Exposing the Kinematic Oversight in Special Relativity : A Geometric Resolution

Abstract

This paper exposes a foundational omission in Special Relativity: the theory constrains speed but never provides an intrinsic rule for how a moving frame should change direction under acceleration. For over a century, SR has relied on external constructions—Fermi–Walker transport, concatenated boosts, and Wigner rotation—that operate correctly but do not arise from SR’s own geometry. The CARD framework shows that this omission originates from treating velocity space as flat. By modeling velocity space as the curved hyperbolic manifold implied by SR’s invariant constraint, we derive and prove—from first principles and with full geometric rigor—the intrinsic directional transport law supplied by the manifold’s torsion‑free Levi‑Civita connection. This intrinsic transport rule explains effects such as Thomas precession as geometric holonomy rather than artifacts of frame switching. Restoring the correct geometry proves the oversight is real, resolves SR’s long‑standing kinematic gap, and completes the theory’s structure from first principles.