QMU–SI Translation and the APM Reference Ledger: Constants, Conversions, and Benchmark Identities

Abstract

This paper constructs a complete, species-indexed translation ledger between the Quantum Measurement Unit (QMU) system and SI, and generalizes the Aether Physics Model (APM) metrology framework from an electron-only sector to electrons, protons, and neutrons. The QMU bases are taken as the set\[\{ m_e,\;\lambda_C,\;F_q,\;e^{2},\;{e_\mathrm{xmax}}^{2} \},\]where $\lambda_C$ is the Compton wavelength, $F_q$ is the chronovibration frequency satisfying $c = \lambda_C F_q$, and ${e_\mathrm{xmax}}^{2}$ is the distributed magnetic charge associated with particle species $x\in\{e,p,n\}$. For each species the fine-structure parameter is\[\alpha_x = \frac{e^{2}}{8\pi\,{e_\mathrm{xmax}}^{2}},\]so that\[{e_\mathrm{emax}}^{2} = \frac{e^{2}}{8\pi\alpha_e},\qquad{e_\mathrm{pmax}}^{2} = \frac{e^{2}}{8\pi p},\qquad{e_\mathrm{nmax}}^{2} = \frac{e^{2}}{8\pi n}.\] Angular momentum is likewise species-indexed:\[h_x = m_x\,{\lambda_C}^{2}\,F_q,\]so that for the electron one has $h = m_e {\lambda_C}^{2} F_q$, while the proton and neutron satisfy $h_p = m_p {\lambda_C}^{2} F_q$ and $h_n = m_n {\lambda_C}^{2} F_q$. These relations make explicit that all particle species share the same Aether substrate $(\lambda_C, F_q)$ and differ only by $(m_x, {e_\mathrm{xmax}}^{2}, \alpha_x)$. The paper reviews the QMU unit grid and the dynamic/substrate dual ontology. Dynamic units place mass in the numerator and distributed charge in the denominator, while substrate units invert this ratio. The Aether rotating-field unit $A_u$, the curl exposure, the Coulomb-geometry factor $k_C$, the Aether Gforce, and the Aether mass scale $m_a$ are treated as primary derived ledger quantities. Their defining closures,\[A_u\,\mathrm{curl} = {F_q}^{2}{\lambda_C}^{2},\qquad\frac{A_u}{k_C} = 16\pi^{2},\qquad\mathrm{Gforce} = \lambda_C {F_q}^{2} m_a,\]follow directly from the QMU base definitions. To connect QMU with SI, which uses the singular charge $e$, the paper introduces a species-anchored charge conversion factor (CCF),\[\mathrm{ccf}_x = \frac{{e_\mathrm{xmax}}^{2}}{e} = \frac{e}{8\pi\alpha_x},\]allowing consistent translation between distributed-charge expressions and singular-charge legacy formulas. Unified rules are provided for CCF application, distinguishing charge in the numerator versus denominator (Rule~A), dynamic versus substrate units (Rule~B), and squared impedance-like classes (MFR/MFF). Five special ledger units (cond, capc, indc, perm, ptty) already incorporate distributed charge and therefore do not receive additional CCF factors. Using these rules, the paper derives benchmark identities in the electron sector:\[\begin{aligned}1\,\mathrm{potn}\cdot\mathrm{ccf}_e &\;\longleftrightarrow\; \frac{m_e c^{2}}{e},\\1\,\mathrm{mflx}\cdot\mathrm{ccf}_e &\;\longleftrightarrow\; \frac{h}{e},\\1\,A_u\cdot\mathrm{ccf}_e &\;\longleftrightarrow\; \frac{h c}{e},\\1\,\mathrm{mchg}\cdot\mathrm{ccf}_e &\;\longleftrightarrow\; \frac{m_e}{e},\\1\,\mathrm{expr}\cdot\mathrm{ccf}_e^{-1} &\;\longleftrightarrow\; \frac{e}{m_e}.\end{aligned}\]These recover well-known SI identities such as the electron rest-energy per charge, the flux-quantum scale, the photon energy–wavelength relation per charge, and the mass/charge ratios. The result is an empirical validation of the QMU ledger. A major conceptual advance is the generalization to proton and neutron sectors.A species-labeled Aether bookkeeping template\[A_{u,x} = \frac{m_x\,{\lambda_C}^{3} {F_q}^{2}}{{e_\mathrm{xmax}}^{2}}\]tracks how each particle species couples to the same Aether substrate. This yields proton and neutron benchmark chains completely analogous to the electron sector once $(m_x, {e_\mathrm{xmax}}^{2}, \alpha_x)$ are specified. The paper includes a TikZ diagram showing how the base electrostatic charge $e^{2}$ branches into species-specific distributed charges ${e_\mathrm{xmax}}^{2}$ through the fine-structure parameters $\alpha_x$, as well as a summary table of species-indexed quantities and corresponding benchmark identities. Appendix~A contains proton and neutron benchmark derivations in QMU form, and Appendix~B provides an optional SI numerical map for readers who require legacy-unit comparison. Together these elements transform the work into a complete, species-indexed metrology ledger for the QMU system, with internal coherence, clear translation rules, and direct links to measurable SI combinations for each particle species.