Unified Time Scale and Time Geometry:\\ Equivalence, Domains, and Solvable Models of Spectral--Scattering--Causal--Entropy
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2025
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| _version_ | 1866901304000905216 |
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| author | Ma, Haobo Zhang, Wenlin |
| author_facet | Ma, Haobo Zhang, Wenlin |
| contents | We propose and rigorously characterize a ``unified time scale'' framework, aligning phase gradient readings, relative state density, and trace of Wigner--Smith group delay within strict scattering theory domain, thus defining time scale as monotonic reparametrization of a class of spectral--scattering invariants. The identity $ \ \frac{\varphi'(\omega){\pi}=\rho_{rel}(\omega)=1{2\pi}TrQ(\omega)\ },\qquad Q(\omega)=-\,i\,S(\omega)^\dagger\partial_\omega S(\omega),\quad \varphi=1{2}\arg\det S holds within energy windows satisfying elastic--unitary scattering and Birman--Kreĭn assumptions; for absorptive/non-unitary and long-range potential cases, we propose verifiable generalizations: introducing complex time delay, dwell time, and phase renormalization, using Poisson--convolution to give existence and affine uniqueness of windowed clocks. Paper further constructs model-based proof of eikonal phase derivative = geometric Shapiro delay in general relativity end (Schwarzschild exterior scalar wave, high-frequency/high-angular-momentum limit), expresses redshift as phase rhythm ratio in cosmological end, and states ``entropy extremality \to$ geometric equations'' as conditional proposition in information--holography end with relative entropy monotonicity and QNEC as core assumptions. Entire text emphasizes domain of equivalence relations and solvable examples, giving engineering-realizable multi-frequency group delay metrology and lensing delay inversion schemes. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17691848 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unified Time Scale and Time Geometry:\\ Equivalence, Domains, and Solvable Models of Spectral--Scattering--Causal--Entropy Ma, Haobo Zhang, Wenlin Unified Time Scale Generalized Entropy Quantum Scattering General Relativity Boundary Time Geometry Causal Structure Information Theory Wigner-Smith Time Delay Modular Flow QNEC Spectral Shift Function Time Geometry We propose and rigorously characterize a ``unified time scale'' framework, aligning phase gradient readings, relative state density, and trace of Wigner--Smith group delay within strict scattering theory domain, thus defining time scale as monotonic reparametrization of a class of spectral--scattering invariants. The identity $ \ \frac{\varphi'(\omega){\pi}=\rho_{rel}(\omega)=1{2\pi}TrQ(\omega)\ },\qquad Q(\omega)=-\,i\,S(\omega)^\dagger\partial_\omega S(\omega),\quad \varphi=1{2}\arg\det S holds within energy windows satisfying elastic--unitary scattering and Birman--Kreĭn assumptions; for absorptive/non-unitary and long-range potential cases, we propose verifiable generalizations: introducing complex time delay, dwell time, and phase renormalization, using Poisson--convolution to give existence and affine uniqueness of windowed clocks. Paper further constructs model-based proof of eikonal phase derivative = geometric Shapiro delay in general relativity end (Schwarzschild exterior scalar wave, high-frequency/high-angular-momentum limit), expresses redshift as phase rhythm ratio in cosmological end, and states ``entropy extremality \to$ geometric equations'' as conditional proposition in information--holography end with relative entropy monotonicity and QNEC as core assumptions. Entire text emphasizes domain of equivalence relations and solvable examples, giving engineering-realizable multi-frequency group delay metrology and lensing delay inversion schemes. |
| title | Unified Time Scale and Time Geometry:\\ Equivalence, Domains, and Solvable Models of Spectral--Scattering--Causal--Entropy |
| topic | Unified Time Scale Generalized Entropy Quantum Scattering General Relativity Boundary Time Geometry Causal Structure Information Theory Wigner-Smith Time Delay Modular Flow QNEC Spectral Shift Function Time Geometry |
| url | https://doi.org/10.5281/zenodo.17691848 |