On Bell's dynamical route to special relativity

TL;DR

This paper explores Bell's approach to special relativity by analytically solving the classical electron dynamics in motion and demonstrating how length contraction and time dilation emerge from electromagnetic forces.

Contribution

It provides an analytical solution to electron dynamics in uniform motion and discusses the electromagnetic origins of relativistic effects within Bell's framework.

Findings

Analytical solution for electron orbiting a nucleus in uniform motion

Numerical simulations for accelerated nucleus

Relativistic effects explained by electromagnetic forces

Abstract

This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed.