Strong Fields and Gravitational Waves in Density Field Dynamics: From Optical First Principles to Quantitative Tests

We extend Density Field Dynamics (DFD)—a scalar-field framework in which photons experience an optical metric n = e^ψ while matter follows universal free fall governed by a = (c²/2)∇ψ—to the strong-field and radiative regimes. Starting from the minimal optical equivalence principle, we show that the governing scalar equation admits unique, convex solutions reproducing general relativity’s weak-field optics while generating self-consistent strong-field structures, including photon spheres, black-hole shadows, and lensing observables. In the radiative sector, we introduce a transverse–traceless mode propagating at speed c and map deviations into the parametrized post-Einsteinian (ppE) formalism, enabling direct comparison with gravitational-wave data.

The decisive laboratory discriminator remains a co-located cavity–atom frequency ratio at two gravitational potentials, which in this framework predicts a slope of:

ΔR / R ≈ (2 g Δh) / c² ≈ 2.2 × 10⁻¹⁴ per 100 m on Earth.

This “slope = 2” factor is the laboratory analogue of the classic light-bending result: DFD provides a physical refractive-index explanation for the same factor-of-two that GR attributes to curved spacetime. The prediction yields a clean, falsifiable separation from general relativity (strictly null) with near-term optical metrology.

Appendices provide technical foundations, including PDE well-posedness, crossover dynamics, EFT embeddings, and cosmological bias estimates. The result is a unified, falsifiable extension of DFD across classical tests, strong-field astrophysics, and laboratory precision experiments.