Mathematical Physics

    

There Is No Matter: Vacuum Knots as Toroidal Resonant Solitons and the Role of αU = keAP

Authors: Pedro A. Kubitschek Homem de Carvalho

We develop a mathematically grounded framework in which what is commonly called "matter" consists of finite—energy, knotted excitations of a nonlinear vacuum field. The model is based on a Faddeev—Skyrme—type Lagrangian for a unit vector field n : R3,1 → S2, coupled to gravity and electromagnetism. Toroidal (Hopf) solitons carry conserved topological charge and exhibit internal "beating" modes. Mass, momentum and spin arise purely from the vacuum stress—energy tensor. The constant αU = keAP (Coulomb constant times Planck area) plays the role of a vacuum rigidity/constitutive scale, controlling EM couplings and regularization. We lay out explicit assumptions, definitions, energy bounds, and geodesic motion of soliton centers, with citations to classical results (Derrick’s theorem, Vakulenko Kapitanskii bound, moduli space dynamics).

Comments: 7 Pages.

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[v1] 2025-09-01 22:38:41

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