While well-tested at solar system scales, Newtonian gravity exhibits anomalies at larger scales and accelerations below \(10^{-9} m/s^2\) . Although Yukawa-like modifications can reconcile these anomalies with general relativity up to solar system scales, they face challenges at galactic scales. Notably, gravitational anomalies at accelerations \(\le 10^{-9} m/s^2\) for separations down to \(50\, \mu\) m remain undetected experimentally. This paper presents a mathematical framework for Yukawa modification of Newtonian gravity in weak acceleration regimes \((\le 10^{-9} m/s^2)\) and small separations ( \(\le 30 \, \mu\) m) using an extended space model with an extra dimension. This model suggests a vacuum-sourced inertia effect from peculiar photons, with implications for the Mach principle. These photons’ entanglement scale ( \(\le 30\, \mu\) m) hints at the possibility of longer-range photon entanglement via analytic continuation, opening new avenues for research in quantum gravity and cosmology.
