At this stage we must mention that as far back as 1827 an English doctor named Brown had noticed that fine particles suspended in a liquid appeared to be quivering when viewed under the microscope. Brown attributed these curious motions to the presence of living organisms; others suggested that they were due to inequalities of temperature brought about by the illumination of the microscope. On the other hand, the adherents of the kinetic theory maintained that these Brownian movements were due to the impacts of the molecules of the fluid on the suspended particles. Now the important point to understand is that this latter hypothesis could serve only as a suggestion. Before any reliance could be placed in it, it would be necessary to prove that the precise Brownian movements actually observed were in complete quantitative agreement with the theoretical demands of the kinetic theory; and a quantitative theory of this sort had never been formulated. Such was the state of affairs when Einstein, in one of his first papers, gave an exhaustive quantitative solution of the problem of Brownian movements (in the case both of translations and of rotations), stating what the precise movements would have to be if the kinetic theory of fluids corresponded to reality.
Perrin then submitted the Brownian movements to precise quantitative measurements with a view to checking up on Einstein’s anticipations. The result was a disappointment; for Perrin found a considerable discrepancy between those anticipations and experiment. And so the kinetic theory of Brownian movements appeared to be untenable, and, more generally, the whole kinetic theory of gases and fluids to be in peril. When informed of Perrin’s results, Einstein went over his calculations afresh and discovered a numerical mistake in his computations. On rectifying this error he found that the theoretical anticipations were in perfect agreement with Perrin’s measurements. About the same time, by means of mathematical calculations based on the quantum theory, Einstein succeeded in accounting for the specific-heat difficulty mentioned previously. As for the arguments directed against the kinetic theory by reason of the “equipartition-of-energy theorem,” they in turn were answered, thanks to the quantum theory, itself a product of quantitative investigation. The net result was that the kinetic theory was finally established, the principle of entropy ceased to be regarded as an absolute principle, and Ostwald surrendered.
Our purpose in giving this brief historical sketch of the problem of Brownian movements has been to show that loose guesses, unless supported by arguments of a precise quantitative nature, are of little interest to physical science. For this reason no great importance is attributed to the vague atomistic speculations of Democritus or to the relativistic speculations of Mach, even though, in the light of subsequent developments, the latter may prove to be correct. In all cases of this sort, the credit goes (and rightly so) to the theoretical investigator who has succeeded in overcoming the major difficulty, that of working out the theory along rigid mathematical lines. To be sure, in many instances the thinker who makes the guess or advances the hypothesis also follows it up mathematically. Such was the case with Einstein when he formulated the postulate of equivalence for the purpose of interpreting the significance of the equality of the two masses. When a dual contribution of this type occurs, the credit is of course twofold.
[150] “The Meaning of Relativity.”
[151] Quite recently Dr. Whitehead has endeavoured to work out the same problem afresh.
[152] A very lucid exposition of Poincaré’s attack is given in Cunningham’s “Principle of Relativity” (1914), pp. 173 ff.
[153] 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.