Quantum Foam Tension as the Origin of Gravity

We propose a novel model where gravity emerges from tension fields driven byspatial gradients of a quantum foam density field ρk(xμ). The effective potentialΦ(ρk) = c2gln(ρk/ρ0) reproduces Newtonian gravity in high-acceleration regimes (e.g.,Solar System) and MOND-like behavior in low-acceleration regimes (e.g., galactic rotationcurves). Fitting 175 SPARC galaxies, the model achieves an average RMS errorof 4.2 km s−1 and R2 ≈ 0.987–0.996 with a universal a0 ≈ 1.2 × 10−10 m s−2, naturallyyielding the Tully-Fisher relation without dark matter. Testable predictions includePlanck-scale Casimir effect corrections, atom interferometry phase shifts, and TeVscalesoliton resonances at the LHC. Deviations in a0 across galaxies would falsify themodel, ensuring robust testability.