Ulianov’s Formulation of the Maxwell’s Equations, from a Spherical-Shell Electron Model

Abstract

Ulianov String Theory (UST) proposes a non–pointlike electron: instead of an infinitesimal particle orbiting the proton, the electron is modeled as a thin spherical shell of negative charge whose radius is comparable to the size of its orbital. The shell rotates at high angular velocity and naturally generates a magnetic field. The negative charge is distributed over the entire membrane in a manner that parallels the quantum mechanical wave function; however, rather than representing a probability density of finding a point particle, the wave equation is interpreted here as a real charge density over a geometrical surface.

All of the rest mass of the electron is concentrated in a single point located at one pole of the shell-the polar mass. This point like mass determines a preferred direction of rotation, so that all electrons share the same intrinsic rotational sense. What quantum theory labels as ”opposite spin” corresponds, in this model, merely to the shell being inverted, with the polar mass located at the opposite pole. Thus, the electron possesses an extended charge distribution but a localized point of inertia.

This microscopic structure allows for a natural and fully geometrical decomposition of macroscopic polarization P and magnetization M. From these fields, the usual conduction-current term μ0J in the Ampère–Maxwell law is not assumed but is instead recovered as an emergent quantity. As a result, Maxwell’s equations can be rewritten in a field-only form:

∇× E = -∂B/∂t,

 ∇ ・ B = 0,

 ∇ ・ D = 0,

∇ ×H =∂D/∂t.

With D =ε_0 E+P and H =1/μ0 B -M.

The central modification introduced by UST concerns the Ampere-Maxwell law. In its standard SI form,

∇ × B =μ_0 J+μ_0 ε_(0 ) ∂E/∂t.

the magnetic field has two distinct sources: electric current and the time derivative of the electric field. This two-term structure reflects the traditional belief that magnetism generated by permanent magnets and magnetism generated by electric currents are fundamentally different.

However, UST provides a unified microphysical explanation. Because every electron is a rotating spherical shell with a mass pole, both forms of magnetism arise from the same underlying mechanism: the alignment or misalignment of the rotation axes of many electrons. An electric current does not create a magnetic field; rather, the preexisting microscopic magnetic fields of the electrons become partially aligned as the shells move and the mass poles lag due to inertia. This alignment process parallels the way sailboats randomly oriented on a calm sea all turn in the same direction under a light wind.

Thus, the magnetic field surrounding a current-carrying wire is not produced but is the collective ordering of microscopic magnetization fields. This perspective removes the need for the explicit sum in the original Ampere –Maxwell law and yields a more uniform and elegant field structure without altering any experimentally verified predictions of classical electromagnetism.