5 6 D O C . 4 4 T H E T H E O R Y O F R E L A T I V I T Y velocity of the light relative to the train car” (“w”) would now appear to be w = c – v. (This is the so-called “addition theorem.” We will denote it as IV.) This, how- ever, contradicts the principle of relativity (II), since that principle requires that ev- ery general law of nature must be the same whether using the train car or the track as our frame of reference and every light beam must then have the same velocity c, both for the track as well as for the train. It thus appears that either the principle of relativity or the simple law of the propagation of light must fail. This dilemma will now be solved by the special theory of relativity. It investi- gates the physical concepts of time and space and shows that, in reality, the incom- patibility of the principle of relativity (II) with the law of light propagation (III) does not exist at all. This is the “special theory of relativity.” It states that there is a “relativity of simultaneity” and a “relativity of spatial dis- tances” that bring the principle of relativity into accord with the law of light prop- agation. It thus says that two events which occur simultaneously with respect to the train tracks are not simultaneous with respect to the train moving on them. Let us imagine (Fig. 1) that at the point M on the track at, the midpoint between A and B, there are two mirrors which are inclined at 90° to each other as in Fig. 2. [1] If two lightning flashes occur at A and at B, then the flashes are “simultaneous” if an observer at M perceives them at the same time (—as long as we agree that the light propagates at the same velocity from A to M as from B to M). The same light flashes A and B also arrive at the train at whose midpoint M I likewise two mirrors are set up perpendicular to each other as in Fig. 2. At the instant of the lightning flashes, M and M I coincide as seen from the track. The observer at M I is however moving rapidly toward the light beam coming from B, since he is moving with the train toward B he thus sees the lightning flash from B earlier than the flash from A. Thus, events which are simultaneous for the track (“a coordinate system at rest”) are not simultaneous with respect to the train (“a moving coordinate system”), and vice versa (the relativity of simultaneity). In a similar manner, we find that the distance AB measured along the track must not have the same length as when it is measured from the moving train (the relativ- ity of spatial distances). We thus see that the temporal distance between two events,