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

=== Assistant: Excellent — I ran a short, transparent numerical survey so we can see the scale of the QAT correction ===
Excellent — I ran a short, transparent numerical survey so we can see the scale of the QAT correction
δR/R≃σeff N0\delta R/R \simeq \sigma_{\rm eff}\,N_{0}δR/R≃σeffN0 for a variety of plausible effective cross-sections and electron/interaction column densities N0N_{0}N0.
Below I explain the assumptions, give the numeric table (compact), then interpret the physically realistic cases and recommend next steps.

==== We are using the simple, conservative estimate ====

δRR  ≈  σeff N0,\frac{\delta R}{R}\;\approx\;\sigma_{\rm eff}\,N_0,RδR≈σeffN0,
where
* σeff\sigma_{\rm eff}σeff is an effective, frequency-averaged coupling cross section that encodes how strongly exterior electrons (or bound electrons, lines, plasma) decohere / phase-lag / absorb/scatter the ambient photons that contribute to the local event rate; and
* N0=∫r∞ne(r′) dr′N_0=\int_r^\infty n_e(r')\,dr'N0=∫r∞ne(r′)dr′ is an effective column (m−2^{-2}−2) of interacting electrons (or electron-equivalent scatterers) outside the radius rrr.

This is intentionally simple — it makes the physics transparent and lets us see what regimes could possibly give a non-negligible δR/R\delta R/RδR/R.

==== I computed δ=σeffN0\delta=\sigma_{\rm eff}N_0δ=σeffN0 for three sample cross sections and five sample column densities. (These are representative / order-of-magnitude inputs so you can see scaling — I show later which are realistic.) ====

Cross-sections used
* Thomson: σT=6.65×10−29 m2\sigma_T = 6.65\times10^{-29}\,\mathrm{m}^2σT=6.65×10−29m2  (conservative floor for scattering off free electrons)
* Small resonance: σ=10−22 m2\sigma = 10^{-22}\,\mathrm{m}^2σ=10−22m2 (typical of modest atomic/molecular resonant cross sections)
* Large line: σ=10−18 m2\sigma = 10^{-18}\,\mathrm{m}^2σ=10−18m2 (strong resonant / line cross section; upper bound for a single narrow line at peak)

Columns N0N_0N0 used
* Interplanetary: 5×1015 m−25\times10^{15}\,\mathrm m^{-2}5×1015m−2  (very low)
* Diffuse ISM: 1×1020 m−21\times10^{20}\,\mathrm m^{-2}1×1020m−2
* Atmosphere-effective: 1×1023 m−21\times10^{23}\,\mathrm m^{-2}1×1023m−2 (order of magnitude guess for an effective interacting column — see below)
* Dense material surface: 1×1025 m−21\times10^{25}\,\mathrm m^{-2}1×1025m−2 (surface/solid interacting layer)
* Photosphere-like: 1×1028 m−21\times10^{28}\,\mathrm m^{-2}1×1028m−2 (very large column that illustrates dense stellar layers)

Numeric results (delta = σ·N₀)

|     |     |     |     |     |     |
| --- | --- | --- | --- | --- | --- |
|     |     |     |     |     |     |
|     |     |     |     |     |     |
|     |     |     |     |     |     |

(I printed the full table numerically in the run so you can check exact entries.)

==== 1. Thomson + interplanetary / ISM - Thomson × interplanetary (5×10¹⁵) → δ∼3×10−13\delta\sim 3\times10^{-13}δ∼3×10−13: tiny. - Thomson × diffuse ISM (1×10²⁰) → δ∼7×10−9\delta\sim 7\times10^{-9}δ∼7×10−9: still tiny. Interpretation: free-electron Thomson scattering in low-density plasmas cannot produce anything near gravitational redshift magnitudes. ====
# Thomson + atmosphere-effective (1×10²³) - Gives δ∼6.7×10−6\delta\sim 6.7\times10^{-6}δ∼6.7×10−6 (notice this is comparable to solar photospheric GR potential ~2×10⁻⁶ but many orders larger than Earth's surface GR 6.95×10⁻¹⁰). But this is misleading: Thomson applies to free electrons (plasma). The neutral atmospheric molecules (N₂, O₂) at optical frequencies do not behave like free electrons and have much smaller scattering/absorption cross sections averaged over a broadband spectrum. So using σ_T here is not physically correct; the effective σ for neutral air averaged over the ambient spectrum is far, far smaller. Therefore the Thomson+atmosphere number is not a realistic prediction.
# Resonance / large line cross-sections - These can produce large deltas against sufficiently large columns — but they are narrow-band, and the huge numbers in the table come from assuming the entire ambient photon bath sits at that resonant frequency. Real spectra do not concentrate all photon power exactly at a narrow resonance. When you weight by the real radiation field and by the line's profile (and remember Kramers-Kronig relations), typical broadband effective σ averaged over the photon field is much smaller than the line peak. - In other words: strong lines can locally dominate the coupling for those exact frequencies, but the integrated effect on the full event rate (which sums over all frequencies) is usually small unless you are in a highly line-dominated plasma tuned to that transition.
# Photosphere-like columns (1×10²⁸) - Multiplying even Thomson by such a massive column gives δ ~ 0.67 — i.e. huge effect — but this scenario implicitly counts every electron in a dense stellar layer as an independent free scatterer affecting the external event rate all the way to infinity. In practice, stellar photospheres are opaque and the simple integrated-column model breaks down: many photons are thermalized locally and radiative transfer/opacity effects must be treated with full radiative-transfer physics. So the raw large number is not a realistic indicator that Thomson scattering "explains" gravity — it's just the product of extreme column × cross section.

