Page:Eddington A. Space Time and Gravitation. 1920.djvu/147

VIII] the sequence we have followed in developing the theory, owing to the necessity of proceeding from the common ideas of space and time to the more fundamental properties of the absolute world. We started with a definition of the interval by measurements made with clocks and scales, and afterwards connected it with the tracks of moving particles. Clearly this is an inversion of the logical order. The simplest kind of clock is an elaborate mechanism, and a material scale is a very complex piece of apparatus. The best course then is to discover $$ds$$ by exploration of space and time with a moving particle or light-pulse, rather than by measures with scales and clocks. On this basis by astronomical observation alone the formula for $$ds$$ in the gravitational field of the sun has already been established. To proceed from this to determine exactly what is measured by a scale and a clock, it would at first seem necessary to have a detailed theory of the mechanisms involved in a scale and clock. But there is a short-cut which seems legitimate. This short-cut is in fact the Principle of Equivalence. Whatever the mechanism of the clock, whether it is a good clock or a bad clock, the intervals it is beating must be something absolute; the clock cannot know what mesh-system the observer is using, and therefore its absolute rate cannot be altered by position or motion which is relative merely to a mesh-system. Thus wherever it is placed, and however it moves, provided it is not constrained by impacts or electrical forces, it must always beat equal intervals as we have previously assumed. Thus a clock may fairly be used to measure intervals, even when the interval is defined in the new manner; any other result seems to postulate that it pays heed to some particular mesh-system.

Three modes of escape from this conclusion seem to be left open. A clock cannot pay any heed to the mesh-system used; but it may be affected by the kind of space-time around it. The terrestrial atom is in a field of gravitation so weak that the space-time may be considered practically flat; but the Rh