Electron EDM in QMU: CP-odd Square-Charge Dipole from Aether-Unit Holonomy

Abstract

Electron EDM in QMU: CP-odd Square-Charge Dipole from Aether-Unit Holonomy This paper reformulates the electron "EDM" observable in the Aether Physics Model (APM) using Quantum Measurement Units (QMU), where the primitive charge dimension is square-charge and electrostatic potential is reciprocal capacitance. In this framework, the natural EDM-like observable is not a linear-charge dipole \(d_e\), but a CP-odd square-charge first moment of a distributed square-charge density. QMU potential and driver. Electrostatic potential is defined as reciprocal capacitance,\[\Phi_Q := \frac{1}{C},\]and the electrostatic driver is its gradient,\[\mathbf{G} := \nabla \Phi_Q.\] Square-charge EDM observable and ledger-closed coupling. Let \(\rho_{e^2}(\mathbf r)\) be the signed distributed square-charge density (magnetic basis). The square-charge dipole vector is the first moment\[\mathbf{D}_{e^2} := \int \rho_{e^2}(\mathbf r)\,\mathbf r\,d^3r.\]The ledger-closed interaction energy with external electrostatic structure is\[\Delta U = -\,\mathbf{D}_{e^2}\cdot\nabla\Phi_Q,\]which replaces the legacy coupling \(-\mathbf d\cdot\mathbf E\) by changing the driver to \(\nabla\Phi_Q\) and the dipole to a square-charge moment. Holonomy origin and CP-odd invariant. The Aether-unit two-sphere chronovibration supports a 5D closed action whose 4D forward-time projection can exhibit holonomy. A CP-odd defect one-form \(\delta\omega_{\mathrm{CP}}\) is defined from the 5D-to-4D connection mismatch, and the dimensionless CP-holonomy invariant is\[\Delta_{\mathrm{CP}} := \frac{1}{2\pi}\oint_{\gamma_+}\delta\omega_{\mathrm{CP}},\]where \(\gamma_+\) is the forward-time leg of the chronovibrational cycle. The square-charge dipole is parameterized by\[\mathbf{D}_{e^2} = {e_\mathrm{emax}}^{2}\,\lambda_C\,\Delta_{\mathrm{CP}}\,\hat{\mathbf s},\]with \({e_\mathrm{emax}}^{2}\) the distributed square-charge unit in the magnetic basis, \(\lambda_C\) the electron Compton length, and \(\hat{\mathbf s}\) the spin direction. Domain taxonomy, seams, and obstruction index. A minimal octant-domain cover of the electron sheet is introduced, with antipodal pairing and a loxodromic seam-crossing loop. Under a local-exactness hypothesis on each octant, the CP-odd holonomy reduces to a seam-sum cocycle. Quantized seam jumps are written as multiples of the octant increment \(\pi/4\), producing an integer obstruction index \(\tau_{\mathrm{CP}}\in\mathbb Z\) and a discrete spectrum\[\Delta_{\mathrm{CP}} = \alpha^{p}\,\frac{\tau_{\mathrm{CP}}}{8},\]where \(\alpha\) is the fine structure constant and \(p\ge 1\) is the leading order at which the CP-odd defect survives seam pairing. Metrology and experimental bridge. An action scale is defined in QMU as\[h_e := m_e\,{\lambda_C}^{2}\,F_q,\]so the measurable frequency shift is \(\Delta f=\Delta U/h_e\). In EDM platforms, the relevant driver is the internal reciprocal-capacitance gradient component\[\mathcal{G}_{\mathrm{eff}} := \hat{\mathbf n}\cdot\nabla\Phi_Q,\]leading to a spin-reversal splitting proportional to \(|\Delta_{\mathrm{CP}}|\,|\mathcal{G}_{\mathrm{eff}}|\). State-of-the-art null bounds from electron-EDM experiments (e.g. ACME) are interpreted here as constraints on admissible microstate classes and packing-weighted populations rather than on an intrinsic point-parameter. Next-step program and parameter-free prediction target. With canonical octant labeling and the loxodromic seam loop fixed, Milestone M1 is to compute the leading CP-odd chirality connection \(\omega^{(1)}_{\chi}\) and the associated seam integers \(m_{ij}\), and to determine whether \(p=1\) (non-canceling order-\(\alpha\) seam cocycle) or \(p\ge 2\) (order-\(\alpha\) cancellation). If the explicit summation yields \(p=1\) and the minimal obstruction \(\tau_{\mathrm{CP}}=1\), then the framework makes a parameter-free magnitude prediction in native QMU units:\[|\mathbf{D}_{e^2}| = {e_\mathrm{emax}}^{2}\,\lambda_C\,\frac{\alpha}{8}.\]For appendix-only SI-bridge purposes, the charge-basis relation\[e^{2} = 8\pi\alpha\,{e_\mathrm{emax}}^{2}\]connects the square-charge unit to the elementary-charge-squared scale used in legacy reporting.