Abstract
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.
Highlights
Bell’s (1964) landmark paper [1] “On the Einstein Podolsky Rosen paradox” led a few years later to a version of his inequality more suitable for experimental purposes, and the focus of a very great deal of both experimental and theoretical work
Pearle (1970) [3] pointed out that the problem of detector efficiency meant that it was easy under local realism to reproduce the famous negative cosine curve of the correlations between spin measurements on particles in the singlet state
Selection of particle pairs such that both particles got detected effectively selects a subpopulation of particle pairs, whose hidden spins depend on the detector settings
Summary
Bell’s (1964) landmark paper [1] “On the Einstein Podolsky Rosen paradox” led a few years later to a version of his inequality more suitable for experimental purposes, and the focus of a very great deal of both experimental and theoretical work. Selection of particle pairs such that both particles got detected effectively selects a subpopulation of particle pairs, whose hidden spins depend on the detector settings. This would result in experimental violation of the CHSH inequality, with the maximal violation predicted by quantum mechanics, even though there is a perfect local realistic explanation of the correlations found. Pearle’s model is the subject of this paper It was the starting shot in a huge literature on the detection loophole, which continues to grow to this day. The landmark paper by Clauser and Horne (1974) [5] already includes another detection-loophole model without the just mentioned bad feature of Pearle’s. It can be skipped; hopefully the figures are well enough explained in the surrounding text
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