Abstract (Theoretical Research; Preprint)
Einstein’s 1911–12 variable light-speed proposal tied c(x) to Newtonian potential but was abandoned in 1915 with the adoption of curved spacetime. The missing pieces were a sourcing principle beyond Newton’s potential and a consistent conservation law. We show that a single scalar field ψ(x), derived from a variational action and coupled universally to density, closes that gap: photons propagate with n = e^ψ (so the one-way phase speed is c₁ = c e^(−ψ)), while matter accelerates as a = (c²/2) ∇ψ. A constrained, monotone family ∇·(∇ψ/a·) ∇·(∇ψ/a·) follows from first principles: GR normalization in the solar regime, Noether scale symmetry in the deep-field regime, and convexity for stability.
In the high-gradient limit the nonlinear field equation reduces asymptotically to Poisson’s equation, fixing the 1/r potential and yielding the exact GR coefficients for deflection, redshift, Shapiro delay, and perihelion (shown explicitly at 1PN). Crucially, a sector-resolved cavity–atom comparison predicts a non-null, geometry-locked slope ΔR/R = ξ ΔΦ/c². In a nondispersive optical band the expectation is ξ ≈ 2, giving ≈ 2.2×10⁻¹⁴ per 100 m — well within current 10⁻¹⁶ optical clock precision (Ludlow et al. 2015; Huntemann et al. 2016).
We state explicit falsification criteria. Thus Density Field Dynamics (DFD) is a minimal, action-consistent completion of Einstein’s abandoned program, experimentally decidable with present technology.
Density_Field_Dynamics__Completing_Einstein_s_1911_12_Variable_c_Program_with_Energy_Density_Sourcing_and_Laboratory_Falsifiability Supplemental_Material__Density_Field_Dynamics_Letter