Theoretical Framework, Research & Explorations

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

Abstract (Theoretical Research; Preprint — proposed experimental test)

Density Field Dynamics (DFD) posits a scalar refractive field ψ(x) such that light propagates with n=e^ψ (one-way phase speed c₁=ce^(-ψ)) and matter accelerates as a=c²∇ψ/2. While cavity-atom redshift tests probe the photon sector, matter-wave interferometers test the external wavefunction coupling. We derive the perturbative phase from the ∇ψ·∇ operator in the DFD-modified Schrödinger equation and obtain a clean discriminator for light-pulse interferometers: Δφ_DFD = (ℏk_eff²/m)(g/c²)T³, in contrast to the standard GR scaling Δφ_GR = k_eff g T². We provide explicit predictions for Kasevich-Chu, Raman, and Bragg geometries (vertical and horizontal), source-mass configurations, and dual-species protocols (Rb/Yb), and analyze systematics with look-alike time scalings. For Earth g and k_eff~1.6×10⁷ m⁻¹ (Rb, 780 nm), the DFD residual is ~2×10⁻¹¹ rad at T=1s, within reach of current long-baseline instruments using rotation, k-reversal, and source-mass modulation.

Matter_Wave_Interferometry_Tests_of_Density_Field_Dynamics

Abstract (Theoretical Research; Preprint — proposed experimental test; Submitted)

We present a sector-resolved framework for testing local position invariance (LPI) using co-located comparisons of optical cavity and atomic clock frequencies transported across gravitational potentials. The method separates three physical contributions to the gravitational redshift: photon wave propagation, solid-state cavity length response, and atomic transition response. By measuring four independent cavity–atom frequency ratios with different cavity materials and atomic species, we obtain an over-determined system that constrains three independent parameters. General relativity predicts all sector differences vanish, corresponding to zero in this basis. Our analysis uses generalized least squares with full covariance propagation, conservative noise modeling including flicker floors, and quantitative environmental thresholds for valid measurement windows. The design includes dual-wavelength checks to suppress residual dispersion, hardware swaps to control for systematics, and orientation flips to bound elastic sag of cavities under transport. We outline realistic implementations over height differences of 30 to 100 m using current optical clock and cavity technology, with projected sensitivities competitive with existing redshift tests. Results are reported directly in the sector basis, with qualitative connections to isotropic Standard Model Extension coefficients provided as context. This approach offers a clean, falsifiable test of the universality of gravitational redshift across distinct physical systems.

Sector_Resolved_Test_of_Local_Position_Invariance_with_Co_Located_Cavity__Atom_Frequency_Ratios__PRD_

Abstract (Theoretical Explorations)

We explore a dynamical alternative to curved spacetime in which the universe is fundamentally three-dimensional and time emerges from dynamics. A single scalar field is proposed to control the local one-way speed of light while preserving the measured two-way speed. In this framework, matter and photons couple to the same field: test bodies would experience accelerations sourced by its gradient, while photons would follow refractive paths. From a local isotropic action we derive a nonlinear field equation that appears to reproduce the classical tests of general relativity, including light deflection, gravitational redshift, Shapiro delay, and Mercury’s perihelion advance. In the low-gradient regime this framework suggests a possible mechanism for flat galaxy rotation curves and Tully–Fisher scaling that might reduce the need for dark matter. On cosmic scales, the optical length integral could introduce a foreground-dependent bias that might contribute to the Hubble tension and mimic cosmic acceleration effects. We present the mathematical framework, conservation laws, and propose falsifiable laboratory tests, including one-way light speed metrology and atom interferometry protocols.

📄 Published Preprint

This paper is now officially available with DOI on CERN’s Zenodo repository:

Density Field Dynamics and the c-Field: A Three-Dimensional, Time-Emergent Dynamics for Gravity and Cosmology

DOI: 10.5281/zenodo.16900767

Published August 19, 2025 on Zenodo – CERN’s open science repository supporting the European Union’s open access mandates for publicly-funded research.

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