Fisher Information Is the Squared Lorentz Factor: Why the Qubit Is Special

This preprint proves that on the open qubit Bloch ball the Beltrami-Klein hyperbolic metric is conformal to the Bures (quantum Fisher information) metric with conformal factor 4γ²(r), where γ²(r) = 1/(1−r²) is simultaneously the squared Lorentz factor and the Fisher information of a binary measurement with visibility V = r. A Weyl-tensor obstruction shows this conformal equivalence fails for all N ≥ 3 quantum systems. We derive a closed-form Thomas-Wigner rotation prediction for sequential non-collinear qubit measurements, testable on current platforms.