What question did this study set out to answer?

The aim is to derive Maxwell's equations from UD theory and demonstrate its implications in electromagnetism.

June 13, 2026Open Access

From UD Theory to Electromagnetism: The Vector Projection and the Rigorous Emergence of Maxwell's Equations

Puntos clave

The aim is to derive Maxwell's equations from UD theory and demonstrate its implications in electromagnetism.
Derived scalar fields $U_d$ and $D_u$ using a coupled Klein–Gordon approach.
Constructed vector potentials through bilinear currents and analyzed electromagnetic field strength.
Showed source-free Maxwell equations and derived the full Maxwell equations from fundamental interaction.
Achieved source-free Maxwell equations via $\partial_\mu F^{\mu\nu} = 0$ with defined scalar fields.
Reproduced the exact Coulomb field of a static point charge.
Identified a massive scalar mode with mass $m_\Psi = m_0/\sqrt{2}$ as a UV signature.

Resumen

We derive classical electromagnetism as the vector projection of UD theory. The dynamical scalar fields Ud and Dᵤ form a coupled Klein–Gordon system. The vector potential is constructed as the bilinear current A^ = (Ud ^ Dᵤ - Dᵤ ^ Ud), where is a constant. The electromagnetic field strength is F^ = ^ A^ - ^ A^. The field equations of Ud and Dᵤ imply _ F^ = 0, giving the source-free Maxwell equations. A massive scalar mode with mass m_ = m₀/2 remains as a UV signature. Coupling to the matter current is derived from the fundamental UD interaction term, yielding the full Maxwell equations _ F^ = e j^ with the electromagnetic coupling constant e expressed in terms of UD parameters. The Coulomb field of a static point charge is exactly reproduced. All derivations are self-contained and rely solely on the UD axioms.

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