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The oldest appearances of causality troubles in modern theories are of course the Kurt Gödel paper (1949), Reichenbach's philosophy of time and space (1927), Weyl's "Space, time and matter" (1922) and then the Tolman paradox in "The theory of the relativity of motion" (1917). There's a few papers on the topic of advanced waves before that but none of them really seem to deal with any causality issues at all.

Are there any older papers concerning hints at causality issues with modern theories or are those the oldest ones?

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  • $\begingroup$ Walter Ritz ca. 1908 notably criticized SR but reached some kind of compromise with Einstein and they wrote jointly a paper in 1909. Such work comes from 19th.c. ideas about fileds, etc. which were invented in order to solve the Newtonian problem about action-at-distance which is perhaps an older causality issue.(?) $\endgroup$ – sand1 Dec 19 '17 at 20:07
  • $\begingroup$ He did write one of those papers on advanced waves! $\endgroup$ – Slereah Dec 19 '17 at 20:31
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    $\begingroup$ By "modern theories" do you mean relativity? Causality issues and paradoxes have been discussed in ancient times, and by Hume in 18th century. Abraham-Lorentz force and its pre-acceleration problems also predate relativity. $\endgroup$ – Conifold Dec 19 '17 at 23:40
  • $\begingroup$ Well as far as I know none of them have dealt with the issue of possible cause preceding effect sort of problems (although I could be wrong), those seem to first occur in relativity (or possibly EM, relatedly). $\endgroup$ – Slereah Dec 20 '17 at 0:19
  • $\begingroup$ *effect preceeding cause $\endgroup$ – Slereah Dec 20 '17 at 1:17
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As far as general relativity is concerned, the issue seems to date back at least to 1914, before general relativity was properly done, in Einstein's paper "Die formale Grundlage der allgemeinen Relativitätstheorie" (formal foundations of relativity). It includes the following statement on the topic :

An even deeper-reaching question of fundamental significance shall now be brought up - and I am not able to answer it. In the ordinary theory of relativity, every line that describes the movement of a material point, i.e., every line consisting only of time-like elements, is necessarily nonclosed, the reason being that such a line never contains elements for which $dx_4$ vanishes. An analogous statement cannot be claimed for the theory developed here. It is therefore a priori possible to imagine a point movement where the four-dimensional curve of the point is almost a closed one. In this case one and the same material point could exist in an arbitrarily small spacetime domain in several seemingly mutually independant representations. This runs counter to my physical imagination in the most vivid manner. However, I am not able to demonstrate that the occurence of such curve can be excluded from the theory that has been developed here.

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