Page:Eddington A. Space Time and Gravitation. 1920.djvu/66

50 rational observer would venture to state that the particle had completed its journey before it had begun it. It would, in fact, be possible for an observer travelling along $$NP$$ to receive a light-signal or wireless telegram announcing the event $$O$$, just as he reached $$N$$, since $$ON$$ is the track of such a message; and then after the time $$NP$$ he would have direct experience of the event $$P$$. To have actual evidence of the occurrence of one event before experiencing the second is a clear proof of their absolute order in nature, which should convince not merely the observer concerned but any other observer with whom he can communicate.

Similarly events in the sector $$U^\prime OV^\prime$$ are indubitably before the event $$O$$.

With regard to an event $$P^\prime$$ in the sector $$UOV^\prime$$ or $$VOU^\prime$$ we cannot assert that it is absolutely before or after $$O$$. According to the time-reckoning of our chosen observer $$S$$, $$P^\prime$$ is after $$O$$, because it lies above the line $$OX$$; but there is nothing absolute about this. The track $$OP^\prime$$ corresponds to a velocity greater than that of light, so that we know of no particle or physical impulse which could follow the track. An observer experiencing the event $$P^\prime$$ could not get news of the event $$O$$ by any known means until after $$P^\prime$$ had happened. The order of the two events can therefore only be inferred by estimating the delay of the message and this estimate will depend on the observer's mode of reckoning space and time.

Space-time is thus divided into three zones with respect to the event $$O$$. $$U^\prime OV^\prime$$ belongs to the indubitable past. $$UOV$$ is the indubitable future. $$UOV^\prime$$ and $$VOU^\prime$$ are (absolutely) neither past nor future, but simply "elsewhere." It may be remarked that, as we have no means of identifying points in space as "the same point," and as the events $$O$$ and $$P$$ might quite well happen to the same particle of matter, the events are not necessarily to be regarded as in different places, though the observer $$S$$ will judge them so; but the events $$O$$ and $$P^\prime$$ cannot happen to the same particle, and no observer could regard them as happening at the same place. The main interest of this analysis is that it shows that the arbitrariness of time-direction is not inconsistent with the existence of regions of absolute past and future.

Although there is an absolute past and future, there is between