The Unified Field Paradox: Restoring Maxwell’s Scalar Potential and Decoupling the Heaviside Vector Reduction via Quaternion Field Formulations

Abstract

Arunas Ostasevicius

This paper performs a systematic deconstruction of the electromagnetic field vector reduction originally executed by O. Heaviside and J. Gibbs. We demonstrate that the forced nullification of the Maxwellian field scalar potential S = Real(DA) = 0 deprived the physical vacuum of its fundamental property of volumetric compressibility. Within the proposed framework, the electron is modeled as a deterministic, non-linear quaternionic vortex structured within a dynamic medium of vacuum bubbles (the Wheeler field), stabilized by a Van der Pol attractor under the governance of the quaternionic Virial theorem. A modified energy-momentum tensor (EMT) incorporating a scalar term S2 is derived, which inherently generates an internal compensating hydrostatic pressure. Operating upon Verhulst-type non-linear logistic equations, it is revealed that the vacuum scalar pressure gradient ∇S acts as the fundamental accelerating force of autowave drift (inertia). Concurrently, the cubic non-linear term completely eliminates infinite electronic energy divergences as r → 0. Finally, a comparative numerical analysis is provided, demonstrating the physical inadequacy of the classical skin-effect framework traditionally used to dismiss the Tesla-Meyl longitudinal wave transmission experiments.

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