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Why are isometries of Minkowski space necessarily linear?
Let's fix notation and define the bilinear form $\eta: \mathbb{R}^4 \times \mathbb{R}^4 \to \mathbb{R}$ by:
$\eta((x,y,z,t),(x',y',z',t')) = xx'+yy'+zz'- tt'$
Given a map $T:\mathbb{R}^4 \to \mathbb{R …