The optical definition presents a marked superiority over those of classical science. Whereas, with the rotation of the earth, we had to assume the correctness of Newton’s law and of those of mechanics in order to determine the compensations necessitated by the earth’s breathing or by the friction of the tides, in the present case we assume practically nothing, and what little we do assume issues from the most highly refined experiments known to science. Now, the importance of Einstein’s definition lies not so much in its allowing us to obtain an accurate definition of time in our Galilean frame as in its enabling us to co-ordinate time reckonings in various Galilean frames in relative motion. So long as we restrict our attention to space and time computations in our frame, we may, as before, appeal to vibrating atoms for the measurement of congruent time-intervals and to rigid rods for the purpose of measuring space. It is when we seek to correlate space and time measurements as between various Galilean frames in relative motion that astonishing consequences follow. We discover that the concepts of spatial and temporal congruence of classical science must be modified to a very marked degree. They lose those attributes of universality with which we were wont to credit them. It is then found that congruence can only be defined in a universal way when we consider the extension of four-dimensional space-time. As we have mentioned, any change in our concepts of space and time congruence is not merely a local affair. Owing to the unity of nature, we shall be led to modify our entire understanding of the relatedness of phenomena, and must not be surprised to learn that a totally new science is the necessary outcome of Einstein’s new definitions. Old laws are cast aside, new ones take their place; and Einstein, by following his mathematical deductions with rigorous logic, without introducing any hypotheses ad hoc, proved that if his new definition of space-time congruence was physically correct, a whole series of hitherto unsuspected natural phenomena should ensue and should be revealed by precise experiment. Wonderful as it may appear, Einstein’s previsions have thus far been verified in every minute detail. [Pg 83] CHAPTER VII SYSTEMS OF CO-ORDINATES AND DISTANCE