behave as a massless particle while having a mass.