All these people saying FTL is impossible
I'm getting really tired of all these offhand dismissals of any possibility of real-time interstellar travel. If we listened to every naysayer who said "that can't be done" we'd still be living in caves hunting wild pigs and being eaten by leopards.
I know that the difficulties imposed by relativity and physics seem insuperable now, but so did going to the moon 100 years ago, and so did flying for thousands of years before that. If we give up now, if we toss in the towel and say "relativity means there will NEVER be FTL travel and that's that, end of discussion", then our civilisation deserves to die. Because we will have turned our backs on every principle that has brought us to where we are.
Consider this: there IS a concept of absolute time, regardless of the relativity of time and space. The one absolute clock, applicable everywhere in the Universe, is seconds elapsed since the Big Bang. At some point in time, on the planets orbiting Alpha Centauri, it is the same number of seconds since the Big Bang as it is here right now. We might not see that moment for another 4.5 years, but it's happening now, or has happened, or will happen. So if FTL is possible, say with an Alcubierre drive or some other functional equivalent, and if the ship does go back in time as a result, then it could be put in stasis (brought as close to 0 Kelvin as possible) and released when the number of seconds since the Big Bang reaches the same as when it left Earth. Thus, zero effective time has passed, both for Earth and for the ship. Repeat again on the return journey, and what you have is essentially instantaneous interstellar travel, for both Earth and ship.
Look, I'm no boffin, and there's likely countless flaws with my ideas that could be brought up. But if we give up, if we just throw our hands in the air and say "that can't be done, because Einstein...", then we have abrogated our right to be called intelligent, and we may as well start heading back for the caves right now.
I will leave you with the words of the great poet Tennyson:
We are not now that strength which in old days
Moved earth and heaven; that which we are, we are;
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.