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

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.

25 pages, 5 figures; second half of Sec. 2 and entirety of Sec. 5 from arXiv:2408.05481v2 separated into this implementation paper following referee's suggestion