Page:The principle of relativity (1920).djvu/38

 Now with regard to this attempt;—the time-estimation of events, we can satisfy ourselves in the following manner. Suppose an observer—who is stationed at the origin of coordinates with the clock—associates a ray of light which comes to him through space, and gives testimony to the event of which the time is to be estimated,—with the corresponding position of the hands of the clock. But such an association has this defect,—it depends on the position of the observer provided with the clock, as we know by experience. We can attain to a more practicable result by the following treatment.

If an observer be stationed at A with a clock, he can estimate the time of events occurring in the immediate neighbourhood of A, by looking for the position of the hands of the clock, which are synchronous with the event. If an observer be stationed at B with a clock,—we should add that the clock is of the same nature as the one at A,—he can estimate the time of events occurring about B. But without further premises, it is not possible to compare, as far as time is concerned, the events at B with the events at A. We have hitherto an A-time, and a B-time, but no time common to A and B. This last time (i.e., common time) can be defined, if we establish by definition that the time which light requires in travelling from A to B is equivalent to the time which light requires in travelling from B to A. For example, a ray of light proceeds from A at A-time t_{A} towards B, arrives and is reflected from B at B-time t_{B}, and returns to A at A-time t´_{A}. According to the definition, both clocks are synchronous, if

t_{B} - t_{A} = t´_{A} - t_{B}.