Note 116 — Chapter XXXIV · THE FINITENESS OF THE UNIVERSE

It is most important to note that the relativity of all motion, as expressed by the general principle of relativity, stands on an entirely different footing from the ultra-relativistic conception of rotation as upheld by Mach. The two forms of relativity have been muddled up so often that it appears necessary to point out their essential differences. The general principle of relativity merely states that the natural laws can be thrown into a form which remains covariant to all choices of mesh-system. In other words, all observers, whether Galilean, accelerated or rotating, will observe the laws of nature under the same tensor form; so that there is no reason to follow classical science and elevate one type of observer above another. This is what Einstein originally meant by the relativity of all motion. Thus the general principle of relativity in no wise implies that an observer would not realise that conditions had changed after the frame to which he was attached had been set into rotation.