Demystifying the Minkowski Sign: A Classroom-Ready Derivation from Standard Euclidean Algebra

In introductory physics education, the transition from Newtonian mechanics to specialrelativity often introduces a significant conceptual hurdle: the sudden inversion of signs (themetric signature) between time and space components in Minkowski spacetime. Traditionalpedagogical approaches almost universally derive this structure by invoking the “constancyof the speed of light” to obtain Lorentz transformations, subsequently presenting the pseudo-Riemannian metric as a counterintuitive, flatly given postulate of modern physics. This notedemonstrates that the signature inversion is not an independent relativistic invention but anabsolute algebraic inevitability already fully embedded within standard 3D Euclidean distanceand basic uniform linear motion.