I am troubled by the comments on this question and many others like it. The (obviously very naive) questioner posits a physically impossible situation (often FTL travel as in this case, but there are other examples), asks what it would imply, and gets jumped on for positing something impossible in the first place.
But positing things and trying to understand their consequences is a perfectly good --- indeed admirable --- way to learn. Professional physicists, mathematicians, and others do it all the time. We trace the consequences of a hypothesis, sometimes discover that those consequences are absurd, and if so reject the hypothesis.
Posters like this one are often doing exactly that, though with hypotheses that more sophisticated readers have already realized are impossible. Instead of telling them "your hypothesis is impossible" in a tone that implies their curiosity is reprehensible, maybe it would be better to encourage that curiosity with pointers to the absurd consequences of the hypothesis.
In particular, I object to the closing message that says this is "Not mainstream physics". On the contrary, thought experiments like this very much are mainstream physics. An experiment (thought or otherwise) does not become non-mainstream just because somebody else has already performed that experiment and knows how it will end.
That doesn't mean we should tolerate questions of the form "Ha ha, you guys think that FTL travel is impossible and I'm going to prove you wrong". It also doesn't mean that questions like this should stay open; in fact they are almost always duplicates and should be closed on those grounds. But it does mean that people who are (as far as we know) making a genuine effort to reason their way through things should not be shamed for their curiosity.
