Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations

Author: Matthew Lukin Smawfield
Version: v0.3 (Tortola)
Date: 19 December 2025
Status: Preprint
DOI: 10.5281/zenodo.17982540
Website: https://matthewsmawfield.github.io/TEP-GL/

Abstract

Standard gravitational lensing analysis relies on the Isochrony Axiom—the implicit assumption that the observed image represents a synchronous spatial snapshot of the source. For evolving sources, this approximation breaks down in the presence of conformal metric couplings, creating a "temporal composite" image. This projects temporal depth onto the spatial plane, generating a Temporal Shear contribution that is mathematically indistinguishable from gravitational shear—a phenomenon defined here as Phantom Mass. Crucially, GW170817 does not constrain the conformal component of this coupling; because photons and gravitational waves traverse the same path, conformal time dilation is common-mode and cancels in differential measurements. While GW170817 constrains disformal propagation speeds, it leaves the conformal "rate of time" unconstrained. Conformal gradients can reproduce specific aspects of dark matter phenomenology—particularly in the time domain—without violating strong-lens arrival time constraints. The dark sector is thus reinterpreted not as an invisible substance, but as the shadow of temporal transport.

The TEP Research Program

When using this work, please cite the paper and theoretical framework listed below.

Key Findings

This paper identifies a critical loophole in multi-messenger constraints: GW170817 bounds differential propagation speeds (disformal sector) but leaves conformal clock-rate variations unconstrained. If time flows at different rates across an extended source, the observed image becomes a "temporal composite" that projects temporal depth onto the spatial plane. This temporal shear is mathematically indistinguishable from gravitational shear—creating "phantom mass" that mimics dark matter. Preliminary FRB observations show ms-scale achromatic residuals consistent with chronometric lensing predictions (4 FRBs tested, all consistent). Unlike dark matter models, TEP-GL predicts unique signatures: variability-dependent phantom mass and non-zero curl (image rotation) in the shear tensor.

Core Hypothesis

If the Isochrony Axiom is violated by differential time dilation (conformal metric coupling), extended images become temporal composites. This projects temporal depth onto the spatial plane, generating a Temporal Jacobian contribution that is mathematically indistinguishable from gravitational shear—a phenomenon defined here as Phantom Mass.

Crucially, GW170817 does not constrain this effect. Because photons and gravitational waves traverse the same null geodesics in the conformal limit, time dilation is common-mode and cancels in differential measurements. While GW170817 constrains disformal propagation speeds, it leaves the conformal "rate of time" unconstrained. Conformal gradients can reproduce specific aspects of dark matter phenomenology—particularly coherent lensing shear and time-domain signatures—subject to Vainshtein screening constraints. The dark sector is thus reinterpreted not as an invisible substance, but as the shadow of temporal transport.

Key Predictions

1. Variability Bias: The inferred "dark matter" mass should correlate with the intrinsic variability of the source. Static sources should show less phantom mass than variable sources.

2. Image Rotation (Non-Zero Curl): Unlike scalar-potential gravitational lensing (which is curl-free), the Temporal Shear Tensor possesses a non-zero curl, predicting unique image rotation effects.

3. Chronometric Lensing: Fast transients (FRBs) should exhibit millisecond-scale achromatic arrival-time residuals ("jitter") that cannot be explained by geometric time delays or plasma dispersion.

4. Achromaticity: Like dark matter, the temporal effect is wavelength-independent.

5. Convergence of Evidence: Existing cosmological tensions (S₈, H₀, flux ratio anomalies) converge on TEP-GL phenomenology—the framework provides a unified explanation for multiple independent anomalies.

Observational Discriminants

The manuscript proposes several tests to distinguish temporal-field effects from dark matter:

• Source Evolution Analysis: Compare apparent dark matter fraction vs source evolutionary timescale
• Variable Source Monitoring: Track morphological changes in strongly lensed AGN/quasars
• Multi-Image Spectroscopy: Search for evolutionary signatures between multiple images
• Statistical Surveys: Correlate lensing anomalies with source properties

Preliminary Observational Support

Recent FRB anomalies show consistency with TEP-GL predictions:

Additionally, FRB 20190520B exhibits a DM Excess (~900 pc cm⁻³) and FRB 20190308C is identified as a lensed candidate—both are priority targets for temporal shear measurement.

Theoretical Framework

This work builds on the Temporal Equivalence Principle (TEP), which proposes:

• Gravity is Geometry; Time is a Dynamical Field.
• The decomposition of proper time accumulation into "mass" and "time dilation" is gauge-dependent.
• Sector Decoupling: The Conformal Sector (clock rates) is unconstrained by GW170817, while the Disformal Sector (speed of transmission) is tightly bound.
• Vainshtein Screening: The "Screening Cliff" objection is addressed; the mechanism is shown to be over-efficient rather than fine-tuned.

TEP Theory Reference:

Smawfield, M. L. (2025). Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed (v0.6 (Jakarta)). Zenodo. DOI: 10.5281/zenodo.16921911

File Structure

TEP-GL/
├── scripts/
│   ├── steps/                      # Analysis pipeline
│   └── utils/                      # Shared utilities
├── site/                           # Academic manuscript site
│   ├── components/                 # HTML section files
│   ├── public/                     # Static assets
│   └── dist/                       # Built site output
├── docs/                           # PDF versions
├── results/
│   ├── figures/                    # Generated plots
│   └── outputs/                    # Analysis results
├── logs/                           # Execution logs
├── manuscript-tep-gl.md            # Auto-generated markdown
└── VERSION.json                    # Version metadata

Requirements

• Python 3.8+
• NumPy, SciPy, Matplotlib
• Astropy (for cosmological calculations)
• Lenstronomy (for lens modeling)

See requirements.txt for complete dependencies.

Methodology

• Lens Modeling: Ray-tracing with temporal field variations
• Source Evolution: Myr-scale evolutionary models for galaxies/AGN
• Time Delay Calculation: Path-dependent proper-time accumulation
• Image Reconstruction: Temporal composite modeling
• Statistical Analysis: Correlation tests with observational data

Related Work

• TEP Theory - Foundational framework

License

This project is licensed under Creative Commons Attribution 4.0 International (CC-BY-4.0). See LICENSE for details.

Citation

@article{smawfield2025tepgl,
  title={Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations},
  author={Smawfield, Matthew Lukin},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.17982540},
  note={Preprint v0.3 (Tortola)}
}

Acknowledgments

The author thanks colleagues for valuable discussions. This research made use of NASA's Astrophysics Data System and the arXiv preprint server.

Open Science Statement

These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons and MIT licenses to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.

Contact: matthewsmawfield@gmail.com
ORCID: 0009-0003-8219-3159