Einsteinian physics shows us that the faster something moves, the slower the effect time has on it. So someone traveling close to light speed would age slower than a person on Earth.
Now what happens if you go FTL? And I don't mean Alcubierre drive which avoids it with exotic matter which has not been proven to exist (negative matter).
I think you wouldn't even make it to FTL. Let alone light speed. But if you did somehow, I think time itself would stop. As that would be the only thing in Einstenian space preventing you from from traveling through time into the past.
So wanna live forever and NEVER age? Then go FTL. You won't age. Period. Unless you slow your speed down somehow.
It least that is what it appears to be.
Or perhaps aging time travel effect ONLY happens to the space craft? Meaning it would get younger and younger until it didn't exist, killing the crew inside once they reach outer space?
This kind of stuff makes your brain explode with all the possiblities.
Another odd possiblity is the takeoff of an FTL spaceship. Remember, it's going faster than light (much faster than light if it wants to get anywhere in reasonable amount of time).
Which means it will look like it's sitting still to an observer, even after it already took off. You could put your hand through it, and it would just be light (like a hologram).
Reason? The ship left before the light of it leaving could catch up.