Closed-Surface Theory of the Electron: Geometric Basis for the Compton Shift and Scattering Phenomena

This work presents a closed-surface geometric theory of the electron that reproduces the Compton wavelength shift without invoking point-particle assumptions. In this framework, the electron is modeled as a finite, curved surface supporting interference patterns, with its curvature density ∇²φ determined directly from measured constants ℏ and mem_eme. The resulting equilibrium radius a₀ ≈ 10⁻¹¹m matches the Bohr radius, and the same method yields the helium nuclear radius in agreement with experiment. When irradiated with X-rays (ν∼10¹⁸ Hz), the electron surface undergoes anisotropic compression to≈ 10⁻¹³, with the forward side (θ=0) experiencing maximum deformation. The deformation geometry naturally introduces the angular factors cos⁡θ and 1−cos⁡θ , corresponding to Lorentz-type contraction and extension. The recovery of the surface produces damped, angle-dependent re-emission, yielding the Compton formula Δλ=(1−cos⁡θ) with a geometric interpretation. Beyond reproducing known results, the model predicts measurable features absent in the point-particle view: systematic linewidth broadening with scattering angle, polarization–angle correlations, and weak higher-order sidebands from ℓ>1 modes. These provide clear experimental tests for the closed-surface framework and link scattering processes to a unified geometric description of space, mass, and fields.