Electricity and Magnetism

Foundations of relativity

We assume that the reader has already been introduced to special relativity. Here we shall review the principal ideas and formulas that are used in the text beginning in Chapter 5. Most essential is the concept of an inertial frame of reference for space-time events and the transformation of the coordinates of an event from one inertial frame to another.

A frame of reference is a coordinate system laid out with measuring rods and provided with clocks. Clocks are everywhere. When something happens at a certain place, the time of its occurrence is read from a clock that was at, and stays at, that place. That is, time is measured by a local clock that is stationary in the frame. The clocks belonging to the frame are all synchronized. One way to accomplish this (not the only way) was described by Einstein in his great paper of 1905. Light signals are used. From a point A, at time t A, a short pulse of light is sent out toward a remote point B. It arrives at B at the time t B, as read on a clock at B, and is immediately reflected back toward A, where it arrives at t′ A. If t B = (t A + t′ A) ∕ 2, the clocks at A and B are synchronized. If not, one of them requires adjustment. In this way, all clocks in the frame can be synchronized. Note that the job of observers in this procedure is merely to record local clock readings for subsequent comparison.