Velocity-Dependent Time and Length Scales as a Foundational Reformulation of Special Relativity

This work presents “Foundational Special Relativity (FSR),” a reformulation of special relativity in which neither the metric nor the invariance of the speed of light is assumed as a primary principle. Instead, the theory is built from two velocity‑dependent physical scales: the time‑update scale T(v) and the space‑update scale L(v). These scales represent the fundamental temporal and spatial resolution of a moving system. A single structural requirement — that the scale ratio L(v)/T(v) remains constant — makes the invariance of the speed of light a derived consequence rather than a postulate. By requiring consistency with the velocity‑addition law and basic symmetry conditions, the Lorentz factor emerges uniquely, and the standard results of special relativity (time dilation, length contraction, Lorentz transformation, invariant interval) follow naturally. In this framework, the metric is not primary; it appears as a secondary structure generated by the underlying scale dynamics. FSR therefore provides a more upstream, physically transparent foundation for special relativity. This approach also forms the kinematic sector of a broader hierarchy that includes “Foundational General Relativity (FGR),” where gravitational effects are likewise encoded in primary scale variations. FSR thus serves as a conceptual bridge toward deeper spacetime‑generation theories involving minimal length, information density, or discrete structure.