Maybe an elementary question:
What is the motivation for defining the vector $X=0$ to be space-like?
2026-03-26 14:33:21.1774535601
Motivation for defining space-like vector
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A spacelike subspace of a Lorentz vector space is one for which the restricted Lorentz scalar product is positive-definite. The restriction of the Lorentz scalar product to the zero subspace is technically positive-definite, because you cannot find a non-zero vector there (!) whose scalar square is non-positive.