If we discover the means to travel faster than light, but researching and developing the technology means that the Earth is destroyed in just a few decades, should the technology still be pursued?
Edit: A bunch of yall don't seem to grasp the concept of a theoretical question
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Where would we go? We don't know of any other planets that we could easily live on.
Kepler-452b for starters but with FTL travel we could probably find quite a few more
Unless FTL travel is significantly faster than light, it's usefulness would be limited. Kepler-452 is located about 1,800 light-years from Earth, which means it would take light 1,800 years to travel that distance. Even if our theoritical FTL travel was twice as fast as light, it would still take us 900 years to get there...
Once we get there, it is still unlikely that the planet would be habitable for humans. Quoting Wikipedia:
There are closer exoplanets (closest one we know about is Proxima Centauri b), but even those are likely to be poorly suited for humans since we evolved to live specifically on Earth.
1800 years as observed from someone else watching the light travel. However, when travelling at c, you experience no time. From a photon's point of view, no time passes between when it is emitted and when it is absorbed.
Earth isn't travelling with you though so Earth would be toast long before you arrive.
And in addition to the peculiarity of relativistic travel, if we were to utilise something like wormholes, the elapsed time would be equivalent to the time traveled across the newly formed wormhole (plus getting to it and from it).
It would depend on the flavour of FTL, if it means physically moving through space at supraluminal speeds (which would of course be impossible according to our current understanding), time would be flowing backwards.
Even traveling at the speed of light would be sufficient as it would mean getting to the destination the instant you achieved that speed.
But we do not even have to go as fast. Even doing constant 1G acceleration half the way with subsequent 1G deceleration for the other would enable us to reach the edge of the obervable universe withing the span of a human lifetime iirc.