Complementarity as Ledger Closure: A QMU Interpretation of Recoil-Tagged Interference

This paper reformulates quantum complementarity as an operational ledger-closure constraint in the Aether Physics Model (APM) using Quantum Measurement Units (QMU) throughout. The central claim is not a reinterpretation of interference as a philosophical duality, but a metrology-ready statement: a single interaction cannot simultaneously close (i) a global rotational coherence ledger supporting two-path interference and (ii) a local torsional record ledger storing which-path (recoil) information, without paying a quantified overlap penalty. The analysis is organized around a recoil-tagged ("recoiling-slit") interference model in which the interference term is suppressed by the overlap of two detector states correlated with opposite recoil displacements. Adopting a squared-overlap convention for fringe visibility, the paper derives the Gaussian-budget visibility law\[V = \left|\langle \psi_1|\psi_2\rangle\right|^{2} = e^{-2\eta^{2}},\qquad\eta=\frac{\Delta p_{\gamma}}{2\,\Delta p_{\mathrm{slit}}},\]and connects which-way distinguishability to the detector-state trace distance, yielding the duality form\[D^{2}+V\le 1\]under the paper’s visibility convention. A key contribution is the QMU-native diagnostic obtained by compressing the recoil-tag control parameter through Ledger One, the APM electromagnetic propagation closure\[A_u\,\mathrm{curl} = {F_q}^{2}{\lambda_C}^{2}.\]Using the action decomposition \(h={e_\mathrm{emax}}^{2}\,\mathrm{mflx}\) and a dimensionless slit momentum budget \(\Pi_p\), the complementarity knob becomes\[\eta=\frac{{e_\mathrm{emax}}^{2}\,\mathrm{mflx}\,\mathrm{freq}}{2\,\Pi_p\,m_e\,(A_u\,\mathrm{curl})},\qquadV=\exp(-2\eta^{2}),\]making complementarity an explicit trade between the Aether rotational geometry (\(A_u\)) and torsional record formation (\(\mathrm{curl}\)). The paper further provides a QMU-thermodynamic bridge by defining the QMU temperature unit \(\mathrm{temp}={\lambda_C}^{2}{F_q}^{2}\) and introducing a dimensionless preparation level \(\vartheta\) such that \(\mathrm{temp}_{\mathrm{state}}=\vartheta\,\mathrm{temp}\). This yields an operational mapping between cooling/heating and the prepared slit momentum budget \(\Pi_p\), clarifying how thermal or engineered broadening washes out which-way records and restores coherence. Finally, the manuscript proposes a laboratory program that treats recoil-tagged interference as a QMU metrology standard: (E1) visibility-collapse curves as a calibration of detector momentum budgets, (E2) squeezed-state deformations as a state-preparation ledger test, and (E3) curl-engineered detector variants as a bridge to QMU material characterization. The result is a generic, ledger-driven complementarity framework designed for falsifiable experimental closure and QMU-native reporting.