Page:Eddington A. Space Time and Gravitation. 1920.djvu/123

Euclidean character of space alone, and this curvature is additional to that predicted by Newton's law. If then we can observe the amount of curvature of a ray of light, we can make a crucial test of whether Einstein's or Newton's theory is obeyed.

This separation of the attraction into two parts is useful in a comparison of the new theory with the old; but from the point of view of relativity it is artificial. Our view is that light is bent just in the same way as the track of a material particle moving with the same velocity would be bent. Both causes of bending may be ascribed either to weight or to non-Euclidean space-time, according to the nomenclature preferred. The only difference between the predictions of the old and new theories is that in one case the weight is calculated according to Newton's law of gravitation, in the other case according to Einstein's.

There is an alternative way of viewing this effect on light according to Einstein's theory, which, for many reasons is to be preferred. This depends on the fact that the velocity of light in the gravitational field is not a constant (unity) but becomes smaller as we approach the sun. This does not mean that an observer determining the velocity of light experimentally at a spot near the sun would detect the decrease; if he performed Fizeau's experiment, his result in kilometres per second would be exactly the same as that of a terrestrial observer. It is the coordinate velocity that is here referred to, described in terms of the quantities $r$, $\theta$, $t$, introduced by the observer who is contemplating the whole solar system at the same time.

It will be remembered that in discussing the approximate geometry of space-time in Fig. 3, we found that certain events like $P$ were in the absolute past or future of $O$, and others like $P^{\prime }$ were neither before nor after $O$, but elsewhere. Analytically the distinction is that for the interval $OP$, $ds^{2}$ is positive; for $OP^{\prime }$, $ds^{2}$ is negative. In the first case the interval is real or "time-like"; in the second it is imaginary or "space-like." The two regions are separated by lines (or strictly, cones) in crossing which $ds^{2}$ changes from positive to negative; and along the lines themselves $ds$ is zero. It is clear that these lines must have important absolute significance in the geometry of the world. Physically their most important property is that pulses of light