section of its light cone at present time expands faster than it can recede, so eventually it must reach the point . This is not necessarily true if the source charge's speed is allowed to be arbitrarily close to , i.e., if for any given speed there was some time in the past when the charge was moving at this speed. In this case the cross section of the light cone at present time approaches the point as the observer travels back in time but does not necessarily ever reach it. Uniqueness For a given point and trajectory of the point source , there is at most one value of the retarded time , i.e., one value such that . This can be realized by assuming that there are two retarded times and , with . Then, and . Subtracting gives by the triangle inequality. Unless , this then implies that the average velocity of the charge between and is , which is impossible. The intuitive interpretation is that one can only ever "see" the point source at one location/time at once unless it travels at least at the speed of light to another location. As the source moves forward in time, the cross section of its light cone at present time contracts faster than the source can approach, so it can never intersect the point again. The conclusion is that, under certain conditions, the retarded time exists and is unique. See also Maxwell's equations which govern classical electromagnetism Classical electromagnetism for the larger theory surrounding this analysis Relativistic electromagnetism Special relativity, which was a direct consequence of these analyses Rydberg formula for quantum description of the EM radiation due to atomic orbital electrons Jefimenko's equations Larmor formula Abraham–Lorentz force Inhomogeneous electromagnetic wave equation Wheeler–Feynman absorber theory also known as the Wheeler–Feynman time-symmetric theory Paradox of a charge in a gravitational field Whitehead's theory of gravitation References External links The Feynman Lectures on Physics Vol. II Ch. 21: Solutions of Maxwell’s Equations with Currents and Charges Electromagnetic radiation Potentials