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 Quote by JesseM What are you talking about? I never said anything about x=6 or x=10, the only coordinates I mentioned in the first frame were (x=0, t=0) and (x=100, t=10), which aren't simultaneous in this frame. And this frame is not "preferred", it's just the one where the tachyon signal is moving at 10c. Er, yes, any events which have the same time-coordinate in a given frame are simultaneous in that frame (in this case the primed frame). Do you disagree?
Of course I disagree; any of those events are seen as happening at the same time in your reference frame. The point made by SR is that those events cannot be simultaneous regardless of how it seems to you. They could only be simultaneous if and only if your frame is the one and only “preferred frame”. And as I said SR does not allow for that.

You set the experiment to for 10 units of time, with your other frame moving 6 units of distance, light moving 10 units of distance and your tachyon moving 100 units in those ten units of time, Is that a trivial part of your own thought experiment you did not see?

You’re the one declaring for a preferred frame for x’ otherwise exactly how do you establish simultaneity of anything anywhere with event x’=117.5 t’=-62.5. In your example SR can only define the causality relationship of that event with one and only one other event t=10 x=100. SR cannot and does not define those two events as simultaneous with any other events includes those with t=10 or t’=-62.5 wherever they may be.

 They are simultaneous in the unprimed frame where they have the same t-coordinate.
Again no, you need to re-read Einstein, there is no such thing as “simultaneous” within a frame – that was his point that events with any space like separation seen as happening at the same time within a single frame still cannot be considered as “simultaneous” by anyone. You’ve been around long enough to know that.

The rest is just not worth commenting on except to say that if there is anything that is FTL such as a Graviton, Higgs Particle or Tachyon it should be obvious they would have to follow rules of physics beyond what know now. And nothing so far shows that such rules exist. But if they do they do not need to cause “backwards time”.