Introduction to Electrodynamics

THE SPECIAL THEORY OF RELATIVITY

Einstein's Postulates

Classical mechanics obeys the principle of relativity: the same laws apply in any inertial reference frame. By “inertial” I mean that the system is at rest or moving with constant velocity. Imagine, for example, that you have loaded a billiard table onto a railroad car, and the train is going at constant speed down a smooth straight track. The game will proceed exactly the same as it would if the train were parked in the station; you don't have to “correct” your shots for the fact that the train is moving—indeed, if you pulled all the curtains, you would have no way of knowing whether the train was moving or not. Notice by contrast that you know immediately if the train speeds up, or slows down, or rounds a corner, or goes over a bump—the billiard balls roll in weird curved trajectories, and you yourself feel a lurch and spill coffee on your shirt. The laws of mechanics, then, are certainly not the same in accelerating reference frames.

In its application to classical mechanics, the principle of relativity is hardly new; it was stated clearly by Galileo. Question: does it also apply to the laws of electrodynamics? At first glance, the answer would seem to be no. After all, a charge in motion produces a magnetic field, whereas a charge at rest does not. A charge carried along by the train would generate a magnetic field, but someone on the train, applying the laws of electrodynamics in that system, would predict no magnetic field. In fact, many of the equations of electrodynamics, starting with the Lorentz force law, make explicit reference to “the” velocity of the charge. It certainly appears, therefore, that electromagnetic theory presupposes the existence of a unique stationary reference frame, with respect to which all velocities are to be measured.