Unified Cosmic Mechanics Evolution Theory (XVI) Derivation and Verification of the Electron Dynamic Radius Formula

Since Newton's classical mechanics established the concept of "point mass", simplifying objects into geometric points without volume or internal structure has become a powerful mathematical tool for physics to handle gravitational and motion problems. However, this idealized assumption has triggered a serious theoretical crisis in quantum electrodynamics (QED) — the infinite divergence of electromagnetic self-energy, the dilemma of artificial cutoff in renormalization, and the ontological ambiguity of the wave function collapse mechanism. Based on the Unified Cosmic Mechanics Evolution Theory, this paper proposes a new ontological perspective: everything in the universe is not composed of abstract "points", but of the only evolutionary carrier — the momentum unit (\ (m₀\) ). Within this framework, all particles are composite entities formed by the vector superposition of multiple momentum units. For fermions (such as electrons), to maintain the stability and symmetry of the evolutionary system, their internal momentum flow must adopt a spherical symmetric encapsulation form, naturally endowing electrons with a clear intrinsic radius and completely abandoning the "geometric point" assumption. The electron is neither a rigid point particle with a fixed state nor a dimensionless singularity, but an adaptive momentum encapsulation body with a dynamic radius \ (R (p) \). This paper will strictly derive the electron dynamic radius formula, conduct self-consistency verification through the hydrogen atom system, and reveal the geometric and physical mechanism behind the dual characteristics of "cloud state" and "particle state" of micro-particles, providing a natural ultraviolet cutoff scheme for solving the QED divergence problem.