Paul Ehrenfest

“ With the aid of process we can send to each other signals with superluminal velocity in all direction. Would this mean "to telegraph into the past" for an observer who is conveniently moving with respect to them? – With a simplicity and clarity, which should have prohibited any further misunderstanding, Einstein showed: [7] Yes. Despite of editorial warning from W. Wien [8] , v. Ignatowsky published his opposite opinion that is evidently wrong. ”

“ Indeed: that Born's rigidity definition allows stationary rotation, is proven for a long time. It's known that the difficulty exclusively lies in the question after the passage from rest to uniform rotation [10] . I have formulated this difficulty in the following way:
"Let a relative-rigid cylinder of radius and height be given. A rotation about its axis which is finally constant, will gradually be given to it. ”

“ For example, if a rigid, homogeneously charged electron having the shape of an ellipsoid of three axes, shall execute an uniform translation inclined to its major axes, then a torque stemming from external forces must compensate the torque exerted by the field of the moving electron upon the electron itself. ”

“ Born has based this definition – in accordance to the basic idea of relativity theory – not on the system of measurement of a stationary observer, but on the (Minkowskian) measure-determinations of, say, a continuum of infinitesimal observers who travel along with the points of the non-uniformly moving body: for each of them in their measure the infinitesimal neighborhood should appear permanently undeformed. ”

“ When one calculates the longitudinal mass of the deformable electron in the usual manner, then one has to ascribe to the electron a non-electromagnetic energy of interior deformation forces, to maintain the energy theorem. ”

“ The electrons actually satisfy the rigidity requirement, yet they don't rotate. The theory of electrons nowhere unconditionally requires the assumption of rotating electrons. 2. The macroscopic "rigid" bodies are molecular aggregates, thus they are elastically deformable, so they don't satisfy the rigidity requirement and are able to rotate. ”

“ In the case of motion, the forces exerted upon each other by the volume elements of the electron, are not directed any more in the direction of the connecting line. Thus every element-couple provides a torque. ”

“ Event is the cause of . This conclusion from the existence of superluminal velocities, is exactly the one alluded to by Einstein (l.c.) , and for which it was recently coined the slogan "to telegraph into the past". ”

“ I assert: The periphery- and radius length upon measured in this way, coincides in the present example exactly with that, what was called by v. Ignatowsky as the disc circumference or disc radius at the stationary rotating disc, "synchronously measured" by the resting observer at moment . ”

“ Thus one could allow those non-electromagnetic forces (similarly to the molecular forces) to compensate the electromagnetic torque. So one would have given up the (pure electromagnetic) energy- and momentum conservations theorems, and would only maintain the center of gravity theorem. ”

“ Ignatowsky, Ann. d. Phys. 33, 607, 1910. ↑ The graphical representation in the Minkowskian -plane admits to conveniently overview the state of facts. The fundamental coordinate system , is chosen from the standpoint of observer . is the "world-line" of observer as protocoled by . is the epitome of all world-points being simultaneous with world-point from the standpoint of . ”