As these
oscillations start and end with the beginning and end of the trip, we must assume that the trip, which lasted twenty years according to the traveller, will have lasted forty years in our own estimation. In other words, any registering device would show when both optical clocks were again placed side by side, that our earth clock had performed
oscillations during the trip, whereas the moving clock had performed just half that number, namely,
. Obviously, there is no illusion about the matter; for, as we have said, the oscillations of the two clocks could perfectly well be registered graphically, so that we should be dealing with a definite enumeration of registrations which any third party could verify.
It is quite easy to understand why these extraordinary results must take place. The cause is to be ascribed entirely to this invariant velocity credited to any light wave in all Galilean frames. Were it not for this postulate, the mere fact that the total length of the zigzag line was twice that of the up-and-down line would not connote any such difference in duration. Classical science would have assumed that since the path was twice as long, the velocity of the light wave along this path would have measured out twice as great; so that finally both durations would have been the same, in full accord with the classical belief in the uniqueness of time. In short, the comparative retardation of the moving clock follows as an inevitable necessity when once we agree to accept the validity of the postulate of the invariant velocity. On no account is it permissible to accept the postulate and then deny its mathematical consequences. If, therefore, the example of the trip to the star is too great a tax on our credulity, we must reject the postulate of invariant velocity and be faced with all the difficulties which surrounded electrodynamics prior to Einstein’s discoveries.
And now we may discuss another type of criticism, not quite so misplaced as that of Bergson, but still utterly erroneous. It has been argued, for instance, that all we have succeeded in proving is that if each Galilean observer measures time with the help of his optical clock, it is true that the duration of the trip will measure out differently according to the observer, but that if, in place of optical clocks, each observer had defined duration in terms of the usual mechanical watches, these strange discrepancies would never have arisen. In other words, the so-called slowing down of time in the frame of the travelling twin would be due entirely to the slowing down, not of time, but of the optical clock wherewith he proposed to measure time. Always according to this same criticism, the optical clock measured duration only in virtue of an artificial convention, and its readings could not be claimed to represent true lapses of time. Real time would flow independently of any clock; and to assert that an arbitrarily postulated clock defined true time would be about as reasonable as claiming that we should be dead were we to forget to wind up our watch. In other words, we might adjust our clock as we pleased, accelerate its motion, retard it, and even stop it completely, but we should go on living just the same.
The only way to refute this fallacious argument is to examine once again the premises of the relativity theory. Einstein starts with the assumption that Galilean motion through the ether is relative. From this it follows that no observer attached to a Galilean frame can by any means whatsoever ascertain whether his frame is in a state of uniform rectilinear motion or in a state of rest (special principle of relativity). Then he lays down his famous postulate on the invariant speed of light (300,000 kilometres per second) through any Galilean frame when measured by the observer attached to the frame. This postulate, as we have seen, enables any Galilean observer to construct an optical clock and to measure duration as referred to his clock, hence to his frame.