Relativistic Aberration: The Transformation of a Propagating Field

TL;DR

This paper derives the retarded electromagnetic field of a moving charge considering relativistic aberration effects, emphasizing the importance of transforming propagation velocities for consistency with special relativity.

Contribution

It introduces a comprehensive transformation of propagating fields that includes velocity vectors, addressing a gap in standard relativistic field transformations.

Findings

Retarded field of a moving charge derived with aberrational effects

Velocity transformations are essential for consistent field transformations

Highlights the necessity of including aberration in all propagating field transformations

Abstract

The fields used to describe the influence of masses and electric charges are generally accepted to propagate at the speed of light from their sources. To obtain these fields for a moving charge which are consistent with special relativity, transformations should be applied to the propagating field in the charge's rest frame to acquire the propagating field in the charge's primed inertial frame. These transformations are of its coordinates, and also the velocity vectors of the field's propagation, which consequently lead to a change in the field's direction and as a result its strength. Yet, the electric field propagation velocities are neglected and not currently transformed. This omission has consequences when it comes to transforming the field from the source's rest frame to the source's primed frame, as this primed frame's field would then be inconsistent with the calculated retarded field's directions and consequently its strengths in this primed frame. Here the retarded field of a moving point charge will be derived and from this the requirement of the velocity transforms and the aberrational effects will be shown. Hence, the full consistent inertial frame transform will be given. This work shows the general theoretical basis and legitimacy of the aberrational effects and acts as an argument for their implementation on all propagating fields.