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

==== Path 1 — Put numbers on time dilation: ====
Pick a simple, realistic spectrum (e.g., room-temperature blackbody ± narrow lines), choose a simple σ(ω)\sigma(\omega)σ(ω) model for an atomic shell, compute RRR, then compute δR\delta RδR from a nearby absorbing sphere (geometric 1/r² “shadow”) and get ΦQAT\Phi_{\rm QAT}ΦQAT → Δf/f\Delta f/fΔf/f. This gives an order-of-magnitude prediction to compare with known gravitational redshift scales.

Path 2 — Do the inertia derivation cleanly:
Start from the Maxwell stress tensor on a thin spherical shell with a simple harmonic drive (absorb/re-emit with phase lag set by h/2πh/2\pih/2π and a linewidth). Compute the cycle-averaged reactive force and extract meffm_{\rm eff}meff explicitly. Show how the familiar radiation reaction is reshaped by the spherical boundary and how the ½ (half-radius/half-spin) appears in the angular decomposition.

If you want me to decide, I’d start with Path 1 (numbers for time dilation via δR\delta RδR), because it connects straight to the “gravity-like” signature (clock rate) and is easier to bound with real constants. Then we’ll circle back and do Path 2 for inertia in the same surface-geometry language.