In the proof of the Bell theorem, we have assumed that all pairs of particles emitted by the source are actually detected, whatever choice is made for the measurement settings a and b; within local realism, the Bell inequalities are then obeyed, which means that it is impossible to reproduce the a and b dependence (4.9) of the correlation function predicted by quantum mechanics (since it allows violations of the Bell inequalities). In this appendix, we examine what happens when the detection process introduces a selection in the ensemble of emitted pairs; in a first step (§E.1), we assume that this selection is independent of a and b, and in a second step (§E.2), we generalize to include a possible dependence. In the latter case, we will see that it then becomes possible to reproduce any variation of the correlation rate as a function of a and b, including the prediction (4.9) in cos(a−b) of quantum mechanics, while remaining within local realism; this is the origin of the “loophole” discussed in §4.5.1.a.