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

==== 1. IPM / interplanetary case (realistic astrophysical test) - For the interplanetary column (N0 ≈ 5×10¹⁵ m⁻²), the spectrally-weighted results give tiny δ: • ≈ 1.5×10⁻⁶ for the 300 K-bath model would be wrong reading — actually for 300 K we got 1.47e-6, but note the Sun (5800K) gave 1.89e-4. - These are much smaller than the gravitational potentials we compare to (Earth ≈ 7×10⁻¹⁰, Sun photosphere ≈ 2×10⁻⁶), except the 5800K/ISPorigin number of 1.9×10⁻4 is still below solar photosphere potential but closer in scale. - Real interplanetary medium is dominated by free-electron (Thomson) behavior at some wavelengths, and narrow atomic lines are not dominant; realistic weighting drops σ_eff further. So the IPM effect is small. ====
# Lab case (300 K vs 4 K) - Spectrally-weighted σ_eff differs only slightly between 300 K and 4 K in this toy model (2.95e-22 vs 2.78e-22 m²). The absolute delta for a large assumed N0=1e23 is huge (tens to thousands), but that large N0 for lab is not physically the same as the astrophysical columns — it implicitly assumes the lab "sees" a huge effective interacting electron column. In a real vacuum cavity the effective interacting column is tiny (vacuum), and photons exchanged with the walls are governed by surface skin depths and cavity Q; the naive N0=1e23 is likely an overestimate for a true free-space lab clock. - Practically: the difference between 300 K and 4 K in σ_eff is small (≈6% in our toy), which leads to a tiny fractional change in δ for realistic N0. That means any QAT-predicted lab clock shift from changing the blackbody environment is likely extremely small — much smaller than current clock sensitivities unless you engineer a very large, resonant, and localized coupling.
# Photosphere / dense stellar layers - For extreme columns (1e28), the deltas become enormous in the toy — but this is not a trustworthy regime for the simple column model because radiative transfer, optical depth, and local thermalization dominate inside stellar photospheres. The simple δ≈σN0 product overcounts (photons don't freely stream through and interact linearly with every electron).