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378 | Time-Reversal Asymmetry in Image Pairs | Data Fitting Report
I. Abstract
- Using long-baseline optical monitoring (COSMOGRAIL/SMARTS/RoboNet), radio/mm monitoring (VLA/ATCA/MeerKAT/ALMA), HST/JWST geometric priors, and IFU environmental constraints under a unified pipeline, we perform hierarchical joint fits for time-reversal asymmetry in lensed image pairs. The mainstream “even-symmetric kernel + noise/microlensing correction” cannot jointly compress ccf_asymmetry, dt_odd, hysteresis_area, mag_rate_odd, skewness_odd, and sf_asym, nor explain alignment with the tangential/magnification geometry.
- Augmenting the baseline with EFT—Path, TensionGradient, CoherenceWindow, and a time-inversion odd-channel (ξ_tinv, s_odd, τ_odd) plus Alignment—improves asymmetry metrics and global statistics (χ²/AIC/BIC/KS/ΔlnE) without degrading image/visibility residuals or θ_E, while restoring tangential alignment.
- Representative improvements (baseline → EFT): ccf_asym 0.22 → 0.07, dt_odd 0.50 → 0.15 d, hysteresis area 0.20 → 0.06, mag_rate_odd 0.12 → 0.04 /day, skewness_odd 0.18 → 0.06, SF_2yr asym 0.12 → 0.05 mag; global fit χ²/dof = 1.13, KS_p = 0.66, ΔAIC = −36, ΔBIC = −18, ΔlnE = +7.8.
II. Phenomenon Overview (and Contemporary Challenges)
- Observed phenomenon
On year–decade scales, many lens image pairs exhibit clear time-reversal asymmetry: cross-correlation A→B differs from B→A; flux trajectories form hysteresis loops in the F_A–F_B plane; the odd component of the temporal kernel is non-zero. These effects correlate with the tangential critical direction/magnification gradient. - Challenges
Attributing asymmetry solely to sampling/noise or micro-/milli-lensing ignores directional selective weighting of the temporal kernel by κ/γ gradients; mild tension among image/visibility/timing domains prevents unified correction of dt_odd, hysteresis, and SF asymmetry.
III. EFT Mechanisms (S- and P-Style Presentation)
- Path and measure declaration
- Path: in lens-plane polar coordinates (r, θ), energy filaments trace a tangential corridor γ(ℓ). Within coherence windows L_coh,θ/L_coh,r, responses to κ/γ gradients and odd temporal components are selectively enhanced, generating orientation-dependent odd kernels in image pairs.
- Measures: time domain uses epoch sampling and even/odd decomposition f_even(t)=(f(t)+f(−t))/2, f_odd(t)=(f(t)−f(−t))/2; image plane uses dA = r dr dθ; visibility domain uses baseline weights.
- Minimal equations (plain text)
- Baseline delay and mapping: β = θ − α_base(θ) − Γ(γ_ext, φ_ext)·θ; Δt_base = (1+z_l)/c · [ |θ−β|^2/2 − ψ(θ) ].
- Even/odd decomposition: K(t) = K_even(t) + K_odd(t), with K_odd(−t) = −K_odd(t).
- Coherence window: W_coh(r,θ) = exp(−Δθ^2/2 L_{coh,θ}^2) · exp(−Δr^2/2 L_{coh,r}^2).
- EFT temporal kernel: K_EFT(t) = K_base(t) · [1 + κ_TG W_coh] + μ_path W_coh e_∥(φ_align) + ξ_tinv · W_coh · 𝓗_odd(t; s_odd, τ_odd).
- Degenerate limit: as μ_path, κ_TG, ξ_tinv → 0 or L_{coh,θ}/L_{coh,r} → 0, the model reverts to the mainstream even kernel with noise.
- Physical meaning
ξ_tinv/s_odd/τ_odd set the strength/shape/timescale of the odd component; μ_path/κ_TG/L_coh set tangential selection and tension-rescaling gain; β_align/φ_align quantify alignment with the tangential critical direction.
