Page:Eddington A. Space Time and Gravitation. 1920.djvu/54

38 geometry, which will be described later. Our present point is that there is but one separation of two events in four dimensions, which can be resolved in any number of ways into the components length and duration.

We see further how motion must be purely relative. Take two events $$A$$ and $$B$$ in the history of one particle. We can choose any direction as the time-direction; let us choose it along $$AB$$. Then $$A$$ and $$B$$ are separated only in time and not in space, so the particle is at rest. If we choose a slightly inclined time-direction, the separation $$AB$$ will have a component in space; the two events then do not occur at the same place, that is to say, the particle has moved. The negation of absolute motion is thus associated with the possibility of choosing the time-direction in any way we please. What determines the separation of space and time for any particular observer can now be seen. Let the observer place himself so that he is, to the best of his knowledge, at rest. If he is a normal human being, he will seat himself in an arm-chair; if he is an astronomer, he will place himself on the sun or at the centre of the stellar universe. Then all the events happening directly to him will in his opinion occur at the same place. Their separation will have no space-component, and they will accordingly be ranged solely in the time-direction. This chain of events, marking his track through the four-dimensional world, will be his time-direction. Each observer bases his separation of space and time on his own track through the world.

Since any separation of space and time is admissible, it is possible for the astronomer to base his space and time on the track of a solar observer instead of that of a terrestrial observer; but it must be remembered that in practice the space and time of the solar observer have to be inferred indirectly from those of the terrestrial observer; and, if the corrections are made according to the crude methods hitherto employed, they may be inferred wrongly (if extreme accuracy is needed).

The most formidable objection to this relativist view of the world is the aether difficulty. We have seen that uniform motion through the aether cannot be detected by experiment, and therefore it is entirely in accordance with experiment that such motion should have no counterpart in the four-dimensional