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

=== QAT postulate: A “tick” is an action quantum hhh transferred across the boundary. Tick rate Γ∼P/h\Gamma \sim P/hΓ∼P/h, where PPP is local power crossing the shell (photon → electron). ===

Let P∝u c AeffP \propto u\, c\, A_{\text{eff}}P∝ucAeff, with uuu the local EM energy density available to couple (including the atom’s own vacuum/stimulated field near resonance). In a static gravitational potential Φ\PhiΦ, GR says the local time dilation is

dτdt  =  g00  ≈  1+Φc2.\frac{d\tau}{dt} \;=\; \sqrt{g_{00}} \;\approx\; 1+\frac{\Phi}{c^2}.dtdτ=g00≈1+c2Φ.
QAT link: Energies of all quanta redshift by g00\sqrt{g_{00}}g00, and so do local frequencies. If each tick consumes a fixed action hhh and incoming quanta are redshifted by g00\sqrt{g_{00}}g00, then the available rate of action transfer scales the same way:

Γ  ∝  g00.\Gamma \;\propto\; \sqrt{g_{00}}.Γ∝g00.
Therefore the clock frequency f∝Γf \propto \Gammaf∝Γ obeys

Δff  =  Δ ⁣(g00)  ≈  ΔΦc2(weak field),\frac{\Delta f}{f} \;=\; \Delta\!\left(\sqrt{g_{00}}\right)
\;\approx\; \frac{\Delta \Phi}{c^2} \quad (\text{weak field}),fΔf=Δ(g00)≈c2ΔΦ(weak field),
exactly the first-order gravitational redshift/time-dilation of GR.

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