Tensorial Reconstruction of Light-Speed Relativity An Epistemic Framework of Observer-Dependent Time and Signal Geometry
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2025
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| author | Yanagi, Takahiro |
| author_facet | Yanagi, Takahiro |
| contents | <p>This preprint serves as a supplemental study to the Tij theory series (DOI: 10.5281/zenodo.16929205), focusing on observer-dependent phase structures and frequency shifts in gravitational-wave ringdown signals.</p> <p>We present a tensorial reconstruction of light-speed relativity, in which the post-merger spacetime is modeled not as a stationary Kerr black hole, but as a dynamically folding information flow described by the tensor field T_ij. By projecting this tensor onto the observer's surface Sigma(U), we provide a natural explanation for chromatic effects and residual oscillations in ringdown waveforms. The analysis highlights a systematic deviation in delta-omega/omega ~ 0.3 in GW250114, reinterpreted as a geometric imprint rather than instrumental noise.</p> <p>This document supports an upcoming PRL submission and includes full derivations, figures, and methodological details that complement the core Tij framework. It features comparisons with GR-based predictions, a detailed analysis of L1 and H1 detectors, and implications for future interferometric observatories.</p> <p>For citation and reference purposes, this document should be treated as Version 4.0 (Supplemental) in the Tij theory publication sequence.<br><br><br></p> <h3>What's New in Version 4.2</h3> <ol> <li> <p><strong>Tensorial Definition Updated</strong><br> The definition of the epistemic tensor <span><span>TijT_{ij}</span><span><span><span><span>T</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span> has been clarified and reformulated to emphasize its divergence structure <span><span>∇kTik\nabla_k T^{ik}</span><span><span><span>∇<span><span><span><span><span><span>k</span></span></span><span></span></span></span></span></span><span><span>T</span><span><span><span><span><span><span><span>ik</span></span></span></span></span></span></span></span></span></span></span> and its role in encoding observer-dependent signal propagation.</p> </li> <li> <p><strong>Black Hole Ringdown Analysis (GW250114)</strong><br> We added a detailed comparison between GR predictions and actual ringdown data from GW250114, demonstrating a significant residual (~30%) unexplained by GR but accounted for by the tensorial projection model.<br> Notably, the asymmetric frequency deviations across detectors (L1: <span><span>cU>1c_U > 1</span><span><span><span><span>c</span><span><span><span><span><span><span>U</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>1</span></span></span></span>, H1: <span><span>cU<1c_U < 1</span><span><span><span><span>c</span><span><span><span><span><span><span>U</span></span></span><span></span></span></span></span></span><span><</span></span><span><span>1</span></span></span></span>) serve as direct evidence for the observer-conditioned geometry of <span><span>Σ(U)\Sigma(U)</span><span><span><span>Σ</span><span>(</span><span>U</span><span>)</span></span></span></span>.</p> </li> <li> <p><strong>Reorganization of Observational Sections</strong><br> The application domains have been reorganized for conceptual clarity. WISPIT 2b now functions as a reference geometry for tensorial curvature reconstruction, and the order of analysis has been adjusted to reflect the flow from foundational testing to broader validation.</p> </li> <li> <p><strong>Abstract and Introduction Enhanced</strong><br> Both abstract and introduction have been revised to clearly define the “gravitational prism” concept, and to position the tensorial framework as a unified explanation for chromatic anomalies in gravitational-wave and lensing observations.</p> </li> <li> <p><strong>Strengthened Theoretical–Phenomenological Link</strong><br> New intermediate derivations have been added to connect the general tensorial definition to specific observable forms such as<br> <span><span>Δθ(ν)∝ν−β\Delta \theta(\nu) \propto \nu^{-\beta}</span><span><span><span>Δ</span><span>θ</span><span>(</span><span>ν</span><span>)</span><span>∝</span></span><span><span><span>ν</span><span><span><span><span><span><span>−<span>β</span></span></span></span></span></span></span></span></span></span></span> and <span><span>Δω/ω\Delta \omega/\omega</span><span><span><span>Δ</span><span>ω</span><span>/</span><span>ω</span></span></span></span>. This enhances the logical flow from theory to empirical fitting.