Mass--Energy Ledgers in QMU and Relativity: Constructive Aether Geometry versus Principle Theory

This article formulates the mass--energy relation in the Aether Physics Model (APM) using Quantum Measurement Units (QMU) and compares it to the relativistic ledger E = m c². In QMU, energy and mass are fixed units enrg and mass defined from quantum constants and Aether geometry, rather than free variables. The propagation constant is not postulated but factored as Ledger One: Aₔ \, curlₐ₌ₔ = Fq^2 C^2, where Aₔ is the Aether unit, curlₐ₌ₔ is the torsion (curl) unit, Fₐ is the quantum frequency, and ₂ is the quantum length. The QMU mass--energy ledger then reads enrg = mass \, Aₔ \, curlₐ₌ₔ = mass \, Fq^2 C^2, with physical configurations described by dimensionless occupancy factors counting fully occupied Aether units. We contrast this constructive, ledger--first formulation with the principle--theory status of E = m c² in relativity, where E and m are Noether--type variables and c is a primitive propagation constant fixed by Lorentz symmetry. The paper highlights that the relativistic ledger is torsion--blind: it constrains only the product Aₔ \, curlₐ₌ₔ (identified with c^2), whereas QMU resolves rotation (Aₔ) and torsion (curlₐ₌ₔ) separately. We summarize experimental classes that test the shared propagation constant and outline torsion--resolved tests, including curl--based material metrology, Aether density--gradient deflection ledgers, and astrophysical applications such as Galactic--center nonthermal radio filaments and galactic black--hole horizons formulated in QMU. These torsion--sensitive regimes provide a constructive completion of E = m c² and a falsifiable framework for relating mass--energy, Aether geometry, and large--scale structure.