Experimental Non-Violation of the Bell Inequality

TL;DR

This paper proposes a deterministic, locally causal framework with a non-Euclidean metric that challenges the experimental violation of Bell inequalities, suggesting the inequalities may not be violated under this new model.

Contribution

It introduces a finite, non-classical geometric framework based on number theory that questions the experimental violation of Bell inequalities.

Findings

Bell inequalities are not violated within the proposed framework.

The framework uses a non-Euclidean metric $g_p$ on cosmological state space.

Violation of Bell inequalities depends on the limit $p= finite$, which recovers classical Euclidean geometry.

Abstract

A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=\infty$, at which $g_p$ is Euclidean. Broader implications are discussed.