# Relationship between Alcubierre drive space-time evolution and speed of gravity

The top rated answer to this question about the Alcubierre drive asserts, "spacetime can dynamically evolve in a way which apparently violates special relativity," but according to the Wikipedia article on the speed of gravity, changes in the gravitational field propagate at the speed of light. The second answer under this question puts the limitation in broader terms: "distortions of spacetime are as limited to travel to the speed of light as any other physical influence."

These statements appear to contradict one another. My question is:

Does the Alcubierre drive depend on space-time distortions propagating at superluminal speeds, and is that possible under general relativity? If Alcubierre drive distortions of space-time can propagate at superluminal speeds under GR then why can't gravitational waves (another traveling distortion of space-time) also propagate at superluminal speeds?

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His statement "spacetime can dynamically evolve in a way which apparently violates special relativity" just refers to apparent superluminal velocity caused by expansion of the space, i.e. cosmic inflation etc. He does explain that. It's a known and well accepted effect. – gecko Feb 28 '13 at 3:03

What is the deal with the nonstop Alcubierre warp drive questions here?

Superluminal speeds relative to what? If you're talking about gravitational waves, you have a weak wave, and a background metric to measure speeds. If you have a solution that differs nonlinearly from the minkowski spacetime, the disturbances are both the thing moving and the measuring stick to measure the moving thing and you're going to have to come up with a consistent way of saying that the speed of the wavefront is X.

And I should say again that this solution requires negatively massed matter. This simultaneously says that it is probably physically unrealistic to build, and that it shouldn't be surprising that it's associated with superluminal behaviour. Give me a tachyon beam and a tachyon detector, and I can transmit FTL signals pretty well already. That's why tachyons are typically indicators of unphysicality/instability in a theory and don't show up in the actual particle spectrum.

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Can't we measure the speed of the wavefront by observing it as it passes through otherwise undisturbed space? If the disturbance detected is small compared to the (Euclidean) distance between detectors (and, I suppose, small compared to the volume of the detection apparatus itself) and the detectors are at rest relative to one another then we should be able to approximate the wavefront's propagation speed as the Euclidean distance between detectors divided by the time between detection events. – Aaron Golden Sep 30 '12 at 22:39
@user37535: yes, you could do something like that (which then creates a background), but the statement "gravitational disturbances may only travel at the speed of light" really only applies in a region where spacetime curvature is negligible. Gravitatonal waves beyond the cosmological horizon, for example, will be observed to be "moving superluminally" relative to an Earthbound observer. – Jerry Schirmer Sep 30 '12 at 23:10

If you start out in a flat Minkowski spacetime and begin to distort it to create an Alcubierre bubble, you won't actually be able to travel to anywhere that wasn't in the future light cone of your position immediately before you started work. For example if you have a network of clocks synchronized in the rest frame of the galaxy, and in 2000 you start work on creating a path for an Alcubierre bubble between Earth and another star 50 light years away, there's no way you can reach that star before the clock there reads 2050, although in 2050 someone might be able to leave Earth and get to the star in 2051, and you might also make a round trip where you leave in 2000, get to the star when the clock there reads sometime after 2050, but then get back to Earth in 2001. See the paper by Everett and Roman here, especially the section on p. 3-4 : http://arxiv.org/abs/gr-qc/9702049

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