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

==== It’s often handier to express things with the saturation parameter ====

s≡IIsat, Isat=πhc Γ3 λ3 s \equiv \frac{I}{I_{\rm sat}},\qquad
\boxed{\ I_{\rm sat} = \frac{\pi h c\,\Gamma}{3\,\lambda^3}\ }s≡IsatI, Isat=3λ3πhcΓ 
(for a closed cycling dipole transition; other transitions differ by order-1 factors).

Define the elastic scattering rate (events per atom per second; absorption + re-emission) as

 Rsc(I,Δ)=Γ2 s1+s+(2Δ/Γ)2 .\boxed{\ R_{\rm sc}(I,\Delta)
= \frac{\Gamma}{2}\,
\frac{s}{1+s+(2\Delta/\Gamma)^2}\ }. Rsc(I,Δ)=2Γ1+s+(2Δ/Γ)2s .
Then a robust, experiment-ready decoherence rate is

 Γ2(I,Δ)≃Γ2  +  Rsc(I,Δ)  +  γenv .\boxed{\ \Gamma_2(I,\Delta)
\simeq \frac{\Gamma}{2} \;+\; R_{\rm sc}(I,\Delta) \;+\; \gamma_{\rm env}\ }. Γ2(I,Δ)≃2Γ+Rsc(I,Δ)+γenv .
* Γ/2\Gamma/2Γ/2 is the irreducible quantum limit from spontaneous emission (geometry of dipole radiation over 4π4\pi4π).
* RscR_{\rm sc}Rsc is how fast the light field “touches” the system (absorption + elastic scattering), i.e. QAT’s photon-event cadence.
* γenv\gamma_{\rm env}γenv accounts for other dephasing (collisions, thermal phonons, technical noise).

This already encodes your idea: no macroscopic change without photon exchange → increase III or resonant overlap (small ∣Δ∣|\Delta|∣Δ∣) and the “unfolding” accelerates (larger Γ2\Gamma_2Γ2); turn the light down or detune (or cool to reduce background photons) and the world “slows” (smaller Γ2\Gamma_2Γ2). In the T→0T\to0T→0 (dark) limit, I→0I\to0I→0, stimulated terms vanish, matching your Third-Law/“field lines lock” picture.