HIDDEN VARIABLES FROM STOCHASTIC PROPER TIME: MASS-DEPENDENT CORRELATIONS AS A TEST OF GEOMETRIC QUANTUM FOUNDATIONS
Azzam Almosallami
We present a local hidden variable model for bipartite correlations where the hidden variable distribution is derived from first principles rather than postulated. The model posits that particles accumulate a geometric phase from proper time fluctuations in a stochastic spacetime. The causal Lorentzian theory (CLT) [26] ensures that for many independent fluctuations, φ is normally distributed; wrapping to the circle [0, 2π) yields a uniform distribution when the phase variance σ_φ ≫ 2π. Two particles sharing the same fluctuating geometry share the same φ, which serves as a common cause for their measurement outcomes. For measurement functions we compute the correlation function exactly. In the uniform limit, we obtain a triangle wave that respects Bell inequalities. For finite σ_φ, the correlation interpolates between deterministic outcomes and the triangle wave, with the interpolation controlled by particle mass, temperature, and proper time. This mass-dependent signature provides a novel experimental test of geometric hidden variable theories using molecular interferometry and cold-atom experiments. The framework offers a physical origin for hidden variable distributions and connects quantum foundations to stochastic gravity.
•Apr 1, 2026•0 citations