This paper explores the extension of free electron behavior to general relativity through a closed algebraic Hamiltonian description of electron micro-oscillations. The author's research, which predicted the anomalous magnetic moment of electrons from first principles using closed algebraic equations, for a single electron oscillator, the time difference between rest and laboratory frames can be explained through the anomalous magnetic moment, providing a concrete mechanism for reconciling quantum and relativistic time concepts. The framework unifies seemingly disparate physical principles - energy conservation, geometric structure, and proper time - while offering an exact mathematical description of quantum phenomena that suggests a natural path toward bridging quantum mechanics and general relativity without requiring modifications to Einstein's theory. We present a detailed analysis of how an electron, when moving from point A to B, completely converts its mass energy into kinetic energy and subsequently reconverts it to mass energy at point B. Our analysis reveals that Snell's law governs these microscopic electron motions; this applicability of Snell's law naturally leads to the principle of least action, enabling us to demonstrate that electrons undergo micro-oscillations along geodesic paths. While conventional quantum theory, based on field theory, has struggled to reconcile its inherent absolute time with the relative time of relativity theory, our proposed 0-Sphere model represents individual quantum particles as micro-oscillators through closed algebraic equations. This enables the incorporation of both rest-frame and laboratory-frame time scales, as the model does not rely on the absolute time of field theory.