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Let's try a thought experiment here....now, without just dismissing it out of hand (because it doesn't fit what we constitute as being "possible"), let's say that UFO's are actually what they say they are...extraterrestrial spacecraft. Now, what does this say about our knowledge of what constitutes as being "possible". What it says is that we have not only a lot to still yet learn, there is something faulty with our understanding of physics. It may not mean that SR/GR is at fault, but it may also mean that there is. There maybe some solution of SR (such as the Alcubierre Spacetime Metric) which might allow us to achieve the same ability to travel FTL as the aliens do. Whilst we can't see how it may work at present and come up with various reasons as to why it doesn't work, it doesn't mean that the negative conjectures have any basis in reality. In all likelihood we don't really understand the physics of it yet. There maybe some other aspect of physics which has been conjectured which may work, or something we are not aware of as yet that maybe the answer.
In order to put the matter to rest, what needs to happen is a concerted effort into experimentation and rigorous testing of all hypotheses into the physical possibility of FTL travel must be carried out. It may take many years to figure out, but what doesn't need to happen is the present disinterest shown by the majority of the scientific community to do those experiments and continue with looking at the idea as nothing more than fantasy. That's nothing more than hubris based on academic and intellectual conceit.
If we had've all thought like that in the past, we'd never have gotten off the ground and probably still thought that travel into space was an impossibility (even flying, for that matter!!!).
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