Note 1 — XIX EINSTEIN’S THEORY OF RELATIVITY

Let us see now how Einstein explains gravitation. When a body is not acted on by any forces (except gravitation) the quantity which remains constant for all changes of coordinates implies that the body will follow that path in the space of an outside observer which takes the least time. It is an observed fact that one body attracts another by gravitation; that is, the path of one body is bent from its course by the presence of another. Now we can bend the path of the fly in our block of film by straining the block in some way. Suppose, therefore, that I strain the world so as to bend the path of a body exactly as the gravitation due to some other body bends it; i.e., by a change of coordinates I have obtained the same effect as that produced by gravitation. Einstein’s theory, therefore, explains gravitation as a distortion of the world of space-time due to the presence of matter. Suppose first that a body is moving with no other bodies near; according to Einstein it will take the path in space which requires the least time, i.e., a straight line as agrees with our experience. If now the world be strained by the presence of another body or by a change of coordinates it will still pursue the path of least time, but this path is now distorted from the straight line, just as in a similar way the path on a globe requiring the least time to travel follows a great circle. So, on Einstein’s view of gravitation, the earth moves in an elliptical path around the sun not because a force is acting on it, but because the world of space-time is so distorted by the presence of the sun that the path of least time through space is the elliptical path observed. There is, therefore, no need to introduce any idea of “force” of gravitation. Einstein’s theory explains gravitation only in the sense that he has explained it away as a force of nature and makes it a property of space-time, namely, a distortion not different from an appropriate change of coordinates. He does not, however, explain how or why a body can distort space-time. It is noteworthy that whilst the law of gravitation and the law of uniform motion in a straight line when no force is acting were separate and independent laws under Newton, Einstein finds one explanation for both under the principle of relativity.1