Retarded time

Lore & Background

In electromagnetism, an electromagnetic wave (light) in vacuum travels at a finite speed, the speed of light c. The retarded time is a wave emission time, which is a wave observation time subtracted by the wave propagation delay between the emission and the observation, since it takes time for information to travel between an emitter and an observer. This arises due to causality. Retarded time t' is calculated with a 'speed-distance-time' calculation for electromagnetic fields. If the EM field is radiated at position vector r' (within the source charge distribution), and an observer at position r measures the EM field at time t, the time delay for the field to travel from the charge distribution to the observer is |r − r'|/c. Subtracting this delay from the observer's time t then gives the time when the field began to propagate, i.e. the retarded time t'.

Reader's Guide

The retarded time is fundamental in electrodynamics, electromagnetic radiation theory, and Wheeler–Feynman absorber theory, as it shows that electromagnetic fields and forces acting on charges depend on their history, not their mutual separation. The calculation of electromagnetic fields at a present time includes integrals of charge density ρ(r', t_r) and current density J(r', t_r) using the retarded times and source positions. This concept ensures causality by linking the positions and times of source and observer, as shown by the equation c = |r − r'|/(t − t'). A related concept is advanced time, which takes the same mathematical form but with a plus sign, representing the time when an EM field originating at (r, t) reaches a position r'.

Did You Know?

• Retarded time is calculated by subtracting the propagation delay |r − r'|/c from the observation time t.
• The equation c = |r − r'|/(t − t') shows how positions and times of source and observer are causally linked.
• Advanced time takes the same mathematical form as retarded time but with a plus sign instead of a minus.
• Electromagnetic fields and forces acting on charges depend on their history, not their mutual separation.