Experimental Non-Violation of the Bell Inequality

Area of Science:

• Quantum Physics
• Cosmology
• Number Theory

Background:

• The Bell Inequality's violation is often cited as evidence against local realism.
• Existing quantum frameworks grapple with reconciling determinism and causality with observed phenomena.

Purpose of the Study:

• To present a novel finite, non-classical framework for qubit physics.
• To challenge the experimental violation of the Bell Inequality.
• To propose an alternative to standard interpretations of quantum mechanics.

Main Methods:

• Postulation of a fractal-like 'invariant set' geometry in cosmological state space.
• Definition of a non-Euclidean metric (g_p) related to p-adic numbers.
• Application of number-theoretic properties of spherical triangles to analyze inequalities.

Main Results:

• The Clauser-Horne-Shimony-Holt (CHSH) inequality is shown to be undefined in the proposed framework.
• Experimentally violated CHSH-like inequalities are demonstrated to be distinct from the standard CHSH inequality within this model.
• The framework is deterministic and locally causal, avoiding conspiratorial explanations.

Conclusions:

• The experimental violation of the Bell Inequality may not be as definitive as commonly concluded.
• The proposed invariant set theory offers a new perspective on quantum foundations and cosmology.
• This non-classical framework provides a deterministic and causal alternative that aligns with experimental observations.