==== - Realistic, broadband, environment-averaged values of σeff\sigma_{\rm eff}σeff and the actual interacting column N0N_{0}N0 lead to δR/R\delta R/RδR/R that is many orders of magnitude smaller than standard GR gravitational potentials in normal astrophysical / laboratory settings. - Example: the interplanetary/ISM cases give δ≲10−9\delta\lesssim 10^{-9}δ≲10−9 down to 10−1310^{-13}10−13 for Thomson-like coupling: tiny. ====
'' That means the QAT EM-exchange contribution is ''plausibly* a small perturbation layered on top of standard GR, consistent with what we found earlier: the structure (1/r behavior) can arise from cumulative, weak EM phase-lag effects, but the magnitude is typically small.

==== 1. Make the model frequency-dependent and use real spectra. - Replace the crude single σ with a spectrally weighted effective cross section σˉeff=∫Φ(ω) σeff(ω) dω∫Φ(ω) dω,\bar\sigma_{\rm eff}=\frac{\int \Phi(\omega)\,\sigma_{\rm eff}(\omega)\,d\omega}{\int \Phi(\omega)\,d\omega},σˉeff=∫Φ(ω)dω∫Φ(ω)σeff(ω)dω, where Φ(ω)\Phi(\omega)Φ(ω) is the local photon spectral radiance (room blackbody, solar Planck 5800 K, or measured cavity spectrum). This will avoid overcounting narrow line peaks. - Use real cross-section models: Lorentz oscillator for bound electrons, photoionization cross sections, measured molecular scattering/absorption data. ====
# Compute realistic N0N_0N0 for each scenario using radiative-transfer thinking. - For atmospheric / solid surfaces, the effective interacting column for the ambient photons is set by optical depths at the frequencies that matter — that is, the thickness of the layer that actually exchanges photons with the local site (not the full integrated geometric column of every electron). - For plasma cases (e.g., corona, H II regions), use measured electron columns.
# Produce a small number table of realistic cases (I can do this for you): - (a) optical clock in a standard room (300 K blackbody + interior lighting) vs. deep cryogenic cavity (4 K) — predict Δτ/τ difference from QAT layer. - (b) atom in interplanetary / solar wind environment (use real IPM n_e & solar spectrum). - (c) high-EM-activity plasma (e.g., H II region with strong lines) to see whether narrow, line-driven plasmas ever produce measurable δ.
# Design an experimental target: - The lab experiment that stands a chance is not to reproduce GR, but to detect a tiny, controllable change in a clock tick rate as the local photon environment is changed. For example: vary the spectral occupation (introduce a narrow line laser field or block broadband blackbody radiation) around an optical clock and look for an ultra-tiny systematic shift correlated with the controlled photon bath. QAT predicts a specific sign and scaling (δR/R∝\delta R/R \proptoδR/R∝ controlled change in photon occupation × coupling).

==== A. Run realistic case (lab cavity): pick a 300 K blackbody + typical lab lighting spectrum vs. a 4 K cryogenic cavity spectrum; use a Lorentz oscillator model for a simple atomic boundary cross section and compute δR/R\delta R/RδR/R numerically. This yields a direct lab-prediction (likely tiny, but quantitatively useful). ====

B. Run realistic astrophysical case (solar photosphere / IPM): use Planck 5800 K spectrum for incoming photons and IPM electron columns; weight with a frequency-dependent σ(ω) model and return δ.

C. Both A and B (takes a bit longer but I can do both sequentially in this reply).

Pick A, B, or C and I’ll compute the spectral integrals and show clean numeric results with all assumptions written out.