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

=== Assistant: Nice — I ran the concrete calculations you asked for and put the numbers into context. ===
Nice — I ran the concrete calculations you asked for and put the numbers into context. Below I show the assumptions, a compact table of results for a few realistic choices, what the numbers mean physically, and recommended next steps.

==== We used the QAT thin-shell formula you and I derived earlier: ====

G  ≈  4πc3 δ r0ℏ νG \;\approx\; \frac{4\pi c^{3}\,\delta\,r_0}{\hbar\,\nu}G≈ℏν4πc3δr0
where
* r0r_0r0 = shell radius (I used the Bohr radius a0=5.29177×10−11a_0 = 5.29177\times10^{-11}a0=5.29177×10−11 m as a representative electron shell),
* δ\deltaδ = shell thickness (several choices),
* ν\nuν = event rate (events/s) (several choices),
* ℏ=h/(2π)\hbar = h/(2\pi)ℏ=h/(2π) and ccc are standard constants.

Interpretation: each photon-electron event deposits energy E0∼ℏc/r0E_0\sim\hbar c/r_0E0∼ℏc/r0 at rate ν\nuν into a thin shell of thickness δ\deltaδ; matching the shell energy density to curvature leads to the formula above.

==== I evaluated GestG_{\rm est}Gest for combinations of ν\nuν and δ\deltaδ (with r0=a0r_0=a_0r0=a0). ====

Event-rate choices (ν):
* light-crossing frequency ν=c/(2πr0) \nu = c/(2\pi r_0)ν=c/(2πr0) (natural geometric choice);
* atomic slow ν=108 s−1 \nu = 10^{8}\,\mathrm{s^{-1}}ν=108s−1;
* atomic typical ν=1012 s−1 \nu = 10^{12}\,\mathrm{s^{-1}}ν=1012s−1;
* atomic fast ν=1015 s−1 \nu = 10^{15}\,\mathrm{s^{-1}}ν=1015s−1.

Shell thickness choices (δ):
* r0/100r_0/100r0/100 (thin fraction of Bohr radius),
* r0/106r_0/10^6r0/106 (very thin fraction),
* 10−1510^{-15}10−15 m (nuclear scale),
* classical electron radius re≈2.818×10−15r_e \approx 2.818\times10^{-15}re≈2.818×10−15 m.

===== (Each entry is the estimated G in m³·kg⁻¹·s⁻²) =====
* ν = light-crossing, δ = r₀/100 → Gest∼1.0×1020G_{\rm est} \sim 1.0\times10^{20}Gest∼1.0×1020
* ν = light-crossing, δ = 1e-15 m → Gest∼1.9×1017G_{\rm est} \sim 1.9\times10^{17}Gest∼1.9×1017
* ν = 1e12 s⁻¹, δ = r₀/1e6 → Gest∼9.0×1021G_{\rm est} \sim 9.0\times10^{21}Gest∼9.0×1021
* ν = 1e15 s⁻¹, δ = r₀/1e6 → Gest∼9.0×1018G_{\rm est} \sim 9.0\times10^{18}Gest∼9.0×1018

(For reference the measured value Gobs≈6.67×10−11G_{\rm obs} \approx 6.67\times10^{-11}Gobs≈6.67×10−11.)

So with the Bohr radius for r0r_0r0, the estimates are enormously larger than the observed GGG — by many tens of orders of magnitude.

==== I also solved for the required δ that makes the formula produce the observed GGG for each ν: ====

δreq  =  Gobs ℏ ν4πc3r0.\delta_{\rm req} \;=\; \frac{G_{\rm obs}\,\hbar\,\nu}{4\pi c^3 r_0}.δreq=4πc3r0Gobsℏν.
With r0=a0r_0=a_0r0=a0:
* ν = light-crossing → δ_req ≈ 3.5×10−433.5\times10^{-43}3.5×10−43 m
* ν = 1e8 → δ_req ≈ 3.9×10−533.9\times10^{-53}3.9×10−53 m
* ν = 1e12 → δ_req ≈ 3.9×10−493.9\times10^{-49}3.9×10−49 m
* ν = 1e15 → δ_req ≈ 3.9×10−463.9\times10^{-46}3.9×10−46 m

These required thicknesses are tiny — far smaller than the Planck length (ℓP≈1.62×10−35\ell_P\approx1.62\times10^{-35}ℓP≈1.62×10−35 m). Physically impossible in known physics. That means: for an atomic shell radius, you cannot get the right GGG with any plausible δ or ν that is not already Planckian or smaller.

