[Paper Review] Local, deterministic hidden variable theories based on a loophole in Bell's theorem

V. Z. Nuri|ArXiv.org|Aug 5, 1998

Quantum Mechanics and Applications14 references3 citations

TL;DR

This paper proposes local, deterministic hidden variable theories that violate Bell's inequality by exploiting a loophole involving probabilistic detection based on hidden variables within measuring devices. Using Fourier analysis, the models show approximate agreement with quantum mechanics and experimental results from Aspect-type experiments, challenging the nonlocality conclusion of Bell's theorem under specific assumptions about detection efficiency and hidden variable distributions.

ABSTRACT

This paper furthers the long historical examination of and debate on the foundations of quantum mechanics (QM) by presenting two local hidden variable (LHV) rules in the context of the EPRB experiment which violate Bell's inequality, but which are nevertheless local and deterministic under reasonable definitions of the terms, and coincide approximately with the conventional QM prediction. The theories are based on the general idea of probabilistic detection of particles depending on an interaction of hidden variables within the measuring device and particle, and relate mathematically to Fourier analysis. The crucial discrepancy of variations in the hidden variable distribution based on relative polarizer orientations is isolated which invalidates assumptions in Bell-type theorems. The first theory can be analyzed completely symbolically whereas the second was analyzed using numerical methods. The properties of the second in particular are shown to be approximately consistent with the reported results and uncertainties in all three Aspect experiments. Variation in the total photon pairs detected over orientations is shown to be a basic characteristic of these theories. Some comments on the relevance of active vs. passive locality are made. Two sections consider these ideas relative to energy conservation and the measurement problem (collapse of the wavefunction). One section proposes new experiments.

Motivation & Objective

• To challenge the universality of Bell's theorem by constructing local, deterministic hidden variable models that reproduce quantum correlations.
• To identify and exploit a loophole in Bell-type theorems related to variable detection probabilities depending on polarizer orientation.
• To demonstrate that such models can approximately match experimental outcomes from the Aspect experiments, including reported uncertainties.
• To examine the implications of these models for locality, energy conservation, and the measurement problem (wavefunction collapse).
• To propose new experimental tests to further validate or refute the proposed hidden variable framework.

Proposed method

• Develops two local hidden variable theories based on probabilistic detection mechanisms influenced by hidden variables in the measuring apparatus and the particle.
• Models detection probabilities using Fourier analysis to describe variations in hidden variable distributions relative to polarizer orientation.
• Applies symbolic analysis to the first theory and numerical simulation to the second for validation.
• Introduces a dependence of detection efficiency on relative polarizer angles, which invalidates key assumptions in Bell-type theorems.
• Uses the relative orientation of polarizers as a control parameter to modulate the distribution of hidden variables and thus the detection rate.
• Analyzes the total number of detected photon pairs across different polarizer orientations to assess consistency with experimental data.

Experimental results

Research questions

• RQ1 Can local, deterministic hidden variable theories reproduce quantum mechanical predictions for EPRB-type experiments without violating locality?
• RQ2 Does a detection loophole based on orientation-dependent hidden variable distributions invalidate the assumptions underlying Bell's inequality?
• RQ3 To what extent do the proposed models match the reported results and uncertainties from the three Aspect experiments?
• RQ4 How does the variation in total detected photon pairs across polarizer orientations affect the validity of Bell-type theorems?
• RQ5 What are the implications of these models for the measurement problem and energy conservation in quantum mechanics?

Key findings

• The proposed models violate Bell's inequality while remaining local and deterministic under reasonable definitions, challenging the necessity of nonlocality in quantum mechanics.
• The first model allows complete symbolic analysis, demonstrating consistency with the framework's core assumptions.
• The second model, analyzed numerically, shows approximate agreement with the results and uncertainties of all three Aspect experiments.
• Variation in the total number of detected photon pairs across different polarizer orientations is a fundamental feature of the models.
• The models suggest that assumptions in Bell-type theorems are invalidated when detection probabilities depend on hidden variables interacting with the measuring device.
• The study identifies a potential loophole in Bell's theorem related to orientation-dependent detection efficiency, which could explain apparent violations of local realism.