Density Field Dynamics (DFD) is a scalar refractive-index theory of gravity defined by the postulate that spacetime is flat but permeated by a scalar field ψ (x, t) establishing an optical refractive index n = exp (ψ). Light propagates according to the eikonal of the optical metric ds̃² = −c²dt²/n² + dx², while matter responds to the effective potential Φ = −c²ψ/2. This framework has an optical scalar sector ψ that governs clock rates, refraction, and quasi-static dynamics, together with a transverse-traceless radiative sector hTTᵢj for gravitational waves—both derived as irreducible components of the same zero-mode parent tensor on CP² × S³. It reproduces all classic tests of general relativity in the weak-field limit (γ = β = 1, all PPN parameters matching GR as output of DFD's own field equations), gravitational waves at speed c with two tensor polarizations, and MOND-like phenomenology at galactic scales through a nonlinear crossover function μ (x) = x/ (1+x) and scale a* = 2√α cH₀, both derived from S³ topology (Appendix N). A dedicated model-independent SPARC shape analysis finds nₒpt = 1. 15 ± 0. 12 (95% CI 1. 00, 1. 50) in the family μₙ (x) = x/ (1+xⁿ) ^1/n, with DFD's n = 1 inside the confidence region and Standard MOND's n = 2 strongly disfavored. The vacuum loading interpretation (§2. 7) provides the physical picture: mass deposits fractional energy loading ψ in the quantum vacuum, which resists deformation with force scale K₀ = c⁴/ (8πG). The crossover function μ (x) acts as a field-dependent gravitational permittivity—reduced at low gradients, amplifying gravitational flux and producing flat rotation curves without dark matter. This paper presents DFD as a unified framework: (1) Fine-structure constant: α⁻¹ = 137. 036 from the microsector spectral action on ℂP² × S³ with Toeplitz truncation at kₘax = 60. The derivation is convention-locked: a forced binary fork between regular-module and fermion-rep microsectors is resolved by a no-hidden-knobs policy, with the surviving branch matching experiment at sub-ppm level. Verified by lattice Monte Carlo (L6–L16; 9/10 at L16 with p 7 yr) Distance duality e^Δψ factor present Etherington reciprocity holds exactly; DDR = consistency check, not estimator (v3. 1 erratum) What's New in v3. 0 Result v
Gary Alcock (Thu,) studied this question.