Framework Comparison — Conceptual Proximity to DFD
The “similarity” scores are a qualitative indication of how closely each framework’s core mechanism matches DFD’s refractive scalar-field picture. They are not rankings of empirical performance or historical importance. “Least-action optics” refers specifically to Fermat’s principle (δ∫n ds = 0), the variational foundation of geometric optics.
| Rank | Theory / Model | Similarity | Core Mechanism | Relation to DFD (ψ-based refractive field) |
|---|---|---|---|---|
| 1 | Density Field Dynamics (Alcock, 2024–) | 100 / 100 | Single scalar ψ defines both n = eψ and a = (c²/2)∇ψ. | Baseline framework: curvature is not fundamental; gravity and optics emerge directly from ψ and its sourcing. |
| 2 | Fermat’s Principle (1662) | 70 / 100 | Light follows extremal optical path: δ∫n(x) ds = 0. | DFD effectively promotes n(x) to n = eψ(x) with ψ dynamically sourced. Fermat provides the variational backbone of DFD’s optical sector. |
| 3 | Einstein’s Variable-c Model (1911–1912) | 65 / 100 | c varies with gravitational potential; early optical-gravity program. | Close conceptual ancestor: DFD can be viewed as completing this program with explicit ψ-field equations, well-defined sourcing, and matter coupling while maintaining energy conservation. |
| 4 | Brans–Dicke Scalar–Tensor Theory (1961) | 45 / 100 | Scalar field φ modifies spacetime curvature (parameter ω). | Shares the idea of a scalar degree of freedom influencing gravity, but the scalar lives on top of GR geometry. DFD instead removes curvature and lets ψ fully replace gμν as the gravitational degree of freedom. |
| 5 | MOND / TeVeS (Milgrom 1983; Bekenstein 2004) | 40 / 100 | Non-linear Poisson or multi-field relativistic extensions designed to capture low-acceleration galaxy dynamics. | There is phenomenological overlap: DFD’s μ(|∇ψ|/a*) ≈ x regime reproduces RAR/Tully–Fisher scaling without parameter tuning. The underlying ontology differs: DFD anchors the modification in ψ-controlled optics, not in an empirical acceleration law. |
| 6 | Emergent Gravity (Verlinde, 2016) | 35 / 100 | Entropic / holographic origin for effective gravity and dark-matter-like behavior. | Shares the goal of addressing galaxy-scale anomalies without particle dark matter. The mechanism is statistical and information-theoretic rather than optical / variational via a refractive scalar field. |
| 7 | River Model of Space (Hamilton & Lisle, 2008) | 30 / 100 | “Flowing space” coordinate picture within GR for black-hole spacetimes. | Provides an intuitive visualization of GR metrics. DFD instead treats the one-way phase velocity c₁ = c e−ψ as a physical flow in a nondispersive band, not a coordinate artifact. |
| 8 | Gordon Optical Metric (1923) | 25 / 100 | Effective metric in a refractive medium: gopt = g + (1 − n−2) u ⊗ u. | Important for analog-gravity and light-in-media studies, but it presumes an underlying GR metric gμν. DFD instead takes the optical metric as primary and ties it directly to ψ. |
| 9 | Eddington’s Optical Analogy (1919) | 20 / 100 | Refractive-picture explanation of light bending in GR. | Useful historical analogy but not a stand-alone field theory. DFD turns what was a heuristic picture into an explicit ψ-field with sourcing, conservation laws, and falsifiable predictions. |
| 10 | Tired-Light Hypotheses (Zwicky, 1929, and variants) | 15 / 100 | Redshift attributed to photon energy loss over distance in a non-expanding universe. | Shares the general idea that optics can bias cosmological inference but lacks a consistent field equation, local tests, and a clear link to gravity. DFD instead uses ψ-driven n(x) to bias optical path lengths in a controlled and testable way. |
| 11 | General Relativity (Einstein, 1915) | 10 / 100 | Gravitation encoded in spacetime curvature gμν; light follows null geodesics of gμν. | GR is the benchmark theory for most precision tests to date but lies at the opposite end of this specific “refractive-scalar” dimension: it begins with curvature as fundamental, whereas DFD replaces curvature with ψ and recovers GR’s classic tests via refractive optics on flat ℝ³. |
In summary: DFD (100) takes the refractive field ψ as fundamental. Fermat and Einstein 1911–12 (≈65–70) are the closest conceptual precursors. Scalar, MOND/TeVeS, and emergent-gravity approaches (≈35–45) share portions of the phenomenology with different underlying mechanisms. Gordon and Eddington (≈20–25) are optical analogs formulated inside GR. GR itself (10) remains the benchmark for data but sits at the curvature-first end of the comparison.