Why Franson’s Experiment Violates Local Realism

It is shown that the model introduced by Cabello et al. to criticize the Franson experiment suffers from the same weakness as the previous model introduced by Aerts et al. with the same purpose. It is also shown why we can assume with confidence that the Franson experiment does violate local realism. In a recent article [1], Cabello et al. introduced a local model which violates a Bell-CHSH inequality [2] for the Franson experiment [3]. However, their model presents the same deficiency as the model proposed by Aerts et al. [4]. As has been pointed out [5], to see this we can consider a Franson experiment in which the long path L1 (followed by photon ν1) and the long path L2 (followed by photon ν2) have different lengths, L1 and L2, respectively. Now, even though the four possible combinations of photon paths, S1-S2, S1-L2, L1-S2, and L1-L2 are distinguishable, the two above models still predict violations of a Bell-CHSH inequality. In consequence, they are totally unsatisfactory (there seems to be no reason to perform an experiment to see this). This also makes evident that “to conceive a local realistic model for Franson’s experiment is far from being an easy task, even considering real inefficient detectors, since the model has to predict an interference when L1 = L2 and no interference when L1 6= L2”[5]. As a result, a model similar to the one discussed by Clauser and Horne [6] and that could mimic the quantum mechanical predictions for the Franson experiment seems much more difficult to be devised. Franson’s experiment can also be modified in order to make evident some of the nonlocal aspects of entangled photons (e.g., the conflict between wavelike and nonlocal properties[7], and the possibility of obtaining interaction-free which-path information [8]). For that reason, a local model also has to mimic