Methodology for Energy-Dependent Fine Structure Constant Tests from Quasar Absorption Systems

The Scalar-Tensor Vacuum Phase Transition (STVPT) framework (Papers I, II) predicts energy-dependent electromagnetic coupling Γ(E) ∝ E0.25. No observational test of this energydependence has been reported. Method: We develop and validate a methodology for measuring thepower-law exponent β in ∆α/α ∝ Eβ from multi-transition quasar absorption systems. Synthetictests recover input β within 0.4σ at SNR=100. We identify optimal targets from the ESO archive,including RVS377 (zabs = 1.70, SNR=111, 11 transitions, 4.43–8.89 eV). Observational test: Reanalysis of 293 ∆α/α measurements from King et al. (2012), stratified by weighted mean transitionenergy ⟨E⟩, yields ρ(|∆α/α|,⟨E⟩) = +0.083 (p = 0.16) and β = 0.61 ± 0.35—consistent with boththe null (1.7σ) and STVPT (1.0σ). This inconclusive result is driven by a strong energy–redshiftconfound (r = 0.89) inherent to inter-system comparisons. Sensitivity analysis: The q ̸ = 0 transitions that measure ∆α/α span only 5.20–6.12 eV (4.2% STVPT signal), limiting single-systemsensitivity to σβ ∼ 0.1–3. Multi-system combination (N ≳ 50) or methods exploiting ancho