by Heinera » Mon May 19, 2014 5:24 am
It is not at all clear that Santos' statistical reasoning is correct. In his analysis of the Christensen et al. data, he computes the following table:
 & C(a,b^{\prime }) & C(a^{\prime }b) & C(a^{\prime},b^{\prime }) \\ Experiment & 29,173 & 34,145 & 34,473 & 1,862 \\ Exper.corrected & 30,008 & 33,721 & 34,687 & 1,867 \\ Quantum & 31,419 & 33,553 & 33,553 & 484\end{array})
He claims that the first three coincidence counts are close enough to the quantum predictions, but then he says "In contrast there is a dramatic difference in the latter correlation
 ,)
where the empirical result is almost four times the quantum prediction."
But the quantum prediction for this combination of settings is a ratio of 0.000933977, hence the small numbers in that column. It is thus not clear that the relative error is meaningful here; if the errors are mainly due to background noise independent of detector settings, then the absolute difference between empirical and predicted counts is what should be compared. And those differences are of the same magnitude for all four correlations.
And also, keep in mind that Christensen et al. did not design their experiment to verify quantum theory; the designed it to rule out the detection loophole for LHV models.
It is not at all clear that Santos' statistical reasoning is correct. In his analysis of the Christensen et al. data, he computes the following table:
[tex]\begin{array}{lllll}Settings & C(a,b) & C(a,b^{\prime }) & C(a^{\prime }b) & C(a^{\prime},b^{\prime }) \\ Experiment & 29,173 & 34,145 & 34,473 & 1,862 \\ Exper.corrected & 30,008 & 33,721 & 34,687 & 1,867 \\ Quantum & 31,419 & 33,553 & 33,553 & 484\end{array}[/tex]
He claims that the first three coincidence counts are close enough to the quantum predictions, but then he says "In contrast there is a dramatic difference in the latter correlation [tex]C\left(a^{\prime },b^{\prime }\right) ,[/tex] where the empirical result is almost four times the quantum prediction."
But the quantum prediction for this combination of settings is a ratio of 0.000933977, hence the small numbers in that column. It is thus not clear that the relative error is meaningful here; if the errors are mainly due to background noise independent of detector settings, then the absolute difference between empirical and predicted counts is what should be compared. And those differences are of the same magnitude for all four correlations.
And also, keep in mind that Christensen et al. did not design their experiment to verify quantum theory; the designed it to rule out the detection loophole for LHV models.
