Geometric Unification of Fields via Closed Surface φ: From Electric Lines to Gravitational Modes

This work presents a unified geometric framework in which all fundamental fields—electric, magnetic, gravitational, and gauge fields—are reinterpreted as manifestations of structured variations on a closed surface φ(x, y, z, t). In this model, electric and gravitational field lines are expressed as imaginary normal vectors (i) orthogonal to equipotential surfaces, while magnetic fields, wavefronts, and topographical contours are described as closed-loop patterns on the real part of φ. Vibrational frequency (ν) and closed-surface thickness (Δiφ) are shown to obey an inverse relation, ν·Δ(iφ) = constant, providing a universal scaling law. This theory proposes that high-frequency φ-structures correspond to particle-scale surfaces (e.g., electrons), while low-frequency thick φ-structures give rise to gravitational curvature. Gauge fields (U(1), SU(2), SU(3)) emerge naturally as topological patterns on φ, redefining field interactions in terms of embedded geometry. The approach offers a geometric unification of quantum fields and spacetime structure via φ as a fundamental physical entity. Author: Tetsuo Konno (今野哲夫) https://orcid.org/0009-0002-1842-7865