G_PT/α_EM

G_PT/α_EM: normalised holonomic relation

In PT, the derived gravitational statement is not a direct SI value for Newton's constant. It concerns the dimensionless holonomic coupling of the sieve geometry:

$$ \frac{G_{\rm PT}}{\alpha_{\rm EM}} = 2\pi(1+\delta_{\rm holo}). $$

With the R39 correction:

$$ \delta_{\rm holo}=2.407268\times10^{-4},\qquad \frac{G_{\rm PT}}{\alpha_{\rm EM}}=6.284697838. $$

Using $\alpha_{\rm EM}=1/137.035999083$, this gives:

$$ G_{\rm PT}=0.0458616559. $$

What this relation does not say

$G_{\rm PT}$ must not be confused with the electron gravitational coupling:

$$ \alpha_G(e)=\frac{G_N m_e^2}{\hbar c}\approx1.75\times10^{-45}. $$

Conversion to the SI Newton constant requires an independent energy scale $E_0$ such that:

$$ G_{\rm PT}=\frac{G_N E_0^2}{\hbar c^5}. $$

Using the measured $G_N$, this scale is Planckian, $E_0\approx2.6\times10^{18}$ GeV. Deriving it autonomously remains an open calibration problem.

Status

Classed [SC] for internal self-consistency of the holonomic ratio. It is not a measurement of $G_N$ and not yet an independent SI prediction for Newton's constant.