Microscopic Derivation

Deriving GG from Proton Structure and Helium-4 Binding

A first-principles derivation of Newton's gravitational constant from quantum mechanical and nuclear properties. The proton's Compton wavelength sets the geometric intake capacity A(t)A(t), and helium-4 binding sets the restoration efficiency R(t)R(t). Their product yields GG to 0.06% accuracy with zero free parameters.

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INPUT 1

mp=1.673×10−27m_p = 1.673 \times 10^{-27} kg

Proton mass (CODATA)

INPUT 2

α=1/137.036\alpha = 1/137.036

Fine-structure constant

INPUT 3

ΔmHe4=28.295\Delta m_{\text{He4}} = 28.295 MeV

He-4 mass deficit (nuclear data)

OUTPUT

G=6.670×10−11G = 6.670 \times 10^{-11}

0.06% from CODATA value

The Microscopic Derivation

The theory proposes that GG is not a fundamental constant but the product of two independently measurable quantities:

G=A(t)×R(t)G = A(t) \times R(t)

Where:

  • A(t)A(t) = geometric intake capacity — the effective area per unit mass-time through which spacetime flows toward matter, set by proton structure
  • R(t)R(t) = nuclear restoration efficiency — a dimensionless measure of how efficiently nuclear binding restores symmetry, set by helium-4

The physical picture: spacetime exhibits a flow toward mass-energy concentrations, analogous to a fluid flowing toward a drain. The strength of this flow — gravity — is determined by (1) the geometric "intake area" of fundamental particles, and (2) the efficiency of energy restoration during nuclear binding.

The proton, as the stable baryon, sets the geometric scale for gravitational interaction. Its Compton wavelength defines its quantum interaction scale:

λp=ℏmpc=1.321×10−15  m\lambda_p = \frac{\hbar}{m_p c} = 1.321 \times 10^{-15}\;\text{m}

The proton creates a 1-dimensional cylindrical channel through time — a "temporal valley" — through which spacetime flows. The raw geometric intake per unit mass is the Compton cross-section divided by the proton mass:

σpmp=λp2mp≈1.044×10−3  m2 kg−1\frac{\sigma_p}{m_p} = \frac{\lambda_p^2}{m_p} \approx 1.044 \times 10^{-3}\;\text{m}^2\,\text{kg}^{-1}

This is the starting point — but three suppression factors reduce this raw intake to the tiny value of A(t)A(t), explaining why gravity is 103810^{38} times weaker than the strong force.

The raw geometric intake λp2/mp\lambda_p^2/m_p is suppressed by three independent physical mechanisms, each with a clear quantum mechanical origin:

1. Retrocausal Damping: α2\alpha^2

Gravity emerges from a standing wave between past→future and future→past temporal directions. This bidirectional temporal coupling is governed by the electromagnetic fine-structure constant, entering twice (once for each direction):

Factor1=α2=(1137.036)2=5.325×10−5\text{Factor}_1 = \alpha^2 = \left(\frac{1}{137.036}\right)^2 = 5.325 \times 10^{-5}

This is the dominant suppression — it reduces the intake by nearly 5 orders of magnitude.

2. Cylindrical Geometry: 1/2π1/2\pi

The "temporal valley" through which spacetime flows is 1-dimensional (cylindrical), not 2-dimensional (spherical). The geometric factor for a cylindrical channel is:

Factor2=12π=0.1592\text{Factor}_2 = \frac{1}{2\pi} = 0.1592

Gravity starts as cylindrical (at the proton) and propagates spherically (at macroscopic distances), preserving the 1/r21/r^2 law.

3. Vacuum Polarization Screening: (1−α)(1 - \alpha)

Virtual e+e−e^+e^- pairs in the vacuum create impedance at the proton-vacuum interface, screening the proton's effective intake area:

Factor3=(1−α)=1−1137.036≈0.9927\text{Factor}_3 = (1 - \alpha) = 1 - \frac{1}{137.036} \approx 0.9927

This is a small correction (~0.7%) but it is a real physical effect from QED vacuum polarization.

Numerical Summary

All input values from CODATA 2018 and nuclear data tables. No fitted parameters.

ConstantValueUncertaintySource
mpm_p1.6726 × 10⁻²⁷ kg0.0003%CODATA 2018
λp\lambda_p1.321 × 10⁻¹⁵ m0.0003%ℏ/(mpc)\hbar/(m_p c)
α\alpha1/137.0360.000001%CODATA 2018
ΔmHe4\Delta m_{\text{He4}}28.295 MeV0.007%Nuclear data
mHe4m_{\text{He4}}3728.401 MeV0.001%Nuclear data
A(t)A(t)8.782 × 10⁻⁹0.07%This work
R(t)R(t)0.0075940.01%This work
GcalcG_{\text{calc}}6.670 × 10⁻¹¹0.08%This work
GCODATAG_{\text{CODATA}}6.674 × 10⁻¹¹0.0015%CODATA 2018
Agreement0.06%

References: [1] Mohr, Newell & Taylor (2016), CODATA recommended values, Rev. Mod. Phys. 88(3), 035009. [2] Tilley et al. (2004), Energy levels of light nuclei A=4, Nuclear Physics A, 745(3-4), 155-362.

Connection to the Mass Gap

This microscopic derivation of GG connects directly to the Yang-Mills mass gap mechanism. The same vacuum strain from the gluon condensate that generates the mass gap also determines the proton's internal structure — which sets A(t)A(t). The chain is:

Proton Structure

λp,α\lambda_p, \alpha → Compton scale

Geometric Intake

A(t)=8.78×10−9A(t) = 8.78 \times 10^{-9}

He-4 Restoration

R(t)=0.00759R(t) = 0.00759

Gravity

G=A×RG = A \times R

Status and Open Questions

Established

The numerical result G=6.670×10−11G = 6.670 \times 10^{-11} matches CODATA to 0.06%. All inputs are measured quantities (proton mass, α\alpha, He-4 binding energy). Zero free parameters.

Needs Formalization

The physical justification for the three suppression factors (α2\alpha^2, 1/2π1/2\pi, 1−α1-\alpha) — while physically motivated — needs rigorous derivation from a Lagrangian formulation. The retrocausal standing wave mechanism requires a formal quantum field theory treatment.

Testable

The smoking gun ΔG/G≈−3 Δα/α\Delta G/G \approx -3\,\Delta\alpha/\alpha is falsifiable with current technology. Proton structure effects on local GG and temporal asymmetry in gravity are testable within 10–15 years.

Explore Further

See how the mass gap and gravity emerge from the same vacuum strain mechanism, or explore the observational evidence supporting emergent gravity.

Mass Gap Derivation Observational Evidence Collaborate