Aether Metrology with STEM--EELS: Experimental Determination of Curl, Aether Rotation, and Magnetic Flux Units (QMU)

This paper develops a Quantum Measurement Unit (QMU) reformulation of electron--magnon scattering in scanning transmission electron microscopy electron energy loss spectroscopy (STEM--EELS). Building on recent theoretical work that separates spin--based and ``charge-based'' scattering channels in magnonic materials, we show that the so--called charge-based interaction is not electrostatic, but the direct coupling of the high-energy electron probe to the Aether curl---the distributed magnetic charge of the Aether Physics Model (APM) encoded in the magnetic vector potential. The central dimensional closure is the Aether Rotational Self--Identity(Ledger One)\[A_u · curl = {F_q}^2 {λ_C}^2,\]where Aᵤ is the Aether unit, curl is the QMU curl, Fq is the quantum frequency, and λC is the Compton length. Since Fq λC = c, this identity can be recognized as\[A_u · curl = c^2,\]which decomposes the Maxwell relation c² = 1/(μ₀ ε₀) into rotational (Aether unit Aᵤ) and torsional (curl) geometries of the Aether. Recasting the STEM--EELS cross--sections in QMU reveals that the charge/curl channel inherits a dominant quadratic term k₀² / q², which becomes\[k_0^2/q^2= A_u/curl K^2/Q^2,\]showing that the charge-channel intensity is an explicit observable of the ratio Aᵤ / curl. The angular dependence follows a cos²θ law, reflecting the projection of the electron momentum onto the loxodromic twist direction of the Aether curl. By isolating the spin and curl channels as functions of momentum transfer Q and sample rotation angle θ, one can extract the Aether unit Aᵤ from the experimentally measured ratio\[Rₑₓₚ(Q,K,θ)={ICB}{ISB},_u=Rₑₓₚ \,curlref\,Q^2/K^2 cos^2θ.\]The magnetic flux unit then follows from the QMU identity\[mflx = A_u/F_q λ_C.\] This work establishes the first practical laboratory metrology protocol for measuring curl, Aether rotation \,λC Fq, and the QMU magnetic flux unit using STEM--EELS. It provides an experimental bridge between magnon spectroscopy and the foundational geometry of the Aether Physics Model.