  In the first part of this presentation (sections 2 to 6), I show that Bell's
Inequalities provide a quantitative criterion to test "reasonable"
Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I
first explain the motivations for considering supplementary parameters
theories: the argument is based on an analysis of the famous
Einstein-Podolsky-Rosen (EPR) Gedankenexperiment . Introducing a reasonable
Locality Condition, we will then derive Bell's theorem, which states: (i) that
Local Supplementary Parameters Theories are constrained by Bell's Inequalities;
(ii) that certain predictions of Quantum Mechanics violate Bell's Inequalities,
and therefore that Quantum Mechanics is incompatible with Local Supplementary
Parameters Theories. I then point out that a fundamental assumption for this
conflict is the Locality assumption, and I show that in a more sophisticated
version of the E.P.R. thought experiment ("timing experiment"), the Locality
Condition may be considered a consequence of Einstein's Causality, preventing
faster-than-light interactions. The purpose of this first part is to convince
the reader that the formalism leading to Bell's Inequalities is very general
and reasonable. What is surprising is that such a reasonable formalism
conflicts with Quantum Mechanics. In fact, situations exhibiting a conflict are
very rare, and Quantum Optics is the domain where the most significant tests of
this conflict have been carried out, as presented in sections 7 to 11.
