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

=== Assistant: Nice — two really good questions packed into one: A Can a dynamic spherical geometry produce the potential for life and… ===
Nice — two really good questions packed into one: (A) Can a dynamic spherical geometry produce the potential for life and ever-more-abstract mathematics? and (B) Can we find Newton’s gravitational constant GGG from geometry?

I’ll answer both carefully: honest, math-grounded, and with concrete next steps you can follow.

==== Short answer: Yes, plausibly — but it’s a scientific hypothesis that needs precise mechanisms and testable consequences. ====

Why it’s plausible (conceptual reasons):
# Self-organization from symmetry breaking. - A repeating process of spherical symmetry forming → breaking → re-forming (your photon ↔ electron exchanges on 4πr24\pi r^24πr2 shells) produces spatial/temporal patterning. Patterning + energy flow are the ingredients of self-organization in many systems (chemical reaction–diffusion, pattern formation, convection rolls, etc.). - Repeated patterning at many scales naturally creates hierarchical structure (cells → tissues → organisms).
# Energy gradients and irreversible processes. - Photon absorption/emission creates localized irreversible transfers of energy (increase of entropy overall, local ordering possible). Life needs energy flows and non-equilibrium steady states, both available in your picture.
# Fractals / scale-invariance → mathematics. - A geometric rule applied recursively (e.g., golden-ratio subdivisions from squared/spherical geometry) produces fractal and self-similar structures. Such structures make Fibonacci, logarithmic spirals and other “abstract math” appear naturally. Those mathematical patterns then become tools for describing emergent complexity.
# Information processing potential. - Repeated local interactions (photon-electron events) can implement state changes that, read out collectively, can store and process information — a precondition for life and cognition.

Cautions / what needs to be shown:
* Plausibility ≠ proof. To be persuasive scientifically you need: 1. A mechanism that relates your geometric dynamics to chemical/biochemical assembly (e.g., how shell interactions produce stable molecules or membranes). 2. Scale bridging: show how atomic-scale geometry robustly drives mesoscopic and macroscopic organization. 3. Testable predictions that differ from standard explanations (e.g., a measurable bias in chirality, a specific spectral signature of shells, or statistical differences in growth patterns).

Recommendation: turn this plausibility into a research program: (i) model a simple chemical system driven by spherical shell interactions, (ii) simulate pattern formation, (iii) look for signatures that could be measured.

==== Short answer: Not directly from geometry alone unless you also predict a physical mass or energy scale. But you can express GGG in terms of fundamental constants and a characteristic mass — and if QAT predicts that mass from geometry, then yes. ====

===== - GGG is a dimensional constant (units m3 kg−1 s−2\mathrm{m^3\,kg^{-1}\,s^{-2}}m3kg−1s−2). To get a number for GGG you need both a geometric relationship and a physical mass (or length/time) scale. Geometry alone (angles, ratios) gives dimensionless results; to get dimensions you must supply a scale (mass, length, time). =====
* Most successful “derivations” of dimensional constants use Planck units (combine c,ℏ,Gc,\hbar,Gc,ℏ,G to define a Planck mass/length/time) — but that treats GGG as fundamental, not derived.

===== If you take the Planck mass mPm_PmP as a defined scale, then =====

  G  =  ℏ cmP2  \boxed{ \; G \;=\; \dfrac{\hbar\, c}{m_P^2} \;}G=mP2ℏc
where ℏ=h2π\hbar=\dfrac{h}{2\pi}ℏ=2πh. This is exact (by definition of Planck mass).

We can show the arithmetic with up-to-date constants:
* ℏ=1.054571817×10−34 J⋅s\hbar = 1.054571817\times10^{-34}\ \mathrm{J\cdot s}ℏ=1.054571817×10−34 J⋅s
* c=299 792 458 m/sc = 299\,792\,458\ \mathrm{m/s}c=299792458 m/s
* mP≈2.176434×10−8 kgm_P \approx 2.176434\times10^{-8}\ \mathrm{kg}mP≈2.176434×10−8 kg (standard Planck mass)

Compute:

G  =  ℏcmP2G \;=\; \frac{\hbar c}{m_P^2}G=mP2ℏc
Numerical evaluation (careful arithmetic) gives:

G≈6.67430×10−11 m3 kg−1 s−2,G \approx 6.67430\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}},G≈6.67430×10−11 m3kg−1s−2,
which matches the measured value to the usual precision.

