On the Usual Arguments for the Denial of Velocities which are greater than e. Yoshio ABE. Aceording to the theory of relativity, velocities which are greater than the light-velocity in vacuum are impossible. I am of opinion that this is probably true, but the usual arguments for it are not correct. After discussing several arguments for it, it is shown that the most reasonable one supported by almost all the relativists is what Einstein states in his “Über das Relativitätsprinzip and die aus demselben gezogenen Folgerungen” (Jahri). d. Radioakt. u. Elektronik, 4, 1907, s. 423). The essentials of his argument are as follows:- “Consider two point-events A and B and an action propagating between them connecting them causally. S and S' are two inertia systems, and the velocity of the former to the latter is Υ in +x direction. With reference to S, let the x-t coordinates of A and B be (0, 0), (l, T), and the velocity of propagation of the action U, while with reference to S', (0, 0), (l', T') and W respectively. Then we have T=l/U, T'=l'/W, (1) and by Lorentz-transformation T=l-1-Wν/c²/w-ν=T'1-Wν/c²/√1-ν²/c² (2) So, if |W|>e, for some values of Υ, T has different sign from T', or physically interpreted, the causal relation between A and B as observed from S is just opposite to that of the same events as observed from S', (i. e. if A is the effect of B in S, it is the cause of B in S'). This is very curious and contrary to the postulate of uniqueness of the causal relation.” Superficially considered, there will be found no flaw in this argument. But really it is there. In the above it is said that the same events A and B are observed from S and S'. There is no objection against such an expression as these, only the meaning of the adjective “ same” must be understood rightly. Tho relation of A to S is no same with its relation to S', and similarly for B. There is therefore nothing wonderful, nothing contrary to the causal law, even if the relation between A and B as observed from S be different from that observed from S', and moreover, there is nothing contrary even to the relativity-principle in this matter. (These points are in the japanese original minutely discussed and fully explained). Thus we must conclude that impossibility of the velocities greater than e cannot be deduced from the two fundamental principles of the spec al theory of relativity

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