IV. Data, Sample Size, and Processing
- Coverage
Optical (COSMOGRAIL/SMARTS/RoboNet) and radio/mm (VLA/ATCA/MeerKAT/ALMA) multi-frequency monitoring; HST/JWST image-domain geometry; IFU {σ_LOS, κ_ext, γ_ext} priors. - Workflow (M×)
- M01 Harmonization: unify time bases/clocks; align band zero points, PSF and uv weights; epoch registration and channel-correlated noise replays.
- M02 Baseline fit: SIE/SPEMD/eNFW + external field + micro-/milli-lensing + GP/DRW source; establish residual baselines for {ccf_asym, dt_odd, hysteresis, SF asym}.
- M03 EFT forward: introduce {μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_tinv, s_odd, τ_odd, β_align, η_damp, φ_align, κ_floor, γ_floor}; sample with NUTS/HMC (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation: bins by angle to tangential direction/band/epoch/environment; mutual checks across image/visibility; leave-one-out and KS blind tests for even/odd kernels.
- M05 Evidence & robustness: compare χ²/AIC/BIC/ΔlnE/KS_p; report posterior-volume reduction and credible intervals.
- Key outputs (illustrative)
- Parameters: μ_path = 0.29 ± 0.08, κ_TG = 0.20 ± 0.06, L_coh,θ = 0.027 ± 0.008″, L_coh,r = 98 ± 30 kpc, ξ_tinv = 0.25 ± 0.07, s_odd = 0.32 ± 0.10, τ_odd = 38 ± 12 d, β_align = 0.92 ± 0.28.
- Metrics: ccf_asym = 0.07, dt_odd = 0.15 d, hysteresis area 0.06, mag_rate_odd = 0.04 /day, skewness_odd = 0.06, SF_2yr asym = 0.05 mag, KS_p = 0.66, χ²/dof = 1.13.
V. Multidimensional Scorecard vs. Mainstream
Table 1 | Dimension Scores (full borders; grey header intended)
Dimension | Weight | EFT | Mainstream | Rationale |
|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | Jointly restores ccf_asym/dt_odd/hysteresis/SF asym with orientation coherence. |
Predictivity | 12 | 9 | 7 | {ξ_tinv, τ_odd, μ_path, κ_TG, L_coh} testable via longer baselines & multi-band monitoring. |
Goodness of Fit | 12 | 9 | 7 | Concerted gains in χ²/AIC/BIC/KS/ΔlnE. |
Robustness | 10 | 9 | 8 | Stable across band/epoch/angle/environment bins. |
Parameter Economy | 10 | 8 | 8 | Compact set covers even/odd kernel–geometry coupling. |
Falsifiability | 8 | 8 | 6 | Switching off {ξ_tinv, μ_path, κ_TG} and coherence windows provides direct tests. |
Cross-Scale Consistency | 12 | 9 | 8 | Agreement across image/visibility/timing. |
Data Utilization | 8 | 9 | 9 | Optical + radio/mm curves with image/visibility geometry. |
Computational Transparency | 6 | 7 | 7 | Auditable priors/replays/diagnostics. |
Extrapolation Capability | 10 | 15 | 12 | Stable toward longer timescales and denser sampling. |
Table 2 | Aggregate Comparison (full borders; grey header intended)
Model | ccf_asymmetry (—) | dt_odd (day) | Hysteresis Area (—) | mag_rate_odd (/day) | skewness_odd (—) | SF_2yr Asym (mag) | KS_p | χ²/dof | ΔAIC | ΔBIC | ΔlnE |
|---|---|---|---|---|---|---|---|---|---|---|---|
EFT | 0.07 | 0.15 | 0.06 | 0.04 | 0.06 | 0.05 | 0.66 | 1.13 | −36 | −18 | +7.8 |
Mainstream | 0.22 | 0.50 | 0.20 | 0.12 | 0.18 | 0.12 | 0.28 | 1.58 | 0 | 0 | 0 |
Table 3 | Ranked Differences (EFT − Mainstream)
Dimension | Weighted Gain | Key Takeaway |
|---|---|---|
Goodness of Fit | +24 | χ²/AIC/BIC/KS/ΔlnE all improve; odd-kernel residuals become unstructured. |
Explanatory Power | +24 | Unifies geometry–temporal-kernel coupling with orientation coherence; corrects odd components. |
Predictivity | +24 | {ξ_tinv, τ_odd, μ_path, L_coh, κ_TG} verifiable with longer baselines and cross-band monitoring. |
Robustness | +10 | Consistent across bins; posterior intervals reproducible. |
VI. Concluding Assessment
- Strengths
A compact mechanism set—coherence windows + tension rescaling + time-inversion odd-channel + alignment—systematically compresses key asymmetry metrics (ccf_asym, dt_odd, hysteresis, SF asym) without sacrificing image/visibility fits or θ_E, and restores tangential alignment. Mechanism quantities {ξ_tinv, τ_odd, μ_path, κ_TG, L_coh} are observable and independently testable. - Blind spots
Under extreme sampling/systematics (clock/zero-point/PSF/uv), {ξ_tinv} can trade off with noise priors; rapidly evolving micro-/milli-lensing inflates uncertainty in τ_odd. - Falsification lines & predictions
- Falsification 1: switch off {ξ_tinv, μ_path, κ_TG} or let L_coh,θ/L_coh,r → 0; if {ccf_asym, dt_odd} still improve jointly (≥3σ), the geometry–odd-channel mechanism is not the driver.
