I wonder what it would be like to be the Nth generation of guys-that-left-in-2016 finally arriving and be greeted by the descendants of the FTL guys that arrived 800 years before you.
It does sound a little bit like "Space Seed" from TOS though, except I don't remember that ship having a particular destination. There was another TOS episode where they find a stray asteroid that turns out to actually be a generation ship inside. And there was some TNG episode where they find a ship with some 20th-century Earthers in cryogenic storage because they had just died of medical ailments. But I don't remember any ENT episodes like this, just some talk about "slow" Earth ships traveling at only Warp 1.5 or so, so that people lived their whole lives on them while on long-term trading missions (their helmsman came from one of these ships).
There's one episode where they visit a colony established decades previous by a warp 1 or warp 2 ship, but they don't beat the colonists to the planet.
[0] I've watched the episode only once (I'm not a Trekkie :) ), but if I remember correctly a synopsis of the plot was that decades (at least...) ago an automated ship containing Klingons in cryogenic suspension was launched to colonise a distant planet; in the time following the launch of that ship, the Federation reached and colonised that planet using faster ships, unaware that the Klingon ship was on the way...
The crew of the Enterprise [D] has to try to figure out how to stop the Klingon ship from introducing the Federation colonists on the planet to the magic of orbital bombardment (a casus belli) without destroying the Klingon ship (a casus belli).
The resulting practical problem is that the energy requirements necessary for the solution are far greater than what we can feasibly achieve now or in the future (exotic matter's existence notwithstanding).
But the fact that a physicist was able to derive this metric (energy requirements aside) is significant. Given the history of science, I would not discount the possibility that someone else will come along in the future with another solution which lowers the energy requirements to something feasible. But we can't predict this.
But isn't it amazing that the math checks out at all? I find it inspiring...
https://en.wikipedia.org/wiki/Alcubierre_drive#Experiments
> In 2012, a NASA laboratory announced that they had constructed an interferometer that they claim will detect the spatial distortions produced by the expanding and contracting spacetime of the Alcubierre metric. The work has been described in Warp Field Mechanics 101, a NASA paper by Harold Sonny White.[5][6] Alcubierre has expressed skepticism about the experiment, saying "from my understanding there is no way it can be done, probably not for centuries if at all".
> In 2013, the Jet Propulsion Laboratory published results of a 19.6-second warp field from early Alcubierre-drive tests under vacuum conditions.[33] Results have been reported as "inconclusive".[34]
> Although the metric proposed by Alcubierre is mathematically valid (in that the proposal is consistent with the Einstein field equations), it may not be physically meaningful, in which case a drive will not be possible.
That drive is nothing more than speculative science fiction.
Also, the energies involved are absurd.