Framework Comparison — Ranked by Conceptual Similarity to DFD
Note: “Least-action optics” here refers precisely to Fermat’s Principle (δ∫n ds = 0), the variational foundation of geometric optics.
| Rank | Theory / Model | Similarity | Core Mechanism | Relation to DFD |
|---|---|---|---|---|
| 1 | Density Field Dynamics (Alcock, 2024-2025) | 100/100 | ψ defines geometry & dynamics; n = eψ, a = (c²/2)∇ψ. | Single scalar field replaces curvature; unifies light, matter, cosmology on flat ℝ³. |
| 2 | Fermat’s Principle (1662) | 70/100 | Light follows extremal optical path: δ∫n ds = 0. | DFD generalizes the variational law via ψ setting n = eψ. |
| 3 | Einstein Variable-c Model (1911–1912) | 65/100 | c varies with potential; early optical gravity program. | Conceptual ancestor; DFD completes with ψ-sourcing & matter coupling in one field. |
| 4 | Brans–Dicke Scalar–Tensor (1961) | 45/100 | Scalar φ modifies curvature (parameter ω). | Shares “scalar gravity” flavor, but still inside GR curvature; DFD replaces it. |
| 5 | MOND / TeVeS (1983 / 2004) | 40/100 | Empirical low-accel scaling; TeVeS covariant version. | DFD reproduces RAR/Tully–Fisher from μ(x)≈x (|∇ψ| regime) without tuning. |
| 6 | Emergent Gravity (Verlinde, 2016) | 35/100 | Entropic/holographic origin for gravity. | Shares “no-DM” aim; mechanism statistical, not optical/variational. |
| 7 | River Model of Space (Hamilton & Lisle, 2008) | 30/100 | “Flowing space” coordinate picture within GR. | Visual kinship only; DFD uses real optical phase flow (c₁ = e−ψ). |
| 8 | Gordon Optical Metric (1923) | 25/100 | Effective metric inside GR: gopt = g + (1−n−2)u⊗u. | Analogy that depends on GR’s gμν; DFD is curvature-free and self-sourcing. |
| 9 | Eddington’s Optical Analogy (1919) | 20/100 | Heuristic refractive picture to illustrate GR lensing. | Conceptual precursor only; no independent field/dynamics. |
| 10 | Tired-Light Hypothesis (Zwicky, 1929) | 15/100 | Photon energy loss over distance. | No field equation or geometry; unrelated to ψ-based optics. |
| 11 | General Relativity (Einstein, 1915) | 10/100 | Gravitation = curvature of spacetime (gμν). | Opposite ontology: curvature assumed vs ψ replacing curvature in DFD. |
Summary: DFD (100) — ψ is the geometry. Fermat & Einstein 1911–12 (65–70) — direct conceptual precursors. Scalar / MOND / Verlinde (35–45) — partial phenomenology overlap, distinct ontology. Gordon / Eddington (20–25) — optical analogs within GR. GR itself (10) — curvature-first vs DFD’s ψ-first.