Pseudo-Finsler geometry extends Riemannian framework to geometrize electromagnetism from Lorentz force and Maxwell equations

The paper builds directly on three prior works showing that the electromagnetic four-potential generates a space-time metric whose components vary with observer four-velocity. Standard Riemannian geometry fails because the norm is non-homogeneous; the authors therefore adopt a pseudo-Finsler structure whose fundamental function reproduces both the Lorentz force law and the source-free Maxwell equations as geodesic deviation and curvature identities. This construction recovers the electromagnetic field tensor from the Cartan connection of the Finsler bundle rather than from an auxiliary vector field. Because the metric is defined on the tangent bundle, the theory automatically incorporates observer-dependent effects that appear as gauge transformations in the usual formulation. The approach revives the program of unified geometry that began with Weyl and Kaluza but replaces their extra dimensions or conformal rescaling with an intrinsic velocity dependence already present in the experimental foundations of electromagnetism. No additional fields or compactification are required; the geometry is fixed once the Lorentz force is accepted as the definition of the connection. The chief limitation is the absence of any quantized or matter-coupled extension, leaving open whether the same Finsler structure can accommodate the Dirac equation or non-Abelian gauge fields.