Paul Sophus Epstein

“ Since the world-line direction coincides with the time axis of the co-moving system, then the plane to be defined is identical with the previously mentioned plane . We want to apply the rule just obtained upon the broken lever of Lewis and Tolman. From the standpoint of the resting observer, the lever arms are: in the -direction and in the -direction (for the sake of generality, we assume them as being different) . Force acts upon the first one; forces and upon . The -plane of the co-moving system is rotated towards plane by the angle around the -plane. ”

“ Let observer be in motion with constant velocity relative to observer . throws an elastic ball towards system perpendicular to velocity ; mass and velocity of the ball (as measured from system ) shall be . At the same time, throws a ball towards perpendicularly to , whose mass and velocity , as measured from system , are exactly the same: and . The experiment is now so executed that the balls are colliding, where the collision diameter is exactly perpendicular to , so that the momentum components are uninfluenced by the collision towards . Now, Lewis and Tolman argued in the following way. ”

“ The transformation equation (11) is only applicable to the pure space components of the six-vector and is not reversible, i.e., it cannot serve to express the components of vector by those of vector . [17] There (as well as in the following) we understand under the total torque, thus the sum of torques of all individual forces. We see, that is not a six-vector like the six-vector of electrodynamics. ”

“ While the dynamics of relativity theory was substantially extended by the foundational papers of Minkowski [1] and Planck [2] , the field of statics – which became important also practically by the Trouton-Noble experiment [3] – experienced no attention from theoretical side up to now. ”