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

=== QAT postulate: a “tick” is one quantum of action hhh transferred across the atomic boundary (photon → electron). The tick rate Γ\GammaΓ is proportional to the available power crossing the shell divided by hhh: Γ∝P/h\Gamma \propto P/hΓ∝P/h. In a static gravitational potential Φ\PhiΦ, GR gives g00≈1+2Φ/c2g_{00}\approx 1+2\Phi/c^2g00≈1+2Φ/c2, so all local frequencies redshift as g00\sqrt{g_{00}}g00: ===

f  ∝  Γ  ∝  g00⇒Δff  =  Δ ⁣(g00)  ≈  ΔΦc2(weak field).f \;\propto\; \Gamma \;\propto\; \sqrt{g_{00}}\quad\Rightarrow\quad
\frac{\Delta f}{f} \;=\; \Delta\!\left(\sqrt{g_{00}}\right)\;\approx\;\frac{\Delta\Phi}{c^2}\quad(\text{weak field}).f∝Γ∝g00⇒fΔf=Δ(g00)≈c2ΔΦ(weak field).
Check vs classic experiments:
* Pound–Rebka (14.4 keV Mössbauer γ\gammaγ-ray, Δh≃22.6\Delta h\simeq22.6Δh≃22.6 m): Δff≈g Δhc2≈9.81×22.6(3.00×108)2≈2.46×10−15,\displaystyle \frac{\Delta f}{f}\approx \frac{g\,\Delta h}{c^2} \approx \frac{9.81\times 22.6}{(3.00\times10^8)^2} \approx 2.46\times10^{-15},fΔf≈c2gΔh≈(3.00×108)29.81×22.6≈2.46×10−15, matching observations. In QAT, this is exactly the same factor because each tick is an hhh-sized action and the available photon energy per tick redshifts by g00\sqrt{g_{00}}g00.
* Modern optical clocks (height change Δh∼0.33\Delta h\sim0.33Δh∼0.33 m): Δff≈g Δhc2≈9.81×0.33(3.00×108)2≈3.6×10−17,\displaystyle \frac{\Delta f}{f}\approx \frac{g\,\Delta h}{c^2} \approx \frac{9.81\times0.33}{(3.00\times10^8)^2} \approx 3.6\times10^{-17},fΔf≈c2gΔh≈(3.00×108)29.81×0.33≈3.6×10−17, which is the observed scale in state-of-the-art comparisons. Again, QAT gives the same first-order law.

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==== 1. Numerical GGG: Use the formula GQAT∼c3κind ℏ L∗2nbdy\displaystyle G_{\rm QAT}\sim\frac{c^3}{\kappa_{\rm ind}\,\hbar}\,\frac{L_''^{2}}{n_{\rm bdy}}GQAT∼κindℏc3nbdyL∗2 to test realistic L∗L_''L∗ and nbdyn_{\rm bdy}nbdy (atoms, solids, plasmas). If we can land near measured GGG without tuning, that’s big. ====
# Universality checks: Show that the induced coupling is to total TμνT_{\mu\nu}Tμν (not just EM), ensuring the equivalence principle and the GR light-bending factor of 2.
# Spin-2 structure: From the boundary path integral, make the symmetric rank-2 propagator explicit (massless, transverse, traceless in the linear limit).

If you want, I can turn (1) into a tiny worksheet (symbolic → plug numbers) or fold this into your canvas doc as a one-page annex.