Scretching–Planck Density and Phase and Bell's Theorem

Bell’s theorem rules out measurement-independent, locally causal hidden-variable accounts of the observed Bell correlations [1, 2]. The Scretching–Planck (SP) density–phase formulation, \(\psi=\sqrt{P}\,e^{iS/\hbar}\), recovers Schrödinger dynamics wherever \(P>0\). With the standard quantum measurement rule, it reproduces the spin-singlet CHSH maximum of \(2\sqrt{2}\). A Monte Carlo simulation of 400,000 pairs gives \(2.8285\), compared with the Bell-local bound of \(2\). The paper uses two spatial states to illustrate how entanglement couples the particles’ coordinates in the SP quantum potential. The median magnitude of the mixed derivative of \(Q_{\mathrm{SP}}\) is \(7.92\) for the entangled state and \(5.9\times10^{-13}\) for the product-state control. In the entangled-state guidance simulation, changing Bob’s local potential shifts Alice’s trajectory endpoints by up to \(2.60\), while her marginal density remains unchanged within numerical precision. The paper compares the standard quantum violations with selected loophole-free Bell tests conducted from 2015 to 2023 and includes eight solved problems [3–6].