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An explicit statistical model for the Bell experiment

David H. Oaknin

TL;DR

The work questions the standard interpretation of Bell inequality violations by highlighting their dependence on an implicit absolute frame. It introduces a geometrically informed, gauge-theory–based framework that uses a non-linear linking of detector frames and a coordinate-invariant hidden-variable distribution to reproduce quantum correlations with a locally defined description. A key result is that $E(Δ) = -cos(Δ)$ and corresponding joint probabilities align with QM predictions, while the non-linear transformation produces a geometric phase over closed sequences, undermining the Bell constraint. The findings suggest that Bell-type nonlocality is not forced by QM violations when gauge-phase effects are accounted for, prompting a reassessment of foundational assumptions in Bell tests.

Abstract

Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing quantum phenomena in terms of locally defined elements of reality. In a series of recent papers, we have noticed, however, that this conclusion inadvertently, yet crucially, relies on the assumed existence of an absolute frame of reference, with respect to which it would be possible to describe independently of each other the hypothetical elements of reality and the measurement devices that test them. Otherwise, a non-zero geometric phase may appear in the description of the former with respect to a closed sequence of settings of the latter, leading to the violation of the inequality. Following this observation, we discuss an explicit statistical model, which fully reproduces the predictions of Quantum Mechanics for the Bell experiment.

An explicit statistical model for the Bell experiment

TL;DR

The work questions the standard interpretation of Bell inequality violations by highlighting their dependence on an implicit absolute frame. It introduces a geometrically informed, gauge-theory–based framework that uses a non-linear linking of detector frames and a coordinate-invariant hidden-variable distribution to reproduce quantum correlations with a locally defined description. A key result is that and corresponding joint probabilities align with QM predictions, while the non-linear transformation produces a geometric phase over closed sequences, undermining the Bell constraint. The findings suggest that Bell-type nonlocality is not forced by QM violations when gauge-phase effects are accounted for, prompting a reassessment of foundational assumptions in Bell tests.

Abstract

Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing quantum phenomena in terms of locally defined elements of reality. In a series of recent papers, we have noticed, however, that this conclusion inadvertently, yet crucially, relies on the assumed existence of an absolute frame of reference, with respect to which it would be possible to describe independently of each other the hypothetical elements of reality and the measurement devices that test them. Otherwise, a non-zero geometric phase may appear in the description of the former with respect to a closed sequence of settings of the latter, leading to the violation of the inequality. Following this observation, we discuss an explicit statistical model, which fully reproduces the predictions of Quantum Mechanics for the Bell experiment.

Paper Structure

This paper contains 4 sections, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Geometric phases in gauge theories
  3. An explicit statistical model for the Bell experiment
  4. Summary

Figures (1)

  • Figure 1: Plot of the transformation $L(\omega; \Delta), \ \omega \in [-\pi,\pi)$, with ${\widetilde{\Delta}}=\pi/3$ (solid line), compared to the corresponding linear transformation (dotted line).