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There is no violation of special relativity since the ship inside the warp bubble is on a zero g-force timelike geodesic. There are several problems. The warp bubble is wall of light in the toy models forbidding signals passing out of the ship to control its path similar to the problem of escaping a black hole. The answer to that is my version post-quantum signal nonlocality of information transfer without energy transport as cited, e.g. by Martin Gardner in 1976 MIT Technology Review (reprinted in "Science, Good, Bad & Bogus" as "Magic and the Paranorma" as well as Robert Anton Wilson's "Cosmic Trigger"). These ideas recently rediscovered by Antony Valentini in e.g.

Subquantum Information and Computation

It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time).

Second, there is the problem that spacetime is too stiff, it takes too much energy density to make the warp bubble. The only solution to that, in my opinion, is to slow light down to snail's crawl inside a very high Tc nano-engineered meta-material fuselage with a negative index of refraction n < 0 in the dispersive region of frequencies and wave vectors for the off-light-cone non-radiating electromagnetic near fields that control the warp bubble.

That is the effective warp-energy density coupling increase by a factor of n^4 and n < 0 means that the applied control electromagnetic stress-energy density tensor will cause artificial effective dark energy anti-gravity for propulsion with zero g-force.

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