Extended Electromagnetic Theory in Quantum Measurement Units: Constitutive Reconstruction with Distributed Charge

Abstract

This paper presents a QMU-native extension of electrodynamics that reconstructs the auxiliary fields $(D,H)$ as a constitutive layer over a geometry-first Maxwell ledger. The central objective is to retain the classical operational split between $(E,B)$ and $(D,H)$ while enforcing QMU semantics: (i) dual charge channels (electrostatic vs magnetic), (ii) explicit singular-to-distributed charge conversion rules with a defined exception class, and (iii) a two-layer field dictionary that cleanly separates flux-density variables from strength variables. \medskipThe vacuum sector is closed by geometric identities rather than empirical medium constants, including the speed closure $c=\lambda_C F_q$, the channel conversion $e^2/{e_\mathrm{emax}}^{2}=8\pi\alpha$, and a seat-map normalization expressed through $A_u/k_C=16\pi^{2}$. Within this framework, permeability and permittivity are treated as QMU substrate ratios,\[\mathrm{perm}=\frac{1}{\mathrm{curl}},\qquad \mathrm{ptty}=\frac{1}{A_u},\]so that the propagation scale factorizes exactly as\[\mathrm{perm}\,\mathrm{ptty}=\frac{1}{c^2}.\]This yields a wave operator that is naturally expressed in terms of the torsion--rotation product. \medskipA two-layer dictionary is introduced in which $(D,B)$ represent flux-density fields and $(E,H)$ represent operational strength fields, connected in uniform Aether by a geometric lift proportional to the quantum length. Independently, the paper defines constitutive-conjugate strengths $(E^{\star},H^{\star})$ that pair directly with the exception-class response operators in boundary-value and material problems. The two strength notions are reconciled algebraically in isotropic vacuum, clarifying how QMU separates local forcing scales from substrate response scales. \medskipFor non-uniform rotating-magnetic-field (rmfd) states, the constitutive law is promoted to a linear operator deformation driven by the rmfd non-uniformity tensor $\Theta_{ij}=\nabla_i U_j$ with dimensionless couplings $(\chi_E,\chi_H)$. In the local plane-wave limit, this produces a first-order polarization eigenproblem whose birefringent splitting is governed by the transverse symmetric strain and the combined coupling $(\chi_E+\chi_H)$. The paper provides compact invariants for the transverse shear sector and an interferometric path-integrated phase observable suitable for QMU-only laboratory discriminators. \medskipAn appendix provides a conventional-constant crosswalk as a reader-facing translation layer only; it is not used in the QMU constitutive derivations.