On the electromagnetic origin of inertia and inertial mass

TL;DR

This paper explores the electromagnetic basis of inertia by analyzing an extended charged particle's motion, linking electromagnetic fields to inertial mass and addressing classical electrodynamics issues like the 4/3 mass paradox.

Contribution

It presents a covariant formulation showing the electromagnetic origin of inertial mass and offers a solution to the 4/3 mass paradox within classical electrodynamics.

Findings

Electromagnetic fields contribute to inertial mass.

Derived a covariant equation resolving the 4/3 mass paradox.

Linked velocity-dependent potentials to relativistic mass increase.

Abstract

We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton's second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle's own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle's vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle's vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the "4/3 mass paradox" for a spherical charge distribution.