Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== 1. This arithmetic shows it is plausible that QAT’s geometric degrees of freedom (r, σ) could map to measurable fractional changes in α — but note: mainstream physics treats e, ħ, c, ε0 as fundamental constants. For QAT to claim variation in α via geometry, it needs a physical mechanism that causes σ or r to change in measurable ways (temperature, plasma state, local fields, cosmic evolution, etc.). You already mentioned plasma and temperature dependence — that's a sensible route to explore. ===
# A promising path (if you want to link to Dirac / Mach and cosmology) is to investigate whether an evolving typical interaction radius r(t) or an average surface-charge distribution σ(t) could scale with cosmic time t (e.g., r ∝ t^n or σ ∝ t^m), because then α would evolve as ∝ t^{4n + 2m} and could be compared with observational bounds on Δα/α over cosmological time.
# Another rigorous route: express σ in terms of microscopic variables (number of elementary charges per shell, temperature-dependent screening in plasma, effective radius determined by electron wavefunction shape) and try to derive dynamics. That provides concrete mechanisms where r and σ can vary.
# A focused experiment: atomic or molecular spectroscopy already constrains fractional changes in α at the 10⁻⁶–10⁻⁷ level (and cosmological tests reach ≲10⁻⁵–10⁻⁶ over Gyr). So QAT would need to predict variations within or beyond those limits. The sensitivity relation above lets you convert any predicted Δr/r or Δσ/σ into predicted Δα/α before checking data.