Lorentz Transformations in Four Dimensions

Abstract

An observer travelling in a straight line at constant speed can determine the coordinates t, x of events that happen along the line by the radar method: x is the distance of an event from the observer and t is the time shown on the observer’s clock at the simultaneous event at the observer’s location. It is built into the definition of x and t that light travels at constant speed; but it is a consequence of it that a second observer moving along the line at a different speed will have a different idea of simultaneity. The coordinate systems of the two observers are related not by the classical Galilean transformation, but by the Lorentz transformation.