Now, in order to avoid any misconception, we may mention that in our example both twins hold in their hands clocks which, when placed side by side, beat out their seconds and minutes in perfect unison. Einstein’s theory indicates that the clock carried by the travelling twin will be behind time when brought back to earth and compared again with the clock that has been left there, in the keeping of the stationary twin. Some critics, such as Bergson, while accepting the postulate of the invariant velocity of light, deny that this slowing down in the beatings of the moving clock is required by the theory in any real sense. It is a mere appearance, Bergson maintains; a mathematical illusion. Just as the gradual shrinking of a man’s apparent size as he moves away from us would not connote any real decrease in his stature, so now, when the travelling twin returns with his clock to his brother on earth, the illusion would vanish, and both twins would recognise that their respective clocks were still marking the same time in perfect agreement, one with the other. Now, it cannot be stressed too strongly that this interpretation of the problem is worse than incorrect. Not only is it incorrect from the standpoint of Einstein’s theory, but it denotes on the part of the critic a colossal ignorance of the significance of a theory of mathematical physics. Here it must be recalled that the comparative retardation of the travelling twin’s clock is an inevitable consequence of the Lorentz-Einstein transformations. To deny, therefore, that these transformations correspond to what would actually occur, to what would be detected and measured by the most accurate instruments, would be to deny that the transformations possess any physical basis. If this be the stand we wish to take, well and good; but the logical outcome of this attitude will be to deny the legitimacy of the entire theory; [Pg 228] it would be quite impossible to retain the theory while contesting the real significance of the transformations. Once again a theory of mathematical physics is not one of pure mathematics. Its aim and its raison d’être are not solely to construct the rational scheme of some possible world, but to construct that particular rational scheme of the particular real world in which we live and breathe. It is for this reason that a theory of mathematical physics, in contradistinction to one of pure mathematics, is constantly subjected to the control of experiment. If, therefore, the Lorentz-Einstein transformations failed to yield the results that would be actually measured, Einstein’s theory as a means of physical discovery, as a co-ordination of physical facts, would be not only useless, but entirely incorrect, and we should have to abandon it.