Inertial Scaling and Relativistic Time Dilation: A Derivation of Equivalence

A universal scaling law is derived from isometric scaling principles in which the ratio of clock rates between any two physical systems equals the fifth root of the inverse ratio of their moments of inertia.This relationship is shown to be algebraically equivalent to the Schwarzschild gravitational time dilation formula of general relativity, with the equivalence mediated by a bridge equation containing a 2/5 exponent that decomposes exactly into the scaling law's dimensional exponent (1/5) multiplied by the quadratic factor (2) inherent in the Riemannian metric.The same framework, applied to linear inertia with a cube root (1/3) exponent, reproduces the Lorentz time dilation of special relativity with identical algebraic structure.General and special relativity are thereby unified as rotational and linear cases of a single inertial scaling principle, distinguished only by the type of inertia and its corresponding dimensionality.All equivalences are exact algebraic identities.No free parameters are introduced.