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

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# Fix QAT micro-parameters you want to test: choose a plausible r₀ (perhaps Bohr radius for atomic processes, maybe a different QAT radius), a thin-shell thickness fraction δ\deltaδ (e.g., r0/10nr_0/10^nr0/10n or physically-motivated fraction from geometry), and a non-Planck event rate ν\nuν (options: c/(2πr0), typical transition rates 10810^8108–101210^{12}1012 s⁻¹, or a parameter to be constrained).
# Compute per-atom power Patom=E0νP_{\rm atom}=E_0\nuPatom=E0ν, power density P=natomPatom\mathcal{P}=n_{\rm atom}P_{\rm atom}P=natomPatom using cosmic number density natomn_{\rm atom}natom, and steady-state energy density u=Pτu=\mathcal{P}\tauu=Pτ for plausible ranges of τ\tauτ (energy storage/dissipation times).
# Compute the implied contribution to cosmological mass-energy ρQAT=u/c2\rho_{\rm QAT}=u/c^2ρQAT=u/c2 and compare to measured baryon & radiation densities.

===== 1. Use aggregated uQAT(t)u_{\rm QAT}(t)uQAT(t) to compute implied cosmological expansion via Friedmann: =====

H2(t)=8πG3(ρmatter+ρQAT(t)+ρrad+⋯ ).H^2(t)=\frac{8\pi G}{3}\left(\rho_{\rm matter}+\rho_{\rm QAT}(t) + \rho_{\rm rad} + \cdots\right).H2(t)=38πG(ρmatter+ρQAT(t)+ρrad+⋯).
If you treat GGG as unknown but assume H(t) observed, invert to find G(t)G(t)G(t) implied by your QAT contribution. Alternatively, assume constant G and see what QAT predicts for H(t).
# Explore scaling laws: assume QAT micro-parameters scale with a(t) (e.g., E0∝1/aE_0 \propto 1/aE0∝1/a because photon energies redshift) and compute whether this produces relations like Dirac’s G∝1/tG\propto 1/tG∝1/t or MU∝t2M_U\propto t^2MU∝t2.

===== 1. Compute observable signatures: (a) tiny time variation in G or α, (b) spectral shifts or line widths in atoms (if shell quantization differs from standard QM), (c) polarization patterns or multipole anisotropies from shell radiation in plasma, (d) differences in stellar structure if QAT modifies energy exchange rates in plasma. =====
# Compare with observational constraints: limits on G˙/G\dot{G}/GG˙/G, limits on α variation, measured CMB, LSS data.