Page:EhrenfestStarr3.djvu/2

 rigidity definition, capable of passing from rest to uniform rotation? – I, have shown : No. claimed that from his calculations it follows: Yes. My protest forced him to admit : a) that no such thing follows from his relevant calculations, b) that his claim is wrong per se.

2. Is a ian body capable of executing curvilinear-translatory motions? – and  have shown: Yes. – claimed that it follows from his calculations, that only rectilinear-translatory motions are possible. – 's protest by letter forced him to admit : a) that no such thing follows from his relevant calculations, b) that his claim is wrong per se.

3. Provided, that a signalization process $$\Omega$$ is of such kind, that a couple of observers (mutually at rest) $$B_1$$ can say about it: With the aid of process $$\Omega$$ we can send to each other signals with superluminal velocity $$C$$ in all direction. Would this mean "to telegraph into the past" for an observer $$B_2$$ who is conveniently moving with respect to them? – With a simplicity and clarity, which should have prohibited any further misunderstanding, showed: Yes. Despite of editorial warning from,  published his opposite opinion that is evidently wrong. The graphical representation in the an $$(x,\ \tau=ct)$$-plane admits to conveniently overview the state of facts. The fundamental coordinate system $$Ox_{2}$$, $$O\tau_{2}$$ is chosen from the standpoint of observer $$B_2$$. $$O\tau_{1}$$ is the "world-line" of observer $$B_1$$ as protocoled by $$B_2$$. $$Ox_{1}$$ is the epitome of all world-points being simultaneous $$\left(\tau_{1}=0\right)$$ with world-point $$O$$ from the standpoint of $$B_1$$. $$OP$$ and $$ON$$ are lines representing the path of two signals, about which $$B_1$$ would say: "I'm signaling from $$O$$ into both direction with a velocity being much higher than the speed of light" ($$OP$$ and $$ON$$ indeed nearly coincide with the "simultaneity line" of observer $$B_1$$, i.e., they are "nearly $$\infty$$ fast to him). $$B_1$$ and $$B_2$$ then have to judge about the couple of world-points $$N$$ and $$O$$ as shown by the drawing, in the following way:

$$B_1$$: Event $$O\left(\tau_{1}=0\right)$$ is the cause of $$N(\tau_{1}$$ with $$ON_{1}>0)$$.

$$B_2$$: Event $$N\left(\tau_{2}=ON_{2}<0\right)$$ is the cause of $$O\left(\tau_{1}=0\right)$$.



This conclusion from the existence of superluminal velocities, is exactly the one alluded to by (l.c.), and for which it was recently coined the slogan "to telegraph into the past". – If would not only have thought about his explanations (of § 6 in his paper) for the case of $$\infty$$ fast, but also for the case of "nearly $$\infty$$ fast" propagation velocities, and followed the two-sided signal propagation from the middle point of his rod, then he surely would have seen that everything written by him in § 6 and lectured in Königsberg, regarding 's remark on superluminal velocity, was wrong. – Incidentally, that the special arrangement given by at that place as an example of signalization, cannot at all be seen as signalization, was additionally shown by  (this journal 12, 85, 1911).

In his paper "The Rigid Body and the Principle of Relativity",  arrives at no other new results than at those three incorrect ones that were previously put together. Then it is surely understandable, that the author – leaving the treatment of the "relative-rigid" body which is all too precisely defined – now turns himself to the stimulating-flexible research area of the "relative-elastic" body. In how far the series of formulas published in this direction by for the time being, has something to do with 's program which he repeatedly cites, can surely be seen in the not too distant future.

, March 15, 1911. (Received March 17, 1911.)