The reconciliation of General Relativity (GR) and Quantum Mechanics (QM) remains the primary objective of modern theoretical physics. A central obstacle in this unification is the "Problem of Time": GR treats time as a dynamic, smooth geometric dimension, whereas QM treats it as a fixed, background parameter. This paper introduces a novel physical property of the temporal dimension: The Alpha Coefficient of Time (α). Defined as a measure of Chronal Rigidity or Metric Stiffness, α quantifies the resistance of spacetime to temporal curvature. By abandoning fluid-dynamic metaphors in favor of solid-mechanics concepts, we postulate that the vacuum possesses a fundamental impedance that manifests as a characteristic length scale. This framework provides a mechanism for the discretization of time, calculates the inertial mass density of the temporal field (approx. 163g/second), and resolves the Schwarzschild singularity. Furthermore, we apply this metric to the supermassive black hole Sagittarius A*, demonstrating that time dilation remains finite at the horizon due to Chronal Stiffness.