We saw, when discussing congruence generally, that mathematical analysis by itself afforded us no means of exalting above all others one particular definition of congruent stretches either for space or for time; but that when we combined physics with mathematics, certain precise methods of defining congruence imposed themselves immediately in any given Galilean frame of reference. In the case of time-congruence we found it necessary to assume that any periodic phenomenon at rest in our frame, in a complete state of isolation from all external influences, would have to be regarded as passing at regular congruent intervals of time through the same initial state. This assumption was demanded by our belief in causality, and by a [Pg 232] justifiable definition of time-congruence we mean to imply one which would satisfy these consequences of causality. When, therefore, we stop to consider whether Einstein’s optical clocks yield us a justifiable definition of equal successive durations, the whole question simmers down to deciding whether or not the oscillations of a ray of light in an optical clock constitute an isolated phenomenon, or whether, according to the motion of the Galilean frame in which the clock is situated, certain perturbating influences may not interfere with the state of isolation we credit to the working of the clock. Until such time as the effect of the ether on an object moving through it had been settled, there was every reason to suppose that in the case of a Galilean frame moving through the ether, the effect of the ether wind would be to disturb the free oscillations of the light rays between the mirrors of the clock. And so the clock could not be considered isolated, and its readings would be valueless, or at least in need of correction. But Einstein’s special principle of relativity has precisely for its object to inform us that the ether behaves as though it were non-existent, so that any perturbative effect which classical science had suspected was ipso facto eliminated. In other words, if we accept the special principle of relativity, the optical clocks may be regarded as perfectly isolated; and their readings must therefore afford us with perfectly reliable measures of congruent time-stretches, as required by the principle of causality.