Electromagnetism in the Chronosphere Model: A Unified Geometric Theory of the Origin of Masses, Charges and Interactions

A unified geometric theory is presented according to which all physical scales arise from the incommensurability between the discrete structure of spacetime (chronons) and its continuously emerging boundary. The theory is based on the fundamental number π-3, which arises from the discretization of a sphere by a regular icosahedron. The following main results are obtained: (1) using Sadovnichii-Fazullin perturbation theory, the logarithmic correction to the spectrum of the Laplace operator on a sphere with point defects at the vertices of an icosahedron is rigorously derived, with a coefficient exactly equal to (π-3)/(4π); (2) a variational principle for a system of 12 chronons on a sphere leads to the icosahedral configuration as the energy minimum; (3) from the spectrum of the Dirac operator on an icosahedral lattice, quark masses are obtained, with three zero modes corresponding to light quarks (u,d,s); (4) an explicit realization of the electric charge operator is constructed in terms of representations of the group I, showing that its eigenvalues take the values +2/3 and -1/3; (5) a gauge-invariant formulation of the relation is proposed within a Lagrangian approach; (6) an analysis of 14 meson trajectories (62 states) yields an experimental value β_exp = 0.0106 ± 0.0022, coinciding with the theoretical β_theor = (π-3)/(4π) within 0.3σ. The theory predicts the existence of torsions (quanta of torsion) with masses 4-10 GeV and deviations from Coulomb's law at scales ∼ 10^{-17} m