Realizability and the Origin of Causality

We show that spacetime causalitylight cones and an in-variant maximal speed arises as a logical necessity from the re-quirement that a fundamental variational law admit an attainable ex-tremum. Under positive-definite (Euclidean) geometry, the minimalaction principle admits only an unattained infimum, rendering non-trivial dynamics unrealizable. Imposing realizability enforces theexistence of zero-cost propagation modes, which exclude Euclideangeometry and force an indefinite (or degenerate) metric signature.Special Relativity emerges as the minimal geodesic dynamics com-patible with this constraint, rather than as a foundational postulate.