: the nature of this field depends on the choice of the motion of
. This enabled Einstein to discover the laws which a gravitational field itself satisfies. It is important to notice that Einstein does not seek to build up a model to explain gravitation but merely proposes a theory of motions. His equations describe the motion of any body in terms of co-ordinates of the space-time manifold, making use of the interchangeability and equivalence implied in relativity. He does not discuss forces as such; they are, after all, as Karl Pearson states, "arbitrary conceptual measures of motion without any perceptual equivalent." They are simply intermediaries which have been inserted between matter 'and motion from analogy with our muscular sense.
A direct consequence of the application of the Principle of Equivalence in its general form is that the velocity of light varies for different gravitational fields, and is constant only for uniform fields (this does not contradict the special theory of relativity, which was built up for uniform fields, and only makes it a special case of this much more general theory of relativity). But change of velocity implies refraction, i.e. a ray of light must have a curved path in passing through a variable field of gravitation. This affords a very valuable test of the truth of the theory, since a star, the rays from which pass very near the sun before reaching us, would have to appear displaced (owing to the stronger gravitational field around the sun), in comparison with its relative position when the sun is in another part of the heavens: this effect can only be investigated during a total eclipse of the sun, when its light does not overpower the rays passing close to it from the star in question.[21] The calculated curvature is, of course, exceedingly small (1·7 seconds of arc), but, nevertheless, should be observable.
[21]We shall return to this test at the conclusion of the chapter.
The motion of the perihelion of Mercury, discovered by Leverrier, which long proved an insuperable obstacle regarded in the light of Newtonian mechanics, is immediately accounted for by the general theory of relativity; this is a very remarkable confirmation of the theory.
Before we finally enunciate the general theory of relativity, it is necessary to consider a special form of acceleration, viz. rotation. Let us suppose a space-time-domain (referred to a rigid body
) in which the first Newtonian Law holds, i.e. a Galilean field: we shall suppose a second rigid body of reference