So if QAT can derive the Planck mass mPm_PmP (or some equivalent mass scale) from its geometry, then QAT would immediately give a value for GGG.

===== If you want GGG from QAT geometry, you must complete one of: =====

Strategy A — predict a fundamental mass from geometry.
* Find a QAT mechanism that produces a natural mass scale MQATM_{\rm QAT}MQAT in terms of h,c,e,αh, c, e, \alphah,c,e,α, and geometry constants (like golden ratio or a characteristic radius r0r_0r0).
* Then set G=ℏc/MQAT2G=\hbar c/M_{\rm QAT}^2G=ℏc/MQAT2. If MQATM_{\rm QAT}MQAT equals the Planck mass (or the theory provides a specific numeric ratio), you recover GGG.

Strategy B — relate GGG to cosmic/global quantities via Mach/Dirac ideas.
* Dirac’s Large Number Hypothesis/relations connect GGG with cosmological scales (age of universe ttt, total mass MUM_UMU, etc.), e.g. constraints like MU∼t2M_U \sim t^2MU∼t2 or G∝1/tG \propto 1/tG∝1/t. If QAT can predict the universe mass/age relation from geometry, you could express GGG in terms of geometry + cosmology. That’s more speculative and requires cosmological dynamics.

===== One way to try to derive GGG inside QAT: =====
# Define an elementary shell energy flux: compute the mean energy per shell event (photon absorbed/emitted) over the electron sphere. Express that in terms of ΔE=hf\Delta E = hfΔE=hf and relevant geometric factors 4πr24\pi r^24πr2.
# Compute an effective energy density ρQAT\rho_{\rm QAT}ρQAT by integrating over typical shell events per volume or per time (requires model of event rate).
# Match this effective energy density to the stress–energy tensor TμνT_{\mu\nu}Tμν term used in Einstein’s equations. In GR, curvature scale R∼κρR\sim \kappa \rhoR∼κρ with κ=8πG/c4\kappa = 8\pi G/c^4κ=8πG/c4. Solve for GGG in terms of ρQAT,ℏ,c\rho_{\rm QAT},\hbar,cρQAT,ℏ,c and geometry constants.
# If QAT supplies a unique ρQAT\rho_{\rm QAT}ρQAT from geometry (no free adjustable scale), that gives a numeric GGG. If not, you’ve reduced the problem to finding the correct QAT energy density.

This approach is essentially what you were already attempting with QAT-adjusted field equations — it just makes explicit the need for a physically computed energy density (or mass scale) to fix GGG.

==== 1. Concrete numerical check (done above): show that G=ℏc/mP2G=\hbar c/m_P^2G=ℏc/mP2 gives the observed value when mPm_PmP is the Planck mass. ✔︎ ====
# If you want me to attempt a QAT-style derivation of a mass scale from your geometry, I can try that next. But I’ll need to pick a specific physical ansatz (example options): - Option 1: Assume each photon-electron event deposits an average energy E0E_0E0 onto a shell of radius r0r_0r0; compute an effective energy density and match to curvature to solve for GGG. - Option 2: Follow a Dirac/Mach path: relate total energy in the universe (expressed via QAT photon budget) to the mass scale and derive G∝1/tG\propto 1/tG∝1/t. - Option 3: Try to express a Planck-like mass purely from geometric constants (α, ϕ, golden ratio, electron charge e, electron mass m_e) and see if a numerically close value emerges (this is often numerology — possible but risky).
# Recommend a cautious program: start with Option 1 (surface energy density → match to curvature) because it most directly follows your QAT picture and yields physical testable intermediate quantities (event energy, event rate, spectral signatures).

Would you like me to proceed with Option 1 and attempt a concrete QAT calculation of an effective energy density and the implied GGG? If so, tell me what QAT parameter you want to use or let me pick reasonable starting values (e.g., electron shell radius ~ Bohr radius, typical photon frequency ~ visible/UV, etc.), and I’ll do the step-by-step computation.