Page:Eddington A. Space Time and Gravitation. 1920.djvu/57

II] relativity of phenomena makes the difficulty all the greater. If we deny a fundamental medium with continuous identity of its parts, motion uniform or non-uniform should have no significance; if we admit such a medium, motion uniform or non-uniform should be detectable; but it is much more difficult to devise a plan of the world according to which uniform motion has no significance and non-uniform motion is significant.

It is through experiment that we have been led back to the principle of relativity for uniform motion. In seeking some kind of extension of this principle to accelerated motion, we are led by the feeling that, having got so far, it is difficult and arbitrary to stop at this point. We now try to conceive a system of nature for which all kinds of motion of the observer are indifferent. It will be a completion of our synthesis of what is perceived by observers having all kinds of motions with respect to one another, removing the restriction to uniform motion. The experimental tests must follow after the consequences of this generalisation have been deduced.

The task of formulating such a theory long appeared impossible. It was pointed out by Newton that, whereas there is no criterion for detecting whether a body is at rest or in uniform motion, it is easy to detect whether it is in rotation. For example the bulge of the earth s equator is a sign that the earth is rotating, since a plastic body at rest would be spherical.

This problem of rotation affords a hint as to the cause of the incomplete relativity of Newtonian mechanics. The laws of motion are formulated with respect to an unaccelerated observer, and do not apply to a frame of reference rotating with the earth. Yet mathematicians frequently do use a rotating frame. Some modification of the laws is then necessary; and the modification is made by introducing a centrifugal force—not regarded as a real force like gravitation, but as a mathematical fiction employed to correct for the improper choice of a frame of reference. The bulge of the earth's equator may be attributed indifferently to the earth's rotation or to the outward pull of the centrifugal force introduced when the earth is regarded as non-rotating.

Now it is generally assumed that the centrifugal force is something sui generis, which could always be distinguished experimentally from any other natural phenomenon. If then