<b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable
<p dir="ltr">This paper demonstrates, with SI-calibrated data and closed-form equations, that frequency is a geometric variable: the spatial curvature of a local clock line f(x) obeys a compact closure that ties geometry and energy to a directly measured “clock-flow.” The central res...
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2025
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| _version_ | 1852016813749043200 |
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| author | Keaton Williams (22195216) |
| author_facet | Keaton Williams (22195216) |
| author_role | author |
| dc.creator.none.fl_str_mv | Keaton Williams (22195216) |
| dc.date.none.fl_str_mv | 2025-09-09T17:10:54Z |
| dc.identifier.none.fl_str_mv | 10.6084/m9.figshare.30087286.v1 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/dataset/_b_Frequency_Is_Geometry_b_One_Scale_Unifies_Light_Mass_Energy_Time_and_Information_-_Horizons_Become_Measurable/30087286 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Quantum computation Foundations of quantum mechanics Quantum optics and quantum optomechanics Quantum physics not elsewhere classified frequency–geometry unification spectral geometry Spectral Einstein–Keaton Equation (SEKE) log-frequency curvature curvature R energy density ρ nonlocal kernels fractional order s≈0.58 horizon thermometry KMS equality time–bandwidth invariant (CUI) temporal Gauss law (TGL) running coupling (tRG) information–curvature coupling topology (Euler characteristic, MDL) Trinity-Σ commuting RG nodal-measure scaling across dimensions metric-affine (Palatini, torsion) signatures holographic capacity per octave Wigner–Smith delay species universality chip-scale analog gravity geometry-from-spectra metrology |
| dc.title.none.fl_str_mv | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| dc.type.none.fl_str_mv | Dataset info:eu-repo/semantics/publishedVersion dataset |
| description | <p dir="ltr">This paper demonstrates, with SI-calibrated data and closed-form equations, that frequency is a geometric variable: the spatial curvature of a local clock line f(x) obeys a compact closure that ties geometry and energy to a directly measured “clock-flow.” The central result is<br>(ln f)'' = α_E R + κ ρ + c<br>with α_E ≈ −0.4796 (dimensionless), κ ≈ −8.72×10^7 m/J, c ≈ 3.87×10^5 m⁻², delivering R² ≈ 0.98596 for D(x) ≡ (ln f)'' and R² ≈ 0.99533 for reconstruction of ln f from R and ρ. A kernelized, scale-aware extension shows the closure commutes with coarse-graining and captures genuine nonlocal response via a fractional tail of order s ≈ 0.58, consistent with the dispersion<br>ω² = v²(x)k² + μ²(x) + Λ_s(x)|k|^{2s}.<br>Three time results make the framework immediately testable: a constant time–bandwidth product Δf·τ = 1/π, a temporal Gauss law ∫(ln Δf)''dx equals the boundary slope jump, and a frequency-running coupling across Δf bins. Cross-dimensional nodal-measure scaling (2D/3D/4D projections) corroborates linear geometry–spectrum growth. A gravity “port” connects the energy term to mass density and yields a chip-scale horizon thermometry gate: the kinematic temperature T_H = ħ|v'|/(2πk_B) matches the sideband temperature from S(−f)/S(f) = e^{−hf/(k_BT)} within experimental error (e.g., ≈0.176 K). Additional sections report holographic capacity per octave, metric-affine and torsion signatures, a one-parameter geometry–energy transport constant D* ≈ −2.28×10⁻⁵ J·m², and practical replication scales. The consequence is practical unification: spectra become meters of curvature, energy/mass, and time; horizons become measurable on a chip; and frequency provides a single operational scale linking light, mass–energy, geometry, and information.</p> |
| eu_rights_str_mv | openAccess |
| id | Manara_d2ef64c8ffe6dbc7a37f72df612c8705 |
| identifier_str_mv | 10.6084/m9.figshare.30087286.v1 |
| network_acronym_str | Manara |
| network_name_str | ManaraRepo |
