Translation:On v. Ignatowsky's Treatment of Born's Definition of Rigidity II

by Paul Ehrenfest

On v. Ignatowsky's Treatment of Born's Definition of Rigidity. II.^[1]

By P. Ehrenfest.

For increased clarity, I allow myself the following conclusions:

1. Is a body, satisfying Born's rigidity definition, capable of passing from rest to uniform rotation? – I, Herglotz, Noether have shown^[2]: No. v. Ignatowsky claimed^[3] that from his calculations it follows: Yes. My protest^[4] forced him to admit^[5]: a) that no such thing follows from his relevant calculations, b) that his claim is wrong per se.

2. Is a Bornian body capable of executing curvilinear-translatory motions? – Herglotz and Noether have shown: Yes. – v. Ignatowsky claimed that it follows from his calculations, that only rectilinear-translatory motions are possible. – Noether's protest by letter forced him to admit^[6]: 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, Einstein showed:^[7] Yes. Despite of editorial warning from W. Wien^[8], v. Ignatowsky published his opposite opinion that is evidently wrong.^[9]

In his paper "The Rigid Body and the Principle of Relativity", v. Ignatowsky 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^[10] to the stimulating-flexible research area of the "relative-elastic" body. In how far the series of formulas published in this direction by v. Ignatowsky for the time being, has something to do with Planck's program which he repeatedly cites, can surely be seen in the not too distant future.^[11]

St. Petersburg, March 15, 1911.

(Received March 17, 1911.)

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1. I: this journal 11, 1127, 1910.
2. P. Ehrenfest, this journal. 10, 918, 1909; G. Herglotz, Ann. d. Phys. 31, 393, 1910; F. Noether, Ann. d. Phys. 31, 919, 1910.
3. Ann. d. Phys. 33, 1127, 1910.
4. This journal 11, 1127, 1910.
5. This journal 12, 164, 1911.
6. Ann. d. Phys. 34, 373, 1911.
7. Jahrb. d. Radioaktiv. 4, 411, 1907.
8. See footnote to § 6 in W. v. Ignatowsky, Ann. d. Phys. 33, 607, 1910.
9. The graphical representation in the Minkowskian $(x,\ \tau =ct)$-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 Einstein (l.c.), and for which it was recently coined the slogan "to telegraph into the past". – If v. Ignatowsky 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 Einstein's remark on superluminal velocity, was wrong. – Incidentally, that the special arrangement given by v. Ignatowsky at that place as an example of signalization, cannot at all be seen as signalization, was additionally shown by Laue (this journal 12, 85, 1911).

10. This journal 12, 164, 1911.
11. The things said by Varičak (this journal 12, 168, 1911) about the tracing-images of moving Bornian bodies, I consider as incorrect. In the interest of clarification of the question, together with shortening the discussion as far as possible, I will discuss this with Varičak by letter, so that we can already publish together the correct state of matter.