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Pearle’s Hidden-Variable Model Revisited

Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands
Entropy 2020, 22(1), 1;
Received: 22 October 2019 / Revised: 2 December 2019 / Accepted: 10 December 2019 / Published: 18 December 2019
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he or she is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle’s formulas (a normalization error) and more importantly show that the model is simpler than first appears. We illustrate with visualizations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed. View Full-Text
Keywords: Bell’s theorem; detection loophole; computer simulation; Pearle’s model Bell’s theorem; detection loophole; computer simulation; Pearle’s model
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Gill, R.D. Pearle’s Hidden-Variable Model Revisited. Entropy 2020, 22, 1.

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