We must not allow ourselves to be misled by a further generalisation of Einstein’s, known as the Postulate of Equivalence, according to which even an accelerated observer may be considered at rest. This new postulate modifies to a certain degree the position of the problem of the two twins. Whereas the special principle did not allow us to consider the accelerated wanderer as at rest, the postulate of equivalence permits us to adopt this alternative view. However, those who hope to discover by this means a logical inconsistency in the theory, will again be disappointed; for the postulate states expressly that an accelerated observer may be considered at rest only if we assume that a field of gravitation takes the place of the field of inertial forces to which the accelerated observer was submitted. Then, in virtue of the postulate of equivalence itself, exactly the same relative rejuvenation will take place except that it will now be ascribed to gravitation instead of to acceleration. It is hoped that the paradox of the two twins has been presented in a sufficient number of ways to enable the conscientious student to master the difficulty. The problem requires a certain effort of introspection; but once we have succeeded in ridding ourselves of our prejudiced ideas regarding space and time, the paradox will vanish of itself. And now let us mention another type of so-called paradox which appears to cause considerable trouble to beginners. We refer to the Einsteinian addition of velocities. Thus, the critic begins by stating that according to the dictates of common sense , so that it is only natural to assume that a velocity of one mile per second plus another velocity of one mile per second equals a velocity of two miles per second. Einstein’s contention that the resultant velocity is slightly less than two miles per second is therefore an absurdity on the face of it. But if we examine these arguments carefully we shall see that they again are based on a faulty understanding of the problem. Even in classical science it is not necessarily correct to state that velocities add up like the numbers of arithmetic. Consider, for instance, the following illustration: If, while we are standing on an embankment, a train moves away from us with a speed and if a rifle bullet is shot from the train with a speed , it is not always correct to state that the velocity of the bullet relatively [Pg 239] to us on the embankment is . This statement is true only when the velocities of the train and the bullet lie along the same straight line. If we neglect to specify this restriction, our statement is incorrect. In Einstein’s theory the problem is very similar.