Dual Tetrad Gravity And The Field Origin
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866902323834388480 |
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| author | Nelson, Stephen |
| author_facet | Nelson, Stephen |
| contents | The companion paper derived the gravitational constant G from spacetime topology with 0.12% accuracy and zero free parameters. This paper asks what else the same geometric structure determines. The (3+1)^2 dual tetrad topology, two tetrahedra with opposite orientations coupled at a shared Field Origin, produces four quantitative results. (1) G from the coupling hierarchy alpha^{1+(3+1)+(3+1)^2}, where changing the exponent by +/-1 shifts the prediction by a factor of 137. (2) The force hierarchy: gravity couples through 21 levels, electromagnetism through 1, giving alpha^{20} ~ 10^{-43}. (3) The dark matter correction factor mu(x) = x/(1+x), derived from detailed balance in field closure, with characteristic acceleration a_0 = k^2 G m_e / r_e^2 (where k = 4 is the tetrahedral coupling number, m_e the electron mass, and r_e the classical electron radius) matching observation to 0.41%. This modifies gravity from 1/r^2 to 1/r at galactic scales, explaining flat rotation curves without invisible mass. (4) The electron mass, from three overdetermined equations spanning gravity, cosmology, and electromagnetism, yielding m_e to 0.1% with no free parameters. The topology also provides geometric interpretations of known physics: the inverse square law from three-dimensional field spreading, E = mc^2 from two closure speeds in the bimetric structure, spin hbar/2 from the stellated octahedron's face ratio (2 of 8 faces point toward the coupling center), the uncertainty principle from the same face ratio, energy quantization from Field Origin boundary conditions, and 1/alpha = 137 as the ratio of field closure rate to Compton frequency. The only external input is the Hubble constant H, a cosmological observable. The cosmological constant, strong force, and weak force are not addressed. The framework connects to established bimetric gravity through the Hassan-Rosen action in vielbein form, with the topology constraining the interaction parameters. Physical law is not arbitrary; behind the equations lies structure. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18505974 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dual Tetrad Gravity And The Field Origin Nelson, Stephen General Relativity G Tetrad Gravity Unified Theory Spacetime Topology Gravitational Constant Dark Matter Hierarchy Problem Inverse Square Law The companion paper derived the gravitational constant G from spacetime topology with 0.12% accuracy and zero free parameters. This paper asks what else the same geometric structure determines. The (3+1)^2 dual tetrad topology, two tetrahedra with opposite orientations coupled at a shared Field Origin, produces four quantitative results. (1) G from the coupling hierarchy alpha^{1+(3+1)+(3+1)^2}, where changing the exponent by +/-1 shifts the prediction by a factor of 137. (2) The force hierarchy: gravity couples through 21 levels, electromagnetism through 1, giving alpha^{20} ~ 10^{-43}. (3) The dark matter correction factor mu(x) = x/(1+x), derived from detailed balance in field closure, with characteristic acceleration a_0 = k^2 G m_e / r_e^2 (where k = 4 is the tetrahedral coupling number, m_e the electron mass, and r_e the classical electron radius) matching observation to 0.41%. This modifies gravity from 1/r^2 to 1/r at galactic scales, explaining flat rotation curves without invisible mass. (4) The electron mass, from three overdetermined equations spanning gravity, cosmology, and electromagnetism, yielding m_e to 0.1% with no free parameters. The topology also provides geometric interpretations of known physics: the inverse square law from three-dimensional field spreading, E = mc^2 from two closure speeds in the bimetric structure, spin hbar/2 from the stellated octahedron's face ratio (2 of 8 faces point toward the coupling center), the uncertainty principle from the same face ratio, energy quantization from Field Origin boundary conditions, and 1/alpha = 137 as the ratio of field closure rate to Compton frequency. The only external input is the Hubble constant H, a cosmological observable. The cosmological constant, strong force, and weak force are not addressed. The framework connects to established bimetric gravity through the Hassan-Rosen action in vielbein form, with the topology constraining the interaction parameters. Physical law is not arbitrary; behind the equations lies structure. |
| title | Dual Tetrad Gravity And The Field Origin |
| topic | General Relativity G Tetrad Gravity Unified Theory Spacetime Topology Gravitational Constant Dark Matter Hierarchy Problem Inverse Square Law |
| url | https://doi.org/10.5281/zenodo.18505974 |