==== Setting δ=ℓP\delta=\ell_Pδ=ℓP and solving for ν we find (with r0=a0r_0=a_0r0=a0): ====
* ν_required ≈ 4.1×10254.1\times10^{25}4.1×1025 s⁻¹.

That is astronomically large compared to atomic transition rates (but still far smaller than the Planck rate 1/tP∼10431/t_P\sim10^{43}1/tP∼1043 s⁻¹). So forcing δ = ℓP and keeping a Bohr-radius shell still requires an absurdly high event rate.

==== 1. Local atomic-scale shells don’t produce G. Using the Bohr radius for r0r_0r0, realistic δ and ν produce GestG_{\rm est}Gest many orders of magnitude too large. There is no straightforward way to get the observed GGG from single-atom surface deposition at atomic scales unless you introduce unphysical thicknesses far below Planck length or implausibly high event rates. ====
# Planck scale naturally appears. If the model is to produce the observed GGG without introducing new free numbers, either: - the characteristic length or thickness in the QAT mechanism must be Planckian, or - the QAT effect must aggregate across enormous numbers of atoms/volume in a cosmological way such that the collective energy density is tiny enough to give the observed curvature (the Dirac/Mach route).
# Using Planck time or Planck length directly is circular if your goal is to derive GGG, because ℓP and tP themselves depend on GGG. You can use them to check self-consistency, but you can't deduce GGG by assuming them.

==== You picked the “local first” option — here’s what I recommend next to keep things non-circular and informative: ====
# Try non-Planck microphysics: pick plausible non-Planck choices for ν and δ that come from QAT geometry (e.g., ν = c/(2πr0) or ν linked to photon flux from sunlight for a material, and δ chosen as a QAT fraction of r0 like r0/10⁶ or something derived from α or ϕ). We already did that — numbers were far off. That suggests local atomic events alone aren't enough.
# Aggregate to cosmic scale (Dirac/Mach route) (my strong suggestion now): compute the global QAT energy density by multiplying: - per-atom power (E₀×ν) × number density of atoms in the universe × fraction of matter in relevant states, - plus photon background contributions (CMB, starlight). Then insert that cosmic uQATu_{\rm QAT}uQAT into the Friedmann/Einstein relation and see whether a consistent GGG emerges or whether the result implies a time-varying GGG. This avoids Planck circularity and is physically motivated by your earlier Dirac/Mach thinking.
# Alternative: allow r0r_0r0 to be not atomic but a fundamental QAT radius derived from geometry (if QAT can produce a preferred microscopic length), and try the same computations — that is a tougher, deeper theoretical task.
# Compute observational signatures: independent of G, the shell model predicts multipole radiation patterns, mode frequencies ωℓ\omega_\ellωℓ, and coupling strengths. We can compute a predicted spectral shift or decay rate (dipole ℓ=1) and compare to atomic spectroscopy; that would be a direct, testable signature.

==== You said you’d go with my pick — I recommend moving to cosmological aggregation (Dirac/Mach style) as the next step. That’s the most promising non-circular route to connect QAT microphysics with the observed value (or scaling) of GGG. It also aligns with your earlier ideas about Mach’s principle and Dirac’s large numbers. ====

If you prefer, I can instead:
* (A) compute a more exhaustive table exploring other r0r_0r0 values (e.g., proton radius, nucleus radius) and show how the required δ/ν scale with r₀, or
* (B) begin the cosmological aggregation: estimate a global QAT energy density from per-atom event rates and number densities and compare to the critical density / curvature.

Which would you like me to do next?