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Pearle's Hidden-Variable Model Revisited.

Richard David Gill¹

¹Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

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This study corrects a hidden variables model that reproduces quantum correlations, simplifying it and demonstrating its effectiveness with simulations. The findings clarify how data-rejection in particle detection influences observed correlations.

Area of Science:

Quantum mechanics
Hidden variables theory
Statistical modeling

Background:

Local hidden variables models attempt to explain quantum correlations without non-locality.
Pearle's (1970) model used data-rejection to reproduce singlet correlations.
Data-rejection in Pearle's model depends on hidden variables and measurement settings.

Purpose of the Study:

To correct a normalization error in Pearle's (1970) hidden variables model.
To demonstrate the inherent simplicity of Pearle's model.
To provide a clearer understanding of data-rejection mechanisms in quantum correlation models.

Main Methods:

Correction of normalization errors in Pearle's model formulas.
Conceptual simplification and analysis of the model's structure.

Keywords:

Bell’s theorem Pearle’s model computer simulation detection loophole

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Visualization of the model's behavior.

Simulation experiment using the R statistical programming language.

Main Results:

A corrected and simplified version of Pearle's local hidden variables model was presented.
The model accurately reproduces quantum singlet correlations through a data-rejection mechanism.
The study highlights the dependence of detected particle subsamples on hidden variables and measurement settings.

Conclusions:

Pearle's model, once corrected, offers a simpler explanation for quantum correlations than previously suggested.
Data-rejection is a crucial factor in understanding how local hidden variables can mimic quantum phenomena.
The findings provide a foundation for further research into local hidden variables models and their implications.