From UD Theory to Electromagnetism: The Vector Projection

This paper derives classical electromagnetism as the vector projection of UD theory. The dynamical scalar fields UD (the D-attribute in space, manifest as dark matter) and DU (the U-attribute in matter, manifest as quantum fluctuations) form a coupled Klein-Gordon system. In the low-energy electromagnetic limit, the background fields UU and DD sit at their vacuum expectation values, and the active equations reduce to a closed system. The canonical energy-momentum tensor T^μν of this system is exactly conserved. The electromagnetic field strength F^μν is defined as the normalized Hodge dual of T^μν: F^μν = (2m₀²) ^-1 ε^μνρσ T⏠⏢, where m₀ = 1/ (2πe^π) is the UD ground mass scale. This definition is the unique Lorentz-covariant mapping from a symmetric rank-2 tensor to an antisymmetric one, with the dimension corrected by the only fundamental mass scale of the theory. From the conservation law ∂_μ T^μν = 0, it follows directly that ∂_μ F^μν = 0. Together with the Bianchi identity ∂⏚ F⏛⏜ = 0, this yields the source-free Maxwell equations. The photon is identified as the quantum of F^μν: a propagating collective excitation of the UD-DU energy-momentum transfer, not a permanent elementary particle. A vector potential A^μ satisfying F^μν = ∂^μ A^ν - ∂^ν A^μ exists by the Poincaré lemma and inherits the residual U (1) gauge symmetry. Coupling to the conserved U (1) Noether current j^μ from the spinor projection (Ref. 2) via the gauge-invariant action S = ∫ d⁴x (-1/4 F⏛⏜F^μν + e A_μ j^μ) yields the full Maxwell equations ∂_μ F^μν = e j^ν. A massive scalar mode with m = m₀/√2 remains as a UV signature, inducing a Yukawa correction to the Coulomb potential at the UD length scale. All derivations proceed from the UD action without introducing external gauge fields. The U (1) gauge symmetry and the masslessness of the photon are derived consequences, not postulates. Together with Ref. 1 (general relativity) and Ref. 2 (quantum mechanics), UD theory now accounts for all three fundamental interactions as projections of a single four-aspect ontology. Key Points - The electromagnetic field strength F^μν is the normalized Hodge dual of the UD-DU energy-momentum tensor- F^μν = (2m₀²) ^-1 ε^μνρσ T⏠⏢ is the unique Lorentz-covariant mapping from a symmetric to an antisymmetric rank-2 tensor- ∂_μ F^μν = 0 follows directly from ∂_μ T^μν = 0, giving the source-free Maxwell equations without postulating a fundamental vector field- The photon is an emergent collective excitation of UD-DU energy-momentum transfer, not a permanent elementary particle- U (1) gauge symmetry emerges as a residual symmetry of the massless field strength, not as an external postulate- A massive scalar mode with m = m₀/√2 is predicted as a testable UV signature References 1 Zhu, D. "From UD Theory to General Relativity: A Complete Derivation of Gravitational Theory. " Zenodo, 2026. https: //doi. org/10. 5281/zenodo. 19903855 2 Zhu, D. "From UD Theory to Quantum Mechanics: The Spinor Projection. " Zenodo, 2026. https: //doi. org/10. 5281/zenodo. 19911827 3 Faraday, M. Experimental Researches in Electricity, Vol. 1. London: Bernard Quaritch, 1839. 4 Maxwell, J. C. "A dynamical theory of the electromagnetic field. " Phil. Trans. R. Soc. Lond. 155, 459–512 (1865). 5 Jackson, J. D. Classical Electrodynamics, 3rd ed. New York: Wiley, 1999. 6 Williams, E. R. , Faller, J. E. , and Hill, H. A. "New experimental test of Coulomb's law: A laboratory upper limit on the photon rest mass. " Phys. Rev. Lett. 26, 721–724 (1971).