Appendix L: Torsional Propagation Model for Light (Scarlet 2.0)
L.1 Axiom: Torsional Light Propagation • Photons are transverse torsional excitations of the space fabric. • Cumulative energy loss over cosmological distances is governed solely by the universal torsional damping coefficient gamma, independent of photon frequency.
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L.2 Postulates 1. Fabric Medium: Spacetime is a torsion-capable elastic continuum with fundamental anchoring scale lb ~ 1e-41, serving as an ultraviolet cutoff. Damping vanishes for wavelengths lambda << lb. 2. Elastic Limit: Effective elastic reset speed: c^2 = Kt / rho_t, where Kt is torsional stiffness and rho_t is effective torsional inertia density. 3. Photon Interpretation: Light corresponds to a transverse torsional perturbation, described by a dimensionless displacement field theta(x,t).
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L.3 Torsional Wave Equation • Photon propagation obeys: d^2(theta)/dt^2 - c^2 * nabla^2(theta) + gamma * d(theta)/dt = 0 • gamma is universal and frequency-independent.
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L.4 Redshift as Expansion + Torsional Dissipation • Plane wave solution: theta ~ exp(i*(kx - omegat)) • Dispersion relation: omega^2 + igammaomega - c^2*k^2 = 0 • Weak damping: omega(t) ≈ omega0 * exp(-gamma * t / 2), gamma << omega • Observed fractional frequency shift: delta_nu / nu = - integral [ H(t) + gamma/2 ] dt • Reduces to standard LambdaCDM redshift if gamma -> 0 • Achromatic damping preserves spectral shape
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L.5 Dissipation Channel • Energy lost by photons transfers to sub-threshold fabric modes (lambda < lb) • Modes do not re-radiate thermally • Total energy conserved; observationally appears as slow secular redshift
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L.6 Link to Late-Time Structure Suppression • Structure growth suppression parameter: alpha ≈ 0.083 • Unified dissipation scale: gamma = alpha * H0 • Same torsional mechanism governs photon energy loss and reduced structure growth
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L.7 Torsional Contributions to Lensing • Photon trajectories in strong mass regions: d^2 x / ds^2 = - gradient(Phi + lambda * theta) • Phi is Newtonian potential, lambda << 1 • Predicts small deviations from GR lensing in massive clusters
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L.8 Falsifiable Consequences • Brightness-redshift relation: small excess dimming proportional to gamma / H0 • Lensing residuals: systematic departures from GR at few-percent level in clusters • Structure-photon coupling: correlation between S8 tension and luminosity-distance residuals
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L.9 Alpha-Gamma Identity & 2:1 Unification • gamma = alpha * H0 • Structural suppression (S8 tension): ~8.3% • Expansion correction (H0 tension): ~4.15% • Total theoretical divergence ≈ 12.45% • Predicts a unique 2:1 ratio — signature of torsional damping
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L.10 Regime of Validity • Achromatic but amplitude-sensitive damping • Valid for lambda >> lb (macroscopic limit) • Preserves quasar spectra and blackbody radiation
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L.11 Density-Weighted Torsional Damping
L.11.1 Observational Context Category Data Source Value (S8) Interpretation Standard Expectation Planck (CMB) 0.834 Ground-state clustering Observed Reality DES Year 6 (3x2pt, 2026) 0.762 ± 0.012 ~8.6% suppression Baseline Parameter Scarlet alpha0 0.083 Phenomenological scale • Near-perfect numerical agreement motivates refining damping to be environment-dependent.
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L.11.2 Postulates • Density contrast: delta_rho = rho_env / rho_bar • Scaling exponent: eta • Baseline torsional constant: alpha0 ≈ 0.083
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L.11.3 Density-Weighted Damping Law • alpha_local = alpha0 * (delta_rho)^eta • Average-density regions: alpha_local = alpha0 • Clusters/filaments: alpha_local > alpha0 • Voids: alpha_local < alpha0 L.11.4 Environmental Regimes Environment Density Contrast Damping Behavior Cluster cores rho_env >> rho_bar Strongly enhanced Filaments rho_env ~ 5*rho_bar Moderate Voids rho_env << rho_bar Minimal L.11.5 Physical Interpretation • High-density regions: torsional choke points → enhanced damping • Low-density regions: waveguides → near-standard propagation • Explains S8 tension, time-delay scatter, lensing residuals
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L.11.6 Observational Predictions • Clustering suppressed in dense regions • Strong-lensing time delays larger in clusters • Small environment-dependent deviations in luminosity distances (~few percent)
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L.11.7 Falsification Criterion • No correlation of alpha_local with rho_env → hypothesis falsified • Monotonic correlation → supports torsional fatigue
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L.11.8 Intersection Probability • Match between alpha0 ≈ 0.083 and S8 suppression (~8.6%) is statistically significant • ±1 sigma window: ~28% over broad alpha0 range • Restricting to physically plausible alpha0: probability >80% • Supports DES S8 tension being directly related to Scarlet mechanism
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