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

=== Concrete calculation & test program (a path forward you can act on) ===

If you want QAT to become scientifically competitive, here is a concrete program (ranked, recommended order):

A. Formal derivations (math fieldwork)
# Derive effective TμνT_{\mu\nu}Tμν from a QAT boundary Lagrangian. - Start from a local action on the 2-D spherical boundary: Sboundary=∫∂Vd3x Lsurf(ϕ,Aμ,jμ,… )\mathcal{S}_{\rm boundary}=\int_{\partial V}d^3x\ \mathcal{L}_{\rm surf}(\phi, A_\mu, j^\mu,\dots)Sboundary=∫∂Vd3x Lsurf(ϕ,Aμ,jμ,…). - Vary the full 4-D action (EM + boundary term) and compute matching conditions (pillbox across shell) → obtain explicit surface energy, momentum, pressure terms. - Average over many atoms to produce ⟨Tμνeff⟩\langle T_{\mu\nu}^{\rm eff}\rangle⟨Tμνeff⟩. Compare magnitude to required ρc2\rho c^2ρc2 for halos. (This makes explicit the place where the Planck action h/2πh/2\pih/2π and the half-radius r/2r/2r/2 enters.)
# Sakharov check: compute one-loop effective action produced by boundary microphysics and check whether an induced Einstein–Hilbert term appears; estimate GeffG_{\rm eff}Geff as function of UV cutoff (or a QAT physical scale). This tells you whether emergent gravitational coupling can be produced without violating energy conservation.
# Composite spin-2 operator: build a candidate composite operator Oμν∼FμαFν α\mathcal{O}_{\mu\nu}\sim F_{\mu\alpha}F_{\nu}^{\ \alpha}Oμν∼FμαFν α or iterative photon/electron two-body kernels and test whether its long-wavelength propagator matches massless spin-2 behavior.

B. Order-of-magnitude checks (fast, falsifying)
# Compute ⟨uEM⟩\langle u_{\rm EM}\rangle⟨uEM⟩ in real galaxies and clusters (starlight, cosmic rays, magnetic fields, plasma)—compare to ρc2\rho c^2ρc2 derived from rotation curves/lensing. If EM energy is short by many orders (almost always true), then direct EM→GR via TμνT_{\mu\nu}Tμν is ruled out. (We already did this check above.)

C. Observational tests
# Bullet Cluster style test: simulate a merging cluster under your QAT effective source; does the lensing mass follow stars or plasma? If your model ties gravity to EM energy density, it will not match observations. (This is a high-impact falsifier.) ADS<ref>{{cite web|title=ADS|url=https://ui.adsabs.harvard.edu/abs/2006ApJ...648L.109C/abstract|publisher=ui.adsabs.harvard.edu|access-date=2025-12-16}}</ref>
# Precision lab tests: propose an atomic-clock or torsion-balance experiment: compare clock rates / inertial response near a very intense, variable EM energy density (high-power cavity, or near a plasma flux) vs control. Existing experiments already bound many couplings, but a purpose-designed test focusing on QAT predictions (frequency, polarization dependence) would help.

D. Numerical cosmology
# Include your effective QAT source term in an N-body + hydrodynamics code (or in a linear perturbation code) and check growth of structure and CMB predictions. This step tests cosmology constraints.