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 observer perceives the world through their past light cone (PLC). The electromagnetic field at each point of this PLC is computed from the subluminal motion of point charges at the intersection of their worldlines with the PLC of that point, ensuring causal consistency and Lorentz covariance. Each charged particle—possibly including the observer—then experiences the Lorentz force from the field at its own spacetime location. This approach offers an interactive and intuitive representation of relativistic electromagnetism: it provides insight into how electric and magnetic fields transform across inertial frames, serves as a bridge between abstract formalism and physical intuition, and lends itself to pedagogical use in courses on special relativity or electrodynamics.