Lorentz invariance doesn’t rule out FTL, it just makes it difficult to reconcile with time imposing a partial order and would require a rethink of strict causality. Alcubierre-like metrics and wormholes are fully compatible with Lorentz invariance, since they use general relativity as part of their base assumptions. Creating such structures poses unsolved and quite likely unsolvable difficulties, though.
Tachyons are also compatible with Lorentz invariance, but we don’t have any quantum theory that works for them. There is the slight problem that no tachyons have ever been observed, and we don’t have any reason to expect that they can exist. They also pose problems for causality.
Lorentz invariance does rule out crossing between disconnected components of the Lorentz group, at least classically, and thus FTL. Tachyons, if they were possible, would require a modification of Lorentz invariance to avoid traveling back in time, which is also prohibited in GR by the uniqueness of the metric.
Alcubierre drive is a slightly different beast. Beside needing negative energy, it has two other issues: the inside is causally disconnected from the outside and so there is no way to start or stop. Additionally, if you overcome this issue and manage to create an Alcubierre drive, you cannot go FTL outside the lightcone of the moment of its creation, though you potentially could travel FTL within the bounds of it. This is because any disturbance of a metric propagates at most at c. Sadly, I don’t have an arxiv reference handy, I remember people publishing on this topic.
Wormholes are indeed within bounds of GR if one allows for negative energy, but they have a whole lot of other issues, one of which is that each traveler adds its mass to the entrance’s mass and subtracts it from the exit’s mass, so a lot of one-way travel would actually create an object with negative mass. There is also the issue pointed out by Novikov long ago, that wormholes tend to create a Cauchy horizon.
Lorentz invariance doesn’t rule out FTL, it just makes it difficult to reconcile with time imposing a partial order and would require a rethink of strict causality. Alcubierre-like metrics and wormholes are fully compatible with Lorentz invariance, since they use general relativity as part of their base assumptions. Creating such structures poses unsolved and quite likely unsolvable difficulties, though.
Tachyons are also compatible with Lorentz invariance, but we don’t have any quantum theory that works for them. There is the slight problem that no tachyons have ever been observed, and we don’t have any reason to expect that they can exist. They also pose problems for causality.
Lorentz invariance does rule out crossing between disconnected components of the Lorentz group, at least classically, and thus FTL. Tachyons, if they were possible, would require a modification of Lorentz invariance to avoid traveling back in time, which is also prohibited in GR by the uniqueness of the metric.
Alcubierre drive is a slightly different beast. Beside needing negative energy, it has two other issues: the inside is causally disconnected from the outside and so there is no way to start or stop. Additionally, if you overcome this issue and manage to create an Alcubierre drive, you cannot go FTL outside the lightcone of the moment of its creation, though you potentially could travel FTL within the bounds of it. This is because any disturbance of a metric propagates at most at c. Sadly, I don’t have an arxiv reference handy, I remember people publishing on this topic.
Wormholes are indeed within bounds of GR if one allows for negative energy, but they have a whole lot of other issues, one of which is that each traveler adds its mass to the entrance’s mass and subtracts it from the exit’s mass, so a lot of one-way travel would actually create an object with negative mass. There is also the issue pointed out by Novikov long ago, that wormholes tend to create a Cauchy horizon.