Vibrational Wave Dispersion Hypothesis (HDOV): unified framework, master equation, and multidomain applications
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2025
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| _version_ | 1866901540725325824 |
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| author | Fernandez, Arnoldo |
| author_facet | Fernandez, Arnoldo |
| contents | <p>This work presents a unified manuscript of the HDOV (Vibrational Wave Dispersion Hypothesis) formalism, which proposes an effective master equation for wave propagation in environments with limited functional accessibility. Starting from a covariant action in which the kinetic term of a scalar field <span><span>Ψ\Psi</span><span><span><span>Ψ</span></span></span></span> is modulated by an environmental gate <span><span>(1+2g χ(I) ηp)(1 + 2g\,\chi(I)\,\eta_p)</span><span><span><span>(</span><span>1</span><span>+</span></span><span><span>2</span><span>g</span><span>χ</span><span>(</span><span>I</span><span>)</span><span><span>η</span><span><span><span><span><span><span>p</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, we derive a projective wave equation that, in the high-frequency and flat-space limit, reduces to a modified Helmholtz equation with an effective complex refractive index.</p> <p>In the eikonal regime we obtain a WKB-type transport law for the amplitude, factorizing into a purely relativistic focusing term and an additional exponential factor associated with vibrational accessibility. On this basis we construct an operational dictionary that allows the same formal scheme to be applied to very different domains: time-resolved X-ray scattering (TRXS) in molecular systems, regime transitions at the heliopause (Voyager missions), variations in the length of day (LOD) and Chandler wobble in geodynamics, and effective cosmological expansion (Pantheon+ and BAO data).</p> <p>The article synthesizes results previously published in separate preprints and shows that the same mathematical structure—effective action with environmental gate, projective master equation, and WKB transport law—consistently describes phenomena across scales ranging from femtoseconds to billions of years. The HDOV framework is explicitly presented as an exploratory proposal, accompanied by data and reproducibility scripts, open to observational testing and independent criticism.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17707613 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Vibrational Wave Dispersion Hypothesis (HDOV): unified framework, master equation, and multidomain applications Fernandez, Arnoldo HDOV, vibrational wave dispersion hypothesis, functional accessibility, modified Helmholtz equation, WKB transport, time-resolved X-ray scattering (TRXS), heliopause, Voyager 1, Voyager 2, geodynamics, Chandler wobble, length of day (LOD), effective dark energy, observational cosmology, gravitational waves, effective action, multidomain framework <p>This work presents a unified manuscript of the HDOV (Vibrational Wave Dispersion Hypothesis) formalism, which proposes an effective master equation for wave propagation in environments with limited functional accessibility. Starting from a covariant action in which the kinetic term of a scalar field <span><span>Ψ\Psi</span><span><span><span>Ψ</span></span></span></span> is modulated by an environmental gate <span><span>(1+2g χ(I) ηp)(1 + 2g\,\chi(I)\,\eta_p)</span><span><span><span>(</span><span>1</span><span>+</span></span><span><span>2</span><span>g</span><span>χ</span><span>(</span><span>I</span><span>)</span><span><span>η</span><span><span><span><span><span><span>p</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, we derive a projective wave equation that, in the high-frequency and flat-space limit, reduces to a modified Helmholtz equation with an effective complex refractive index.</p> <p>In the eikonal regime we obtain a WKB-type transport law for the amplitude, factorizing into a purely relativistic focusing term and an additional exponential factor associated with vibrational accessibility. On this basis we construct an operational dictionary that allows the same formal scheme to be applied to very different domains: time-resolved X-ray scattering (TRXS) in molecular systems, regime transitions at the heliopause (Voyager missions), variations in the length of day (LOD) and Chandler wobble in geodynamics, and effective cosmological expansion (Pantheon+ and BAO data).</p> <p>The article synthesizes results previously published in separate preprints and shows that the same mathematical structure—effective action with environmental gate, projective master equation, and WKB transport law—consistently describes phenomena across scales ranging from femtoseconds to billions of years. The HDOV framework is explicitly presented as an exploratory proposal, accompanied by data and reproducibility scripts, open to observational testing and independent criticism.</p> |
| title | Vibrational Wave Dispersion Hypothesis (HDOV): unified framework, master equation, and multidomain applications |
| topic | HDOV, vibrational wave dispersion hypothesis, functional accessibility, modified Helmholtz equation, WKB transport, time-resolved X-ray scattering (TRXS), heliopause, Voyager 1, Voyager 2, geodynamics, Chandler wobble, length of day (LOD), effective dark energy, observational cosmology, gravitational waves, effective action, multidomain framework |
| url | https://doi.org/10.5281/zenodo.17707613 |