A Unified Electro-Gravity Framework from Planck-Scale Symmetry

This paper presents a unification framework linking Newtonian gravity and Coulomb’s electrostatic force, revealing a structural symmetry between two fundamental interactions governed by inverse-square laws. While Newton’s law describes the gravitational attraction between masses on cosmic scales, Coulomb’s law governs charge interactions at atomic and subatomic levels. Despite their vastly different strengths, both forces share a common mathematical architecture when expressed in Planck units. We demonstrate that Coulomb’s constant (Ke) and the gravitational constant (G) possess an identical Planck-based numerator (mplpc2 = ℏc), differing only in their denominators—the squared Planck charge and squared Planck mass, respectively. This symmetry enables the formulation of a unified electro-gravity interaction that introduces dimensionless coupling constants, αGe » 2.4×10−43 for electrons and αGp » 8.1×10−37 for protons, which precisely quantify gravity’s relative weakness compared to electromagnetism. Unlike higher-dimensional or particle-based unification models, this framework is minimalist, relying only on known physical constants. Most importantly, it leads to experimentally relevant predictions: suppressed gravitational corrections to the fine-structure constant, potential charge-to-mass deviations in extreme astrophysical systems, and possible cosmological signatures in the CMB and primordial gravitational wave spectra. By interpreting gravity and electromagnetism as distinct manifestations of a single Planck-scale scaling principle, this work advances a phenomenological and testable step toward unification that complements existing approaches to quantum gravity.