Note 153 — Chapter XXXVIII · THE METHODOLOGY OF SCIENCE (continued 3)

In defence of an absolute space-time, flat everywhere and everywhen, Dr. Whitehead argues that the variable curvature forced upon space-time by matter in Einstein’s theory “leaves the whole antecedent theory of measurement in confusion” and hence must render knowledge impossible.

We do not consider the argument sound, for the absolute magnitudes of the relativity theory never were spatial or temporal, even in the special theory with its flat space-time. It was only the space-time interval that was absolute. As for the charge that the general theory renders knowledge impossible, it is refuted by the fact that Einstein’s astronomical predictions are of so precise a nature that it has required the most perfect instruments and most competent astronomers to detect them. This would scarcely be expected of a theory which had rendered knowledge impossible.

A further argument of Dr. Whitehead’s deals with the ambiguity in the measure of rotation which is entailed by Einstein’s matter-modified space-time theory of gravitation. Thus he writes: “The Einstein theory in explaining gravitation has made rotation an entire mystery.” Following this criticism, Dr. Whitehead proceeds to confuse the general theory of gravitation with the cylindrical universe and Mach’s mechanics, neglecting to notice that the former does not necessarily entail the latter. Einstein has insisted on this point repeatedly; besides, the gravitational equations themselves make it quite clear.

At all events, it is difficult to see any merit in the criticism based on rotation. All that we have a right to demand of any theory is that it be in harmony with the existence of an inertial frame with respect to which rotation develops centrifugal forces; for these forces have been detected by experiment. But we have no right to maintain that any experiment performed to this day has ever been sufficiently precise to demonstrate the absolute fixity of the inertial frame, or to deny that the frame may not suffer from a certain measure of indeterminateness when large masses move in its neighbourhood. Dr. Whitehead’s argument, which he claims is “based entirely on the direct results of experience,” would thus appear to be scientifically unsound.

As a matter of fact, calculations have been performed by J. A. Schouten (see Eddington’s illuminating discussion of the matter in “The Mathematical Theory of Relativity,” pp. 99-100), and the results have been to show that the indeterminateness of rotation resulting from the sun’s relative motion is no more than 1".94 a century in Einstein’s theory. And, most certainly, neither Newton’s experiment of the rotating bucket of water nor even the more precise tests taken with pendulums and gyroscopes would be able to detect a negligible magnitude of this sort. Hence it would appear that the general theory, though necessitating a fluctuating space-time background, is yet in perfect harmony with those dynamical facts of rotation which drove Newton to absolute space more than two hundred years ago.