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arXiv:1112.3399

Explaining Counts from EPRB Experiments: Are They Consistent with Quantum Theory?

James H. Bigelow

Published Dec 15, 2011• 3 citations

Abstract

I have fit data from EPRB experiments of Weihs et al to a model that consists of an EPRB thought experiment whose output is filtered. The filter implements the assumptions made by most investigators: that EPRB experiments satisfy a fair sampling assumption; and that detections and coincidences occur randomly with Poisson distributions (this provides a basis for calculating standard errors of coincidence counts, correlations, and so forth). The model does not fit the data-predicted and observed counts of detections and coincidences differ far too much, by a chi-square criterion. Logically, one must give up fair sampling and/or Poisson errors and/or the assumption that the data derive ultimately from an EPRB thought experiment. In the literature, giving up fair sampling seems to be coupled to giving up EPRB, but to me it seems just as sensible to keep EPRB and to give up fair sampling and Poisson errors. Some rather ordinary mechanisms can violate fair sampling, and there is the possibility in any experiment for uncontrolled and unmonitored factors to contribute to unwanted variation. By sufficiently relaxing the fair sampling and Poisson assumptions-it doesn't take much-my model can be made to fit the data.

DOI: 10.48550/arxiv.1112.3399

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I have fit data from EPRB experiments of Weihs et al to a model that consists of an EPRB thought experiment whose output is filtered. The filter implements the assumptions made by most investigators: that EPRB experiments satisfy a fair sampling assumption; and that detections and coincidences occur randomly with Poisson distributions (this provides a basis for calculating standard errors of coincidence counts, correlations, and so forth). The model does not fit the data-predicted and observed counts of detections and coincidences differ far too much, by a chi-square criterion. Logically, one must give up fair sampling and/or Poisson errors and/or the assumption that the data derive ultimately from an EPRB thought experiment. In the literature, giving up fair sampling seems to be coupled to giving up EPRB, but to me it seems just as sensible to keep EPRB and to give up fair sampling and Poisson errors. Some rather ordinary mechanisms can violate fair sampling, and there is the possibility in any experiment for uncontrolled and unmonitored factors to contribute to unwanted variation. By sufficiently relaxing the fair sampling and Poisson assumptions-it doesn't take much-my model can be made to fit the data.

We analyse optical EPR experimental data performed by Weihs et al in Innsbruck 1997–1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behaviour that a more general source state (like non-maximally entangled state) cannot straightforwardly account for. We attempt to explain these anomalies by taking account of the relative efficiencies of the four channels. For this purpose, we use the fair sampling assumption, and assume explicitly that the detection efficiencies for the pairs of entangled photons can be written as a product of the two corresponding detection efficiencies for the single photons. We show that this explicit use of fair sampling cannot be maintained to be a reasonable assumption as it leads to an apparent violation of the no-signalling principle.

A recent experiment presented, for photons, the first violation of a Bell inequality closing the fair-sampling loophole, i.e., without having to assume that the sample of measured photons fairly represents the entire ensemble. In this note, we discuss a detailed quantum mechanical model for the experimental data. Within experimental error the experiment agrees with quantum mechanical prediction. We also discuss the effects of drifting laser intensity and show that it could not have mimicked a violation of the Bell inequality. Therefore, the experiment was immune to the "production-rate loophole."

In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role. Here, we want to show that the interpretation of these experiments could be feasible, if some different alternative assumptions other than the fair sampling were used. For this purpose, we derive an efficient Bell-type inequality which is a CHSH-type inequality in real experiments. Quantum mechanics violates our proposed inequality, independent of the detection-efficiency problems.

Data sets produced by three different Einstein-Podolsky-Rosen-Bohm (EPRB) experiments are tested against the hypothesis that the statistics of this data is described by quantum theory. Although these experiments generate data that violate Bell inequalities for suitable choices of the time-coincidence window, the analysis shows that it is highly unlikely that these data sets are compatible with the quantum theoretical description of the EPRB experiment, suggesting that the popular statements that EPRB experiments agree with quantum theory lack a solid scientific basis and that more precise experiments are called for.

Data sets produced by three different Einstein-Podolsky-Rosen-Bohm (EPRB) experiments are tested against the hypothesis that the statistics of this data is described by quantum theory. Although these experiments generate data that violate Bell inequalities for suitable choices of the time-coincidence window, the analysis shows that it is highly unlikely that these data sets are compatible with the quantum theoretical description of the EPRB experiment, suggesting that the popular statements that EPRB experiments agree with quantum theory lack a solid scientific basis and that more precise experiments are called for.