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

The work compares two conceptually different mass--energy ledgers: The relativistic ledger, written as E = mc², where E and m are dimensionful variables related by the postulated propagation constant c. The Quantum Measurement Unit (QMU) ledger of the Aether Physics Model (APM), written as \[ enrg = mass · Aᵤ · curl = mass · {F_q}² {λ_C}², \]where enrg and mass are fixed QMU base units, Aᵤ is the Aether unit, curl is the torsional (curl) unit, Fq is the quantum frequency, and λC is the Compton quantum length. The central theme of the paper is an ontological comparison between: Principle theory (relativity):The mass--energy relation E = mc² follows from Lorentz symmetry and the postulate that the speed of light c is constant in all inertial frames. Mass is treated as a Poincar\'e-invariant parameter, energy as a Noether charge for time translations, and c² appears as a single, undifferentiated propagation constant. Constructive theory (APM/QMU):The mass--energy ledger enrg = mass · Aᵤ · curl arises from a geometric model of a quantized Aether. The Ledger One identity Aᵤ · curl = Fq² λC² factors the propagation constant into rotational and torsional contributions of a single Aether unit. The unit mass is defined as the mass of exactly one Aether unit fully occupied by the primary angular momentum (dark matter) emerging from the Singularity, so physical masses are counted as dimensionless occupancies of these Aether units. Within this framework, the paper: Derives the QMU mass--energy ledger from Ledger One and the chronovibrational relation Fq λC = c, showing that c² = Aᵤ · curl = Fq² λC². Reviews how E = mc² appears in special relativity from the invariant norm of the energy--momentum four-vector and the symmetry structure of the Poincar\'e group. Compares the meanings of ``mass'' and ``energy'' in each paradigm: as variable slots anchored by symmetry in relativity, versus fixed QMU base units counting occupied Aether units in APM. Presents a side-by-side table contrasting the two ledgers in terms of: the definition of mass, the definition of energy, the nature of the propagation constant, and the governing principle (postulate-based versus constructive). The paper also outlines three classes of experiments and observations that bear on the mass--energy ledgers: Combined propagation-constant tests, such as annihilation and creation processes, nuclear mass defects, and relativistic kinematics, which confirm that energy scales as mass times a universal propagation constant but do not probe its internal structure. Factorization tests, in which independent metrology of the Aether unit Aᵤ, the curl unit, the quantum frequency Fq, and the quantum length λC can be used to test the closure condition Aᵤ · curl ?= Fq² λC². Gradient-ledger tests, where circular deflection angles, gravitational redshift, and tiny Aether-induced electric potential differences are interpreted as Aether density gradients coupled through the curl unit. In particular, the paper notes that extremely small potential differences per unit length, when integrated over astronomical scales (comets, magnetospheres, nebulae), can accumulate into substantial electromagnetic energy, providing a constructive alternative to unseen mass distributions in large-scale structures. Together, these elements frame the relativistic mass--energy relation E = mc² and the QMU ledger enrg = mass · Aᵤ · curl as two different ontologies for the same measured propagation constant. The work emphasizes that experiments tightly constrain the value of the propagation constant but do not uniquely fix its interpretation, leaving open the question of whether a postulate-based symmetry description or a constructive Aether geometry provides the more complete account of mass and energy.