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PhilGoetz comments on Particles break light-speed limit? - Less Wrong
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What do you mean by "spacelike"?
IIRC, movement in spacetime is the same no matter which axis you designate as being time.
No. The metric treats time differently from space even as they are all on a single manifold. The Minkowski metric has three spacial dimensions with a +, and time gets a -. This is why space and time are different. Thinking of spacetime as R^4 is misleading because one doesn't have the Euclidean metric on it.