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

==== Below is a step‑by‑step practical program to formalize and test the ideas you described. I give the key equations and the specific calculation you can ask me to do next. ====

===== Write a bulk + boundary action (SI): =====

S=∫d4x[−14μ0FμνFμν+Lmatter]  +  ∫Σd3y −h Lbdy(ψ,A,h),S = \int d^4x\big[ -\tfrac{1}{4\mu_0}F_{\mu\nu}F^{\mu\nu} + \mathcal{L}_{\rm matter}\big]
\;+\; \int_{\Sigma} d^3y\,\sqrt{-h}\,\mathcal{L}_{\rm bdy}(\psi,A,h),S=∫d4x[−4μ01FμνFμν+Lmatter]+∫Σd3y−hLbdy(ψ,A,h),
with boundary coupling Lbdy\mathcal{L}_{\rm bdy}Lbdy containing AajaA_a j^aAaja. Variation gives:
* Maxwell with surface current ∇νFμν=μ0(Jbulkμ+jΣμδ(Σ))\nabla_\nu F^{\mu\nu}=\mu_0(J^\mu_{\rm bulk}+ j^\mu_\Sigma \delta(\Sigma))∇νFμν=μ0(Jbulkμ+jΣμδ(Σ)).
* Surface stress energy Sab=−2−hδSbdy/δhabS_{ab}=-\tfrac{2}{\sqrt{-h}}\delta S_{\rm bdy}/\delta h^{ab}Sab=−−h2δSbdy/δhab.

I can write this out in full and derive the boundary conditions (pillbox) for you.

===== Use electric dipole operator d=qr \mathbf d = q\mathbf rd=qr. The single‑photon absorption rate from level iii to fff: =====

Γi→f=2πℏ∣⟨f∣d⋅ϵ ∣i⟩∣2 ρ(ℏω).\Gamma_{i\to f}=\frac{2\pi}{\hbar} | \langle f |\mathbf d\cdot \mathbf\epsilon\, |i\rangle|^2 \, \rho(\hbar\omega).Γi→f=ℏ2π∣⟨f∣d⋅ϵ∣i⟩∣2ρ(ℏω).
Compute these for hydrogen (e.g., 1s→2p1s\to 2p1s→2p, Hα etc.). That gives ∆E & rates and connects to your idea of atomic-scale photon-by-photon unfolding.

I can compute the dipole matrix elements and rates for hydrogen lines (SI).

===== If an atom of mass MMM absorbs a photon of frequency fff, =====

vrecoil=pγM=hfcM.v_{\rm recoil} = \frac{p_\gamma}{M} = \frac{hf}{c M}.vrecoil=Mpγ=cMhf.
For hydrogen this recoil is tiny; for boundary shells it may be small but conceptually important (the boundary can take recoil and thus supports conservation).

I can evaluate recoil velocities for chosen transitions.

===== Model the atom‑plus‑shell as a system coupled to many degrees of freedom (photon bath, phonons). The off‑diagonal density matrix element ρij\rho_{ij}ρij decays approximately as ρij(t)∝e−Γdect \rho_{ij}(t)\propto e^{-\Gamma_{\rm dec}t}ρij(t)∝e−Γdect with =====

Γdec∼g2S(ω)\Gamma_{\rm dec}\sim g^2 S(\omega)Γdec∼g2S(ω)
where ggg is coupling, S(ω)S(\omega)S(ω) environmental spectral density. Stronger photon exchange → larger ggg or spectral intensity → faster decoherence. QAT’s “each photon → new now” is equivalent to short decoherence time per photon event.

I can set up a simple Lindblad model and compute decoherence times as function of photon flux and dipole coupling.

===== Compute the surface stress‑energy SabS_{ab}Sab (EM energy + tension) and plug into Israel junction conditions: =====

[Kab]−hab[K]=−8πGc4Sab.[K_{ab}]-h_{ab}[K] = -\frac{8\pi G}{c^4} S_{ab}.[Kab]−hab[K]=−c48πGSab.
Take weak‑field limit and extract the Newtonian potential produced by the surface energy density. This connects QAT’s boundary mass formation to curvature.

I can work a weak‑field example numerically (use the R=re/2R=r_e/2R=re/2 shell) and estimate the tiny GR effect.