Deriving the Gravitational Constant from Electromagnetic Coupling and Z₃ Wave Geometry
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2026
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| _version_ | 1866902314210557952 |
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| author | Miller, James |
| author_facet | Miller, James |
| contents | <p>The gravitational constant G is derived from the electromagnetic fine structure constant α, the proton mass, and the geometric structure of Z₃ strip topology. The formula G = √3 · α¹⁸ · ℏc/m²_p reproduces the measured value to 0.99% with zero adjustable parameters. The factor √3 is the amplitude amplification at a three-phase convergence point. The exponent 18 is derived from group theory: the gravitational interaction must be invariant under Z₃ × Z₃ × Z₂ — the full symmetry group of two three-mode convergences coupled through a chiral channel — whose order is 3 × 3 × 2 = 18. Each group element contributes one factor of α, yielding α¹⁸.</p> <p>Within the complete framework, α is not an independent input. It derives from the observer's angular position on the strip: α = 6sin²δ, where δ = 2° is the offset from the anti-gravity node (0.14% error). The formula for G is therefore fully geometric — G = √3 · (6sin²δ)¹⁸ · ℏc/m²_p — with one mass scale as the only external input. The hierarchy problem dissolves: the 10³⁶ ratio between electromagnetic and gravitational strength is α⁻¹⁷/√3, a geometric identity, not a fine-tuning puzzle.</p> <p>Verified against twelve independent gravitational measurements, all within 1.4%. The predicted G = 6.740 × 10⁻¹¹ matches Cavendish's 1798 value exactly. A complete mass chain follows: proton mass M_Pl · 3^(1/4) · α⁹ (0.5%), pion mass m_p × 4/27 (0.4%), proton radius 4ℏ/(m_p·c) (0.05%). The full 14-constant derivation chain is developed in the companion paper "From One Axiom to Fourteen Constants."</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19442661 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Deriving the Gravitational Constant from Electromagnetic Coupling and Z₃ Wave Geometry Miller, James gravitational constant fine structure constant hierarchy problem three-phase interference Z3 topology Planck mass envelope modulation Dimensional Oscillation Theory coupling constants gravitational coupling proton mass pion mass mass hierarchy group theory Dimensional Scaling Theorem observer position wave persistence helical wave unified field theory electromagnetic coupling <p>The gravitational constant G is derived from the electromagnetic fine structure constant α, the proton mass, and the geometric structure of Z₃ strip topology. The formula G = √3 · α¹⁸ · ℏc/m²_p reproduces the measured value to 0.99% with zero adjustable parameters. The factor √3 is the amplitude amplification at a three-phase convergence point. The exponent 18 is derived from group theory: the gravitational interaction must be invariant under Z₃ × Z₃ × Z₂ — the full symmetry group of two three-mode convergences coupled through a chiral channel — whose order is 3 × 3 × 2 = 18. Each group element contributes one factor of α, yielding α¹⁸.</p> <p>Within the complete framework, α is not an independent input. It derives from the observer's angular position on the strip: α = 6sin²δ, where δ = 2° is the offset from the anti-gravity node (0.14% error). The formula for G is therefore fully geometric — G = √3 · (6sin²δ)¹⁸ · ℏc/m²_p — with one mass scale as the only external input. The hierarchy problem dissolves: the 10³⁶ ratio between electromagnetic and gravitational strength is α⁻¹⁷/√3, a geometric identity, not a fine-tuning puzzle.</p> <p>Verified against twelve independent gravitational measurements, all within 1.4%. The predicted G = 6.740 × 10⁻¹¹ matches Cavendish's 1798 value exactly. A complete mass chain follows: proton mass M_Pl · 3^(1/4) · α⁹ (0.5%), pion mass m_p × 4/27 (0.4%), proton radius 4ℏ/(m_p·c) (0.05%). The full 14-constant derivation chain is developed in the companion paper "From One Axiom to Fourteen Constants."</p> |
| title | Deriving the Gravitational Constant from Electromagnetic Coupling and Z₃ Wave Geometry |
| topic | gravitational constant fine structure constant hierarchy problem three-phase interference Z3 topology Planck mass envelope modulation Dimensional Oscillation Theory coupling constants gravitational coupling proton mass pion mass mass hierarchy group theory Dimensional Scaling Theorem observer position wave persistence helical wave unified field theory electromagnetic coupling |
| url | https://doi.org/10.5281/zenodo.19442661 |