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The conceptual problems that quantum mechanics poses has been noticed by numerous authors [1]. From the early beginnings it has been questioned even by some of its creators: Planck, Eherenfest, Einstein, Schrodinger and de Broglie [2-9]. The problem of the collapse of the wave function, its compatibility with special relativity, the question of its completeness, the meaning of the uncertainty relations, etc., are some of the points that have still not received a satisfactory answer. Certainly a large part of these problems would not exist if the theory could get a realistic and local formulation. On the other hand, quantum mechanics has proven to be extremely good from a pragmatic point of view. It seems to make sense to create a theory that at the same time is realistic and local and close to quantum mechanics, without coinciding exactly with it, because Bell's theorem [10] forbids explicitly this possibility. The hope of a realistic and local explanation of the world has not been excluded experimentally. However, since the most extended opinion in the scientific community is just the opposite, we shall explain once more where lies the error of their arguments. Section 1 deals with the weak and strong Bell's inequalities, quoting the different approaches to solve the EPR paradox. In Sec. 2 one of these approaches is developed, the one usually called “Enhancement” or “Variable-Detection-Probability Model.” In Sec. 3, and with the same approach, we display one of these models that is basically an enrichment of the Einstein-de Broglie's version of quantum mechanics.

We report here the results obtained by applying a local and realistic theory to photon intereference phenomena [1], recently observed in a set of experiments performed by Mandel and co-workers [4,6]. In these papers Mandel discarded the possibility of a rational explanation of his results, in the sense that the high visibility obtained was according to him far above the maximum allowed by a “classical” theory. We shall see how a small set of hypotheses, highly plausible for a realistically minded physicist, drives us to a large visibility in agreement with these experiments.