</p> </li> </ol> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17347505 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Tensorial Reconstruction of Light-Speed Relativity An Epistemic Framework of Observer-Dependent Time and Signal Geometry Yanagi, Takahiro Tij tensor observer-dependent time gravitational prism ringdown GW231123 GW250114 PKS 1830-211 WISPIT 2b Black holes Light-speed relativity Δω/ω, <p>This preprint serves as a supplemental study to the Tij theory series (DOI: 10.5281/zenodo.16929205), focusing on observer-dependent phase structures and frequency shifts in gravitational-wave ringdown signals.</p> <p>We present a tensorial reconstruction of light-speed relativity, in which the post-merger spacetime is modeled not as a stationary Kerr black hole, but as a dynamically folding information flow described by the tensor field T_ij. By projecting this tensor onto the observer's surface Sigma(U), we provide a natural explanation for chromatic effects and residual oscillations in ringdown waveforms. The analysis highlights a systematic deviation in delta-omega/omega ~ 0.3 in GW250114, reinterpreted as a geometric imprint rather than instrumental noise.</p> <p>This document supports an upcoming PRL submission and includes full derivations, figures, and methodological details that complement the core Tij framework. It features comparisons with GR-based predictions, a detailed analysis of L1 and H1 detectors, and implications for future interferometric observatories.</p> <p>For citation and reference purposes, this document should be treated as Version 4.0 (Supplemental) in the Tij theory publication sequence.<br><br><br></p> <h3>What's New in Version 4.2</h3> <ol> <li> <p><strong>Tensorial Definition Updated</strong><br> The definition of the epistemic tensor <span><span>TijT_{ij}</span><span><span><span><span>T</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span> has been clarified and reformulated to emphasize its divergence structure <span><span>∇kTik\nabla_k T^{ik}</span><span><span><span>∇<span><span><span><span><span><span>k</span></span></span><span></span></span></span></span></span><span><span>T</span><span><span><span><span><span><span><span>ik</span></span></span></span></span></span></span></span></span></span></span> and its role in encoding observer-dependent signal propagation.</p> </li> <li> <p><strong>Black Hole Ringdown Analysis (GW250114)</strong><br> We added a detailed comparison between GR predictions and actual ringdown data from GW250114, demonstrating a significant residual (~30%) unexplained by GR but accounted for by the tensorial projection model.<br> Notably, the asymmetric frequency deviations across detectors (L1: <span><span>cU>1c_U > 1</span><span><span><span><span>c</span><span><span><span><span><span><span>U</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>1</span></span></span></span>, H1: <span><span>cU<1c_U < 1</span><span><span><span><span>c</span><span><span><span><span><span><span>U</span></span></span><span></span></span></span></span></span><span><</span></span><span><span>1</span></span></span></span>) serve as direct evidence for the observer-conditioned geometry of <span><span>Σ(U)\Sigma(U)</span><span><span><span>Σ</span><span>(</span><span>U</span><span>)</span></span></span></span>.</p> </li> <li> <p><strong>Reorganization of Observational Sections</strong><br> The application domains have been reorganized for conceptual clarity. WISPIT 2b now functions as a reference geometry for tensorial curvature reconstruction, and the order of analysis has been adjusted to reflect the flow from foundational testing to broader validation.</p> </li> <li> <p><strong>Abstract and Introduction Enhanced</strong><br> Both abstract and introduction have been revised to clearly define the “gravitational prism” concept, and to position the tensorial framework as a unified explanation for chromatic anomalies in gravitational-wave and lensing observations.</p> </li> <li> <p><strong>Strengthened Theoretical–Phenomenological Link</strong><br> New intermediate derivations have been added to connect the general tensorial definition to specific observable forms such as<br> <span><span>Δθ(ν)∝ν−β\Delta \theta(\nu) \propto \nu^{-\beta}</span><span><span><span>Δ</span><span>θ</span><span>(</span><span>ν</span><span>)</span><span>∝</span></span><span><span><span>ν</span><span><span><span><span><span><span>−<span>β</span></span></span></span></span></span></span></span></span></span></span> and <span><span>Δω/ω\Delta \omega/\omega</span><span><span><span>Δ</span><span>ω</span><span>/</span><span>ω</span></span></span></span>. This enhances the logical flow from theory to empirical fitting.</p> </li> </ol> |
| title | Tensorial Reconstruction of Light-Speed Relativity An Epistemic Framework of Observer-Dependent Time and Signal Geometry |
| topic | Tij tensor observer-dependent time gravitational prism ringdown GW231123 GW250114 PKS 1830-211 WISPIT 2b Black holes Light-speed relativity Δω/ω, |
| url | https://doi.org/10.5281/zenodo.17347505 |