| oai_identifier_str | oai:figshare.com:article/30087286 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become MeasurableKeaton Williams (22195216)Quantum computationFoundations of quantum mechanicsQuantum optics and quantum optomechanicsQuantum physics not elsewhere classifiedfrequency–geometry unificationspectral geometrySpectral Einstein–Keaton Equation (SEKE)log-frequency curvaturecurvature Renergy density ρnonlocal kernelsfractional order s≈0.58horizon thermometryKMS equalitytime–bandwidth invariant (CUI)temporal Gauss law (TGL)running coupling (tRG)information–curvature couplingtopology (Euler characteristic, MDL)Trinity-Σ commuting RGnodal-measure scaling across dimensionsmetric-affine (Palatini, torsion) signaturesholographic capacity per octaveWigner–Smith delayspecies universalitychip-scale analog gravitygeometry-from-spectra metrology<p dir="ltr">This paper demonstrates, with SI-calibrated data and closed-form equations, that frequency is a geometric variable: the spatial curvature of a local clock line f(x) obeys a compact closure that ties geometry and energy to a directly measured “clock-flow.” The central result is<br>(ln f)'' = α_E R + κ ρ + c<br>with α_E ≈ −0.4796 (dimensionless), κ ≈ −8.72×10^7 m/J, c ≈ 3.87×10^5 m⁻², delivering R² ≈ 0.98596 for D(x) ≡ (ln f)'' and R² ≈ 0.99533 for reconstruction of ln f from R and ρ. A kernelized, scale-aware extension shows the closure commutes with coarse-graining and captures genuine nonlocal response via a fractional tail of order s ≈ 0.58, consistent with the dispersion<br>ω² = v²(x)k² + μ²(x) + Λ_s(x)|k|^{2s}.<br>Three time results make the framework immediately testable: a constant time–bandwidth product Δf·τ = 1/π, a temporal Gauss law ∫(ln Δf)''dx equals the boundary slope jump, and a frequency-running coupling across Δf bins. Cross-dimensional nodal-measure scaling (2D/3D/4D projections) corroborates linear geometry–spectrum growth. A gravity “port” connects the energy term to mass density and yields a chip-scale horizon thermometry gate: the kinematic temperature T_H = ħ|v'|/(2πk_B) matches the sideband temperature from S(−f)/S(f) = e^{−hf/(k_BT)} within experimental error (e.g., ≈0.176 K). Additional sections report holographic capacity per octave, metric-affine and torsion signatures, a one-parameter geometry–energy transport constant D* ≈ −2.28×10⁻⁵ J·m², and practical replication scales. The consequence is practical unification: spectra become meters of curvature, energy/mass, and time; horizons become measurable on a chip; and frequency provides a single operational scale linking light, mass–energy, geometry, and information.</p>2025-09-09T17:10:54ZDatasetinfo:eu-repo/semantics/publishedVersiondataset10.6084/m9.figshare.30087286.v1https://figshare.com/articles/dataset/_b_Frequency_Is_Geometry_b_One_Scale_Unifies_Light_Mass_Energy_Time_and_Information_-_Horizons_Become_Measurable/30087286CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/300872862025-09-09T17:10:54Z |
| spellingShingle | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable Keaton Williams (22195216) Quantum computation Foundations of quantum mechanics Quantum optics and quantum optomechanics Quantum physics not elsewhere classified frequency–geometry unification spectral geometry Spectral Einstein–Keaton Equation (SEKE) log-frequency curvature curvature R energy density ρ nonlocal kernels fractional order s≈0.58 horizon thermometry KMS equality time–bandwidth invariant (CUI) temporal Gauss law (TGL) running coupling (tRG) information–curvature coupling topology (Euler characteristic, MDL) Trinity-Σ commuting RG nodal-measure scaling across dimensions metric-affine (Palatini, torsion) signatures holographic capacity per octave Wigner–Smith delay species universality chip-scale analog gravity geometry-from-spectra metrology |
| status_str | publishedVersion |
| title | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| title_full | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| title_fullStr | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| title_full_unstemmed | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| title_short | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| title_sort | <b>Frequency Is Geometry</b>: One Scale Unifies Light, Mass, Energy, Time, and Information - Horizons Become Measurable |
| topic | Quantum computation Foundations of quantum mechanics Quantum optics and quantum optomechanics Quantum physics not elsewhere classified frequency–geometry unification spectral geometry Spectral Einstein–Keaton Equation (SEKE) log-frequency curvature curvature R energy density ρ nonlocal kernels fractional order s≈0.58 horizon thermometry KMS equality time–bandwidth invariant (CUI) temporal Gauss law (TGL) running coupling (tRG) information–curvature coupling topology (Euler characteristic, MDL) Trinity-Σ commuting RG nodal-measure scaling across dimensions metric-affine (Palatini, torsion) signatures holographic capacity per octave Wigner–Smith delay species universality chip-scale analog gravity geometry-from-spectra metrology |