Relativistic dynamics of accelerating particles derived from field equations

TL;DR

This paper derives relativistic particle dynamics and Einstein's energy-mass relation from a neoclassical field theory where charges are distributions, revealing complementary mass concepts and predicting a small mass difference for electrons.

Contribution

It introduces a neoclassical field theory approach to derive relativistic mechanics and Einstein's relation, bridging classical and relativistic mass concepts.

Findings

Derivation of relativistic dynamics from field equations.

Prediction of a small electron mass difference.

Reconciliation of Newtonian and Einsteinian mass concepts.

Abstract

In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein's energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements.