1
$\begingroup$

The principal source of the widely known "Train and Embankment" thought experiment is -- by all appearances as well as by expert judgement -- Albert Einstein's booklett "On the Special and the General Theory of Relativity (A Popular Account)"; originally in German (1917), with translations appearing soon afterwards.

(Earlier works by other authors may have already described somewhat similar setups, for instance D. F. Comstock (1910); but by now, Einstein's account has surely become the most popular.)

In Einstein's booklett, the first and definitive mentioning of "the train" appears in chap. IX ("The Relativity of Simultaneity"); where we find the corresponding "Fig. 1":

A. Einstein, On SR and GR (A popular account), Fig. 1

"We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1."

Notably, "the embankment" had already been introduced in the preceding chap. VIII ("On the Idea of Time in Physics"):

"Lightning has struck the rails on our railway embankment at two places A and B far distant from each other."

Also, a more detailed description of "the train", in relation to the two places (also: in the sense of constituents) of the railway embankment, A and B, mentioned earlier, continues (only) in chap. X ("On the Relativity of the Conception of Distance"):

"two particular points on the train -- e.g. the middle of the first and of the hundredth carriage -- travelling along the embankment with the velocity v [...] call A′ and B′ the two points on the train [...] In the first place we require to determine the points A and B of the embankment which are just being passed by the two points A′ and B′ at a particular time t -- judged from the embankment [...] determined by applying the definition of time given in Section VIII."

But this description appearing only in chap. X is remarkable because: Einstein managed to write and to conclude the entire preceding chapter IX without any explicit mentioning of the designations A' nor B' at all ! Evidently, there are no labels A' nor B' shown in "Fig. 1" of chap. IX (which is the only figure in chap. IX) !

The purpose and the merits or consequences of this particular way of presentation may surely be debated -- elsewhere. My request, which is spelled out below, is merely based on my observation that it seems possible, even straightforward, and at least for some authors desirable, to add the labels A' and B' appropriately into a depiction of the "Train-and-Embankment" setup, namely labelling the corresponding points, a.k.a. constituents, of the train; in addition to the label M' which already appears in "Fig. 1"; as shown for instance in this picture (which was not produced by myself, btw.):

Just some image of the TETE containing the labels A' and B'

Therefore

My specific-reference request:

Which is the earliest reference of a picture of the "Train and Embankment" thought experiment setup in which the relevant three constituents of the train are shown and explicitly individually labelled ?

(The specific designations A' and B' along with Einstein's given M' for these three relevant constituents of the train might be considered the most obvious. But I'm looking for the earliest reference to a picture with any explicit individual labelling regardless of any particular designations; as long as the designations and corresponding labels of all three relevant constituents of the train and of all three relevant constituents of the embankment are all distinct.)

$\endgroup$
9
  • 3
    $\begingroup$ I’m voting to close this question because it belongs on the history of science and math stack exchange: hsm.stackexchange.com $\endgroup$
    – Dale
    Commented Oct 13, 2023 at 16:09
  • $\begingroup$ @Dale: "I’m voting to close this question because it belongs on the history of science and math stack exchange [...]" -- Thanks for the heads-up. Do you agree that strictly all questions on [specific-reference] belong on the history of science (since, generally, there's a date attached to a specific references), and to you strictly vote accordingly ? Before my question might be closed for good, would I get a warning and the chance to (try to) convert to a [resource-recommendation] question, remaining on PSE ? $\endgroup$
    – user12262
    Commented Oct 13, 2023 at 20:48
  • $\begingroup$ Request for reference questions are pretty tightly controlled here, but no, not all such questions belong on HSM. This specific one does, because the criterion for your requested reference is merely that it is the first. That is a historical question which belongs on HSM. $\endgroup$
    – Dale
    Commented Oct 13, 2023 at 21:06
  • 1
    $\begingroup$ I think Dale's point is right. The essence of your question is when was the first time a particular set of symbols was added to a diagram, which has nothing to do with the underlying physics. Einstein might have considered symbols for A' and B' to be superfluous, given that in his accompanying narrative he explicitly states that A' and B' are alongside A and B, so what is there to be confused about? $\endgroup$ Commented Oct 14, 2023 at 9:05
  • 1
    $\begingroup$ I’m voting to close this question because it's not a question about the meaning of physics but essentially about when a diagram was first labelled with a particular pair of symbols. $\endgroup$ Commented Oct 14, 2023 at 9:08

0