Zapisane w:
| 1. autor: | |
|---|---|
| Format: | Recurso digital |
| Język: | |
| Wydane: |
Zenodo
2026
|
| Hasła przedmiotowe: | |
| Dostęp online: | https://doi.org/10.5281/zenodo.20115134 |
| Etykiety: |
Dodaj etykietę
Nie ma etykietki, Dołącz pierwszą etykiete!
|
| _version_ | 1866901517632536576 |
|---|---|
| author | Ghidan, Florin |
| author_facet | Ghidan, Florin |
| contents | <p>We present a geometric extension of the Ghidan throughput framework in which the Bloch sphere is supplemented by an embedded informational cube. The outer Bloch sphere preserves continuous normalized state geometry, while the inner cube introduces discrete directional informational channels and projection structure. The cube is identified as a Planck-scale informational substrate composed of elementary cubes of edge length ℓ_P, the Planck length.</p> <p> </p> <p>This construction resolves the central open question of the earlier scalar framework: the geometric origin of the radial metric component g_rr = 1/χ². In the proposed model, temporal suppression arises from Bloch normalization (yielding g_tt = −χ²), while radial suppression emerges from cube-diagonal projection compression (yielding g_rr = 1/χ²). The resolution is complete: because χ is defined as the fraction of full capacity available, a radial interval dr in coordinate space corresponds to a proper interval dr/χ, since routing that covers dr at full capacity covers only χ·dr_proper when operating at reduced throughput χ. This gives g_rr = 1/χ² directly and without additional postulates.</p> <p> </p> <p>Rotational cube dynamics, governed by an SO(3) rotation operator acting on the directional load vector, naturally generate Kerr-like azimuthal shear and the weak-field frame-dragging cross term g_tφ ≈ −2GJ sin²θ/(c²r). The rotational capacity length a = J/(Mc) follows from the dimensional requirement that all load terms in χ² + L = 1 must be dimensionless, establishing it as a necessary consequence of the conservation law rather than a free parameter.</p> <p> </p> <p>The framework reproduces: Schwarzschild time dilation, the full radial metric structure, Mercury perihelion precession (42.98 arcsec/century), Shapiro-delay structure, and weak-field Kerr/Lense–Thirring rotational effects. The construction suggests that observable spacetime geometry may emerge from lower-dimensional projections of discrete Planck-scale informational routing rather than from continuous manifold curvature alone.</p> <p>The Ghidan throughput framework is built on a single scalar conservation law:</p> <p>χ² + L = 1</p> <p>where χ ∈ [0, 1] is the local informational throughput fraction and L ∈ [0, 1] is the committed load fraction. This law expresses a finite-capacity constraint: local physical capacity is exactly partitioned between free propagation (χ²) and committed load (L). The framework has been shown to reproduce a broad range of gravitational phenomena from this single primitive, including:</p> <p>• Schwarzschild time dilation and the full exterior line element</p> <p>• de Sitter and Reissner–Nordström geometry</p> <p>• Mercury perihelion precession (42.98 arcsec/century)</p> <p>• Shapiro delay structure</p> <p>• Weak-field gravitational effects and Newtonian limit</p> <p>• Bekenstein–Hawking entropy with the 1/4 factor derived geometrically</p> <p>• Flat galactic rotation curves and the MOND acceleration scale</p> <p>Keywords: Ghidan framework, Bloch sphere, informational cube, Planck scale, χ² + L = 1, Schwarzschild metric, Kerr metric, g_rr, frame dragging, emergent gravity, informational substrate, projection compression</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20115134 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Ghidan Cube Inside the Bloch Sphere A Discrete Informational Geometry for Emergent Gravity, Radial Compression, and Kerr-Like Rotational Structure Ghidan, Florin Physics Physics Mathematical physics Physics/methods Physics/standards Quantum physics Solar physics Theoretical physics Quantum computers Quantum Theory <p>We present a geometric extension of the Ghidan throughput framework in which the Bloch sphere is supplemented by an embedded informational cube. The outer Bloch sphere preserves continuous normalized state geometry, while the inner cube introduces discrete directional informational channels and projection structure. The cube is identified as a Planck-scale informational substrate composed of elementary cubes of edge length ℓ_P, the Planck length.</p> <p> </p> <p>This construction resolves the central open question of the earlier scalar framework: the geometric origin of the radial metric component g_rr = 1/χ². In the proposed model, temporal suppression arises from Bloch normalization (yielding g_tt = −χ²), while radial suppression emerges from cube-diagonal projection compression (yielding g_rr = 1/χ²). The resolution is complete: because χ is defined as the fraction of full capacity available, a radial interval dr in coordinate space corresponds to a proper interval dr/χ, since routing that covers dr at full capacity covers only χ·dr_proper when operating at reduced throughput χ. This gives g_rr = 1/χ² directly and without additional postulates.</p> <p> </p> <p>Rotational cube dynamics, governed by an SO(3) rotation operator acting on the directional load vector, naturally generate Kerr-like azimuthal shear and the weak-field frame-dragging cross term g_tφ ≈ −2GJ sin²θ/(c²r). The rotational capacity length a = J/(Mc) follows from the dimensional requirement that all load terms in χ² + L = 1 must be dimensionless, establishing it as a necessary consequence of the conservation law rather than a free parameter.</p> <p> </p> <p>The framework reproduces: Schwarzschild time dilation, the full radial metric structure, Mercury perihelion precession (42.98 arcsec/century), Shapiro-delay structure, and weak-field Kerr/Lense–Thirring rotational effects. The construction suggests that observable spacetime geometry may emerge from lower-dimensional projections of discrete Planck-scale informational routing rather than from continuous manifold curvature alone.</p> <p>The Ghidan throughput framework is built on a single scalar conservation law:</p> <p>χ² + L = 1</p> <p>where χ ∈ [0, 1] is the local informational throughput fraction and L ∈ [0, 1] is the committed load fraction. This law expresses a finite-capacity constraint: local physical capacity is exactly partitioned between free propagation (χ²) and committed load (L). The framework has been shown to reproduce a broad range of gravitational phenomena from this single primitive, including:</p> <p>• Schwarzschild time dilation and the full exterior line element</p> <p>• de Sitter and Reissner–Nordström geometry</p> <p>• Mercury perihelion precession (42.98 arcsec/century)</p> <p>• Shapiro delay structure</p> <p>• Weak-field gravitational effects and Newtonian limit</p> <p>• Bekenstein–Hawking entropy with the 1/4 factor derived geometrically</p> <p>• Flat galactic rotation curves and the MOND acceleration scale</p> <p>Keywords: Ghidan framework, Bloch sphere, informational cube, Planck scale, χ² + L = 1, Schwarzschild metric, Kerr metric, g_rr, frame dragging, emergent gravity, informational substrate, projection compression</p> |
| title | The Ghidan Cube Inside the Bloch Sphere A Discrete Informational Geometry for Emergent Gravity, Radial Compression, and Kerr-Like Rotational Structure |
| topic | Physics Physics Mathematical physics Physics/methods Physics/standards Quantum physics Solar physics Theoretical physics Quantum computers Quantum Theory |
| url | https://doi.org/10.5281/zenodo.20115134 |