In an Alcuibierre like warp drive, what is the velocity of the object after the warp trip?

Question

Presume a ship is traveling in an Alcubierre-like warp bubble. For concreteness, let us say that it began in a geostationary orbit (that term is used to indicate that the ship is in fact orbiting Earth at the appropriate altitude and velocity) and then the warp drive is activated and the ship + bubble travel through space at some new velocity. Presumably the ship itself is stationary with respect to that warp bubble. At the end of the warp trip, the warp drive turns off and the bubble no longer exists. What happens to the ship? Does it maintain the same velocity that it had at the beginning of the trip? Would it somehow maintain some of the velocity that the bubble had?

Answer 1

As I understand it, the "derivation" of the warp-drive associated with Alcubierre has the form

{S , E} together imply F

where S is a spacetime configuration, E is the Einstein equation and F is the fast-moving bubble. However GR does not allow just any S. It places strong constraints on S via constraints on the stress-energy tensor. And it is found that those constraints rule out the assumed S. Therefore the situation is physically impossible.

In view of this, the question as to what happens when the warp drive is turned on or off cannot be answered within the science of physics. All one can say is that the local spacetime does whatever impossible thing it is made to do by the impossible warp drive. Different people may specify different behaviours for their proposed warp drive, and give an answer determined by whatever behaviour they assumed, but none of these behaviours can manage to evolve the spacetime configuration from a physically not-allowed form to a physically allowed form without also failing to respect the constraints on the stress-energy tensor.

So the warp drive idea, interesting though I think it is, has to remain at the margins of science unless someone can manage to place it on a more convincing footing. One of the difficulties is that if one abandons a constraint such as the weak energy condition then it seems that spacetime would then become unstable, but since spacetime has managed to persist for billions of years such instability is ruled out by observation. However this is a difficult area of mathematics and this is why I said "seems that", meaning I do know if it has been proved without exception.