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

==== If we want Newtonian gravity (Poisson equation) to emerge from the same picture: ====
# Compute the full stress–energy tensor TμνT^{\mu\nu}Tμν of the combined system (bulk EM + boundary energetic contributions). The EM stress tensor is standard:

TEMμν=ε0(FμαFνα−14gμνF2).T^{\mu\nu}_{\rm EM} = \varepsilon_0\left(F^{\mu\alpha}F^{\nu}{}_{\alpha}-\tfrac14 g^{\mu\nu}F^2\right).TEMμν=ε0(FμαFνα−41gμνF2).
Boundary shells contribute localized energy density usurf(t,Ω)u_{\rm surf}(t,\Omega)usurf(t,Ω) (from absorbed photons and matter excitations) and momentum; when coarse-grained this contributes a mass–energy density ρ(x,t)=utot(x,t)/c2\rho(\mathbf{x},t)=u_{\rm tot}(\mathbf{x},t)/c^2ρ(x,t)=utot(x,t)/c2.
# In the weak-field (Newtonian) limit of GR, the metric potential Φ\PhiΦ satisfies Poisson:

∇2Φ=4πG ρ.\nabla^2\Phi = 4\pi G\,\rho .∇2Φ=4πGρ.
So if QAT computes ρ\rhoρ from the average energy density of photon-electron exchange and matter excitations, then the Newtonian potential follows unchanged. In earlier exploratory numerics we saw the same dimensional structure: event time scales τ and ħ lead to order-of-magnitude relations for G. QAT gives a mechanistic origin for the energy density that sources gravity — again, without changing the Poisson equation.

Important note: this route shows gravity emerges from bookkeeping of energy flows. To recover full Einstein GR, one would couple the full coarse-grained TμνT^{\mu\nu}Tμν into Einstein equations. The classical Einstein/Poisson equations stay the same — they are satisfied by the emergent coarse-grained source.