there is the proposed Alcubierre drive that would allow you to get from point A to point B faster than light. The reason is that you are not traveling through space-time but you are causing space-time to move. It is a clever way around "the rules" but it does require some exotic (and unproven) concepts like negative energy to work. It even sounds like a "warp drive".
My understanding is that they have yet to come up with a warp solution where you can cause the warp to accelerate. So, at this point drive is a bit of a misnomer.
my suspicion is that FTL travel wouldn't work with this drive because of what the wikipedia article states here:
"Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel (see the chronology protection conjecture) and thus make the Alcubierre drive invalid."
My fun layman conjecture based on absolutely no credible knowledge of this area beyond reading articles like this is:
-- the universe has a forward direction of time & causality that is as unbreakable as exiting from a black hole is
-- in a black hole space & time are so warped they sort of switch roles - any direction you try to move in X,Y,Z only brings you closer to the singularity. In much the same way I think the outside universe operates in Time - no matter what you do, you move forward in time.
-- My somewhat unpleasant belief here is the reason you and everything in the universe can only move forward in Time is because of the Block universe[1] concept: all of X,Y,Z,T are already set & predetermined, so it makes no sense to actually try to change your path through it.
-- All of these things put together invalidate the concept of FTL travel, because FTL travel (even with a clever trick like warping spacetime) would violate causality & allow travelers to go back in time
Keeping an open mind about it, our understanding of physics is based on light-enabled observations, so if there is something that moves faster than light, we wouldn't be able to detect it anyway, yes?
You can hear things that are going faster than the speed of sound, so I don't see why something that is outrunning its own light would be invisible. You wouldn't see it coming, but you would see it leaving. If it's not transparent then you'd see its shadow, if it smashed its way through a planet you'd see the hole, etc.
If there was something that moved faster than light, that still interacted with regular matter in some way, then yes, we would be able to detect it by the effects.
