A Scalar Formulation of Inertia in the Stationary Relativistic Regime

This paper presents a scalar formulation of inertia in the stationary relativistic regime, based on the dimensionless ratio M = γ_local / √g_tt ≥ 1, defined for static, asymptotically flat spacetimes with conserved rest energy E₀ = mc². The central result is the conservation identity E₀ = E_in · M, from which kinematic time dilation (SR), gravitational redshift (GR), and a gravitational phase accumulation analogous to the Aharonov–Bohm effect follow as special cases of a single local energy balance. The scalar M admits four equivalent representations — geometric, energetic, frequency-based, and quantum — unified for the first time in a single observable. The paper introduces the reactive inertial scalar I ≡ 1/M, which obeys a Bernoulli dynamical equation and constitutes the internal response of the mass to external perturbations. Weight and momentum are identified as the gravitational and kinematic manifestations of a single conservative wave-particle mapping E_in ↔ λ_E, mediated by hc. A thermal extension completes the framework by decomposing the locally available energy as E₀/M = E_in + Q, where Q is the thermal energy already contained within E₀. The thermal reactive scalar I_Q ≡ QM/E₀ satisfies the completeness identity I + I_Q = 1. The framework connects to relativistic kinetic theory, the Maxwell–Boltzmann and Jüttner distributions, and the Tolman–Ehrenfest relation. Falsifiable predictions are derived for high-energy interferometry, optical clock networks, and precision thermal measurements. Current optical lattice clocks at precision 7 × 10⁻¹⁶ already resolve the predicted variations.