Spatial Guidance Field Theory: From Gradient Postulates and Charge Conservation to Gauge Group Structure

Abstract

We construct a unified framework for interactions from three postulates: (1) all elementary forces arise as gradients of guidance potentials, (2) the charges that generate these potentials are conserved, and (3) the internal symmetry group must accommodate chiral fermions. The chirality postulate forces the internal symmetry group to be non-Abelian. In the non-relativistic limit, a scalar guidance field reproduces Newtonian gravity and Coulomb's law, and relativistic consistency upgrades the potentials to a spacetime metric and gauge vector fields. The central result is a rigorous derivation that the internal symmetry group must be a compact Lie group; combined with anomaly cancellation and minimal rank and representation content, this uniquely selects the Standard Model's $SU(3)_c \times SU(2)_L \times U(1)_Y$. We present a guidance-field description of strong and weak interactions, and derive coupling-modified Tolman--Oppenheimer--Volkoff equations for neutron stars, obtaining a theoretical maximum mass of $M_{\rm max}^{\rm th} \approx 2.8 \pm 0.4\,M_\odot$, naturally accommodating the $2.6\,M_\odot$ companion of GW190814. We further derive quantitative predictions for equivalence principle violation from nonlinear superposition of guidance potentials, with a QCD-scale benchmark within reach of next-generation experiments. Finally, we discuss implications for black hole interiors within a geometric framework in which charges are topological invariants of a generalized space, and provide the mathematical formulation of the total connection, its action functional, and field equations.