"Relativistic" particle dynamics without relativity

TL;DR

This paper reveals that the correct formulas for high-speed particle momentum and energy were implicitly known since Maxwell's era, demonstrated through a thought experiment inspired by Einstein that does not rely on relativity postulates.

Contribution

It shows that the fundamental expressions for relativistic momentum and energy were already implicit in classical physics, demonstrated via a modified Einstein thought experiment.

Findings

Correct high-speed particle momentum and energy formulas are historically implicit in Maxwell's physics.

A modified Einstein thought experiment can derive these formulas without relativity postulates.

The approach offers a new perspective on relativistic dynamics grounded in classical physics.

Abstract

It is shown that the correct expressions for momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he derived the inertial equivalence of energy, independently of the relativity postulates. A simple modification of the same experiment does the rest.