Self-Consistent Quantization, the Three-Dimensional Kepler Law, and Standing-Wave Quark Positions from the Clausius-Mossotti Metric
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901750705815552 |
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| author | Singh, Mandeep |
| author_facet | Singh, Mandeep |
| contents | <p>We study the Klein-Gordon wave equation in the Clausius-Mossotti (CM) metric in two settings. Part I (Exterior): The KG equation coupled to the CM field equation converges self-consistently at all seven coupling strengths tested, with back-reaction modifying binding energies by 7–20%. The proper volume (W^{-1/3}) produces 2.2–2.8× more equal probability shells than coordinate volume — a 3D Kepler law. Part II (Interior): Solving KG inside a finite sphere with hard wall at the proton surface, standing-wave nodes appear at volume fractions f = 1/3 (0.2% deviation) and f = 2/3 (0.4% deviation), matching d-quark and u-quark positions from the Damru geometry (Singh 2026d), outperforming JLAB pressure measurement (3.9%). Zero free parameters throughout. Paper 2026s in the Speed Gap Framework series (papers 2026a–r published).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19598344 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Self-Consistent Quantization, the Three-Dimensional Kepler Law, and Standing-Wave Quark Positions from the Clausius-Mossotti Metric Singh, Mandeep Clausius-Mossotti metric KleinKlein-Gordon equation self-consistent quantization 3D kepler law quark positions standing waves proton structure modified gravity zero free parameters speed gap framework <p>We study the Klein-Gordon wave equation in the Clausius-Mossotti (CM) metric in two settings. Part I (Exterior): The KG equation coupled to the CM field equation converges self-consistently at all seven coupling strengths tested, with back-reaction modifying binding energies by 7–20%. The proper volume (W^{-1/3}) produces 2.2–2.8× more equal probability shells than coordinate volume — a 3D Kepler law. Part II (Interior): Solving KG inside a finite sphere with hard wall at the proton surface, standing-wave nodes appear at volume fractions f = 1/3 (0.2% deviation) and f = 2/3 (0.4% deviation), matching d-quark and u-quark positions from the Damru geometry (Singh 2026d), outperforming JLAB pressure measurement (3.9%). Zero free parameters throughout. Paper 2026s in the Speed Gap Framework series (papers 2026a–r published).</p> |
| title | Self-Consistent Quantization, the Three-Dimensional Kepler Law, and Standing-Wave Quark Positions from the Clausius-Mossotti Metric |
| topic | Clausius-Mossotti metric KleinKlein-Gordon equation self-consistent quantization 3D kepler law quark positions standing waves proton structure modified gravity zero free parameters speed gap framework |
| url | https://doi.org/10.5281/zenodo.19598344 |