It is well known that gravity does distort space. However, his original paper claimed that it would take a lot of matter, and an awful lot of energy (the amount of energy locked into that matter according to E=mc2) to distort spacetime significantly. This is the real reason for Miguel Alcubierre's pessimistic calculations of how much negative energy a warp drive would require. There is hope though. If another force can be directly converted into gravity, that would avoid those extreme energy requirements. String theory predict that gravity and electromagnetism unify in hidden dimensions.
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