Nonion Algebra and the Unified Field Equations: Restoring Maxwell's Scalar Term via Discrete Plenum Theory

Abstract

We propose a nine-component algebra — the nonion — as the natural mathematical framework for a unified description of electromagnetic and gravitational fields within a discrete plenum model. The nonion extends the classical octonion by replacing the single gravitational unit e7 with a doublet (e7, e8) representing the downward and upward components of the gravitational flux. This extension restores the scalar longitudinal term eliminated by Heaviside in 1880 from Maxwell’s original quaternionic formulation, and yields a fully symmetric set of eight field equations in which electric field, magnetic field, and gravity appear on equal footing. The 96 discrete states of the nonion algebra correspond to the 96 stable chemical elements through a geometric construction based on two quaternary sets derived from the generators of the discrete plenum. Anomalous gravitational modulation in pendulum experiments and energy anomalies in resonant electromagnetic systems are interpreted as consequences of local conversion between longitudinal plenum flux and transverse electromagnetic field.