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The models/depictions I've seen of warp bubbles show space compressed ahead of the bubble and expanded behind, so that the space inside the bubble moves with respect to the space outside. If that is so, then what is happening at the sides? It would seem that there is some sort of shear taking place between the space inside and outside. Is that correct, or is that based on a misinterpretation of the model?

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I don't really know the answer, so this is just speculation. "In front" of the bubble could span side to side, and "behind" the bubble could be the remaining 180 degrees. There is no "side" in the sense you mean, though the sides require negative energy. –  markovchain Aug 6 '13 at 17:06
There aren't really sides, there are places where the spheres overlap, touch or don't meet based on their radius. –  user6972 Aug 7 '13 at 7:22

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