Seeing through the light cone: Visualizing electromagnetic fields in special relativity

TL;DR

This paper introduces a relativistic computer simulation that visualizes electromagnetic fields from a moving observer's perspective, enhancing understanding of how electric and magnetic fields transform in special relativity.

Contribution

It presents a novel, fully relativistic visualization tool that demonstrates electromagnetic phenomena from the viewpoint of a moving observer, aiding conceptual learning.

Findings

Provides an interactive visualization of electromagnetic fields in special relativity.

Shows how electric and magnetic fields transform across inertial frames.

Supports pedagogical understanding of relativistic electromagnetism.

Abstract

The theoretical framework of electromagnetism played a foundational role in Einstein's development of special relativity. To support conceptual understanding, we present a fully special relativistic computer simulation that visualizes electromagnetic fields from the perspective of a moving observer. In this simulation, the user observes electromagnetic phenomena through their past light cone and directly experiences the Lorentz force acting at that spacetime point. The electromagnetic field is computed from the subluminal motion of point charges at the intersection of their worldlines with the observer's past light cone, ensuring causal consistency and Lorentz covariance. This approach offers an interactive and intuitive representation of relativistic electromagnetism. It provides insight into how electric and magnetic fields transform across inertial frames, and serves as a bridge between abstract formalism and physical intuition. The simulation also lends itself to pedagogical use in courses on special relativity or electrodynamics.