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

=== Define the huge dimensionless ratio ===

D  ≡  e24πε0 G mpme  ∼  1039.\mathcal{D}\;\equiv\;\frac{e^2}{4\pi\varepsilon_0\,G\,m_p m_e}\;\sim\;10^{39}.D≡4πε0Gmpmee2∼1039.
If gravity in QAT is an induced response of boundary modes, then the coupling GGG could be suppressed by the enormous number of EM degrees of freedom in the universe (a Mach-like “cosmic participation”). A toy scaling that matches the spirit:
'' Suppose GQAT−1∼NmodesL∗2G_{\text{QAT}}^{-1}\sim \frac{N_{\text{modes}}}{L_''^{2}}GQAT−1∼L∗2Nmodes, with NmodesN_{\text{modes}}Nmodes the effective count of boundary EM modes up to a cosmic infrared/ultraviolet cutoff (set by cosmic size and micro thickness).
'' Then D∼α ℏcmpme 1G∼α ℏcmpme NmodesL∗2\mathcal{D}\sim \frac{\alpha\,\hbar c}{m_p m_e}\,\frac{1}{G} \sim \frac{\alpha\,\hbar c}{m_p m_e}\,\frac{N_{\text{modes}}}{L_''^{2}}D∼mpmeαℏcG1∼mpmeαℏcL∗2Nmodes.
'' If NmodesN_{\text{modes}}Nmodes scales like a surface (∝ RU2R_{\text{U}}^2RU2)—your “universe as a sphere of probability”—then D\mathcal{D}D inherits a cosmic factor. Roughly, D∝(RU/L∗)2\mathcal{D}\propto (R_{\text{U}}/L_'')^2D∝(RU/L∗)2.

Why this is only suggestive (not a proof):
* We must derive (not assume) the precise counting, cutoffs, and how universality (equivalence principle) is preserved.
* Observations tightly bound G˙/G\dot{G}/GG˙/G. If GGG tracks cosmic size, it must do so in a way consistent with these bounds (or be effectively constant after some epoch).

Still, conceptually this cleanly expresses your intuition: gravity’s smallness is a global dilution (a universal recoil of the whole field of boundary modes), while EM is local and strong.