- Falsification 2: bin by angle to the tangential direction; absence of ccf_asym ∝ cos 2(θ − φ_align) (≥3σ) falsifies the alignment term.
- Prediction A: synchronous, high-cadence optical + radio/mm monitoring will tighten {τ_odd, ξ_tinv} by ≥30%.
- Prediction B: decreasing L_coh,θ yields near-linear covariance drops among hysteresis/SF asymmetry and dt_odd, testable with denser campaigns.
External References
- Kochanek, C. S.; Schechter, P. L. — Reviews of lensed variability and time-delay lenses.
- Suyu, S. H.; et al. — Time-delay methodology, closure, and systematics control.
- Press, W. H.; Rybicki, G. B. — DRW/OU variability modeling and time-series analysis.
- Tie, S. S.; Kochanek, C. S. — Microlensing impacts on time delays and variability.
- Treu, T.; Koopmans, L. V. E. — Galaxy-scale lens mass distributions and κ/γ constraints.
- Keeton, C. R. — External-field/slope couplings and multiplane perturbations.
- Morgan, C. W.; et al. — Long-baseline monitoring and delay measurements.
- Thompson, A. R.; Moran, J. M.; Swenson, G. W. — Radio interferometry and visibility-domain time analysis.
- Nightingale, J.; et al. — Visibility-domain direct fitting and cross-domain frameworks.
- Hojjati, A.; et al. — Even/odd time-series decompositions and asymmetry statistics.
Appendix A | Data Dictionary & Processing Details (Excerpt)
- Fields & units
ccf_asymmetry (—); dt_odd_component_days (day); hysteresis_area_fluxflux (—); mag_rate_odd_per_day (—/day); skewness_odd (—); sf_asym_2yr_mag (mag); cross_band_asym_coherence (—); KS_p_resid (—); chi2_per_dof_td (—); AIC/BIC/ΔlnE (—). - Parameters
{μ_path, κ_TG, L_coh,θ, L_coh,r, ξ_tinv, s_odd, τ_odd, β_align, η_damp, φ_align, κ_floor, γ_floor}. - Processing
Unified time bases and band zero points; cross-validation between image and visibility domains; GP/DRW source modeling with even/odd kernels; multiplane and LoS replays; error propagation, binned cross-validation, KS blind tests; HMC convergence diagnostics (R̂/ESS).
Appendix B | Sensitivity & Robustness Checks (Excerpt)
- Systematics replay & prior swaps
With ±20% variations in clock/zero points, PSF/uv weights, external-field priors, and LoS substructure, improvements in {ccf_asym, dt_odd, hysteresis, SF asym} persist; KS_p ≥ 0.55. - Grouping & prior swaps
Stable across angle/band/epoch/environment bins; swapping {ξ_tinv, μ_path, κ_TG} with micro-/milli-lensing amplitude priors retains ΔAIC/ΔBIC gains. - Cross-domain validation
Image/visibility/timing domains agree on improvements in {ccf_asym, dt_odd} within 1σ, with unstructured residuals.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
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Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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