I have a physics question, and it's a rather foolish one, but please bear with me.
It is taken as read that faster-than-light travel has an inescapable corollary: a faster-than-light spacecraft is also a time machine, and not just a time machine in the telescope sense, but a time machine in the go-back-in-time-and-shoot-your-own-grand
But... why is that the case, that FTL == time machine?
To make this a concrete situation, let's say I have a ship that can travel at some arbitrary multiple of the speed of light. (Never mind what it runs on. It's an absurd idea no sane person would put their faith in, so we'll say it's powered by fairy dust, unicorn horns, and Middle East peace agreements.) How precisely can I create a time paradox with it?
Now obviously you can, by definition, get outside your own light cone with a faster-than-light spaceship -- that is to say, you can outrace the light emitted at your time of departure -- and thus acquire information you could not have acquired otherwise. But unless you can somehow physically return to an earlier era, or at least broadcast information back into it, I'm going to state that this is not actually a problem.
I have the vague idea it has to do with there being no privileged reference frame, but I've never heard the "and therefore" part of that explanation.