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The paper in question is https://arxiv.org/abs/1407.2528 . But it contradicts known theory. Could someone ELI5? Is it legit? Are there any gotchas or catches?

Abstract

Seeing the many examples in the literature of causality violations based on faster-thanlight (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibility of time travel. We show that this logical inference is invalid by demonstrating a model, based on (3+1)-dimensional Minkowski spacetime, in which FTL motion is permitted (in every direction without any limitation on speed) yet which does not admit time travel. Moreover, the Principle of Relativity is true in this model in the sense that all observers are equivalent. In short, FTL motion does not imply time travel after all.

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    $\begingroup$ What is the first line in the argument that you don't follow? $\endgroup$
    – WillO
    Jan 23, 2020 at 22:50
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    $\begingroup$ What is an ELI5? $\endgroup$ Jan 23, 2020 at 23:11
  • $\begingroup$ @CinaedSimson “Explain Like I’m 5” $\endgroup$
    – G. Smith
    Jan 24, 2020 at 0:52
  • $\begingroup$ I don’t know whether it is correct, but it appears “legit”. It doesn’t look anything like what crank physics looks like. $\endgroup$
    – G. Smith
    Jan 24, 2020 at 0:55
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    $\begingroup$ A theory of physics can't prove anything. Only experiments can. I think you mean to say the theory of special relativity predicts this. $\endgroup$ Jan 24, 2020 at 5:02

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The bulk of the paper seems fine to me, but at the very end they seem to make an unjustified leap:

In this paper, we have exhibited a model of Rn1 which is inhabited by observers/particles moving at all (non-light) speeds relative to one another, but in which time travel is not possible – it follows that the existence of FTL signals does not logically entail the existence of ‘time travel’ scenarios. Nor, therefore, does it inevitably lead to the causality paradoxes arising from those scenarios.

All they've proved is that you don't get closed, timelike curves just because you have FTL. (See p. 4 and their definition of "time travel is possible," which is really just a description of a CTC.) This is kind of obvious anyway. But that doesn't mean you don't get causality paradoxes. The tachyonic antitelephone exists any time you have tachyons.

I skipped section 2.2, but people should realize that if you have FTL observers in 3+1 dimensions, then there will not be anything like a Lorentz transformation between STL and FTL observers.

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