3 - The Principle of Special Relativity

Abstract

This chapter describes the principle of special relativity. Considerations of relativity require that the uniformity of expansion of the wavefront in one inertial frame entail its uniformity in every inertial frame. The alternative would be to abandon the concept of inertial frame. The preservation of uniformity provides the valuable clue that the transformation be linear. Combining the property of linearity with the natural requirement of dimensional homogeneity that distances be transformed into distances and times into times, it follows that there can be no relative acceleration between the two frames. It is of some methodological significance that the absence of mutual acceleration need not be employed in the definition of an inertial frame, although most writers do so, but may be deduced as a consequence of the two frames being inertial. The time interval that is determined by the spreading of time through space, by spatially separated clocks which have been synchronized by means of a procedure which is appropriate to the particular reference frame in which the clocks are at rest, is called coordinate time.