Non-Linear Saturation in Quaternionic Electrodynamics: Regularization of Boundary Singularities

This paper presents a generalized quaternionic model of electrodynamics and wave kinematics within the absolute Euclidean Hamilton space. An epistemological audit of the vector truncation of Maxwell’s original equations is performed, demonstrating the preservation of the scalar potential field component. Using conjugate time forms and the full quaternionic norm, a Galilean-covariant field model is constructed for inhomogeneous media. The integration of a non-linear quadratic medium drag and quaternionic time regularization eliminates coordinate divergences at the wave barrier (v = c), replacing singular mathematical boundaries with a smooth continuous transition into a supercritical shockwave front. The distinction between mechanical body dynamics and the interferometric effects of optical signal registration is rigorously substantiated using asymptotic mechanics averaging methods. Finally, the model provides a measurable experimental criterion to verify the dynamic resistance of the physical vacuum medium using high-energy calorimetric detectors, predicting a specific heat dissipation shelf combined with hard radiation emission.