Robustness of an Experimental Result: The Example of the Tests of Bell’s Inequalities

Abstract

Bell’s inequalities provide a quantitative criterion to test experimentally the local hidden variables theories (LHVT) versus standard quantum mechanics (SQM). From the early 1970s to the present, a huge number of experimental tests have been performed. We will discuss their independence. The outcomes – except one – are consistent with SQM and inconsistent with LHVT. At a first glance, one can consider that the result of the experimental tests of Bell’s inequalities is robust if one follows the statement of Wimsatt (1981): “the robustness of a result is characterized by its invariance with respect to a great number of independent derivations”. This opinion is implicitly shared by many physicists. However, real experiments differ from the ideal experiment used to derive Bell’s theorem in several respects. Two kinds of problems are mainly emphasized. First, in all the experiments an additional assumption is used due to the fact that a part of the experimental set-up is not 100% efficient. This leads to the detection loophole. Second, the experiments do not fulfill one of the requirements of the theorem, for example the locality condition. This leads to the locality loophole. Consequently, one cannot strictly speaking conclude that the experimental tests have ruled out the LHVT. We argue that, for experimental tests of a given theoretical question to be robust, one has to consider the validity of the various independent derivations carefully. In order to find a way to increase robustness, we will discuss the following questions: Do both loopholes have the same importance? Are they both crucial? Is an ultimate experiment closing both loopholes simultaneously necessary to conclude that the result favouring SQM is robust? Or, are a couple of experiments, each one closing a given loophole, enough?