Topological vortex solitons in nonlinear Maxwell equations: Origin of electron spin and rest mass from unified field simulation

The intrinsic spin of electron has remained a puzzling topic in physics. Classical physics cannot explain the origin of electron spin, and quantum mechanics only describes its properties mathematically without revealing the physical mechanism. This research constructs a vortex model based on modified Maxwell equations, demonstrating that localized electromagnetic vortex structures naturally possess intrinsic angular momentum analogous to particle spin. Using numerical simulation, the study establishes a steady-state vortex solution in cylindrical coordinates. The geometric parameters of the vortex correspond to intrinsic angular momentum, and the energy scale matches the static mass-energy relation. Furthermore, this article discusses the formation conditions of such electromagnetic vortices, and explores the possibility that elementary particles are stable self-confined electromagnetic vortex configurations. The model provides a new classical physical interpretation for quantum spin phenomena, and offers a feasible research path for bridging classical electromagnetism and quantum theory.