Bell's Theorem : The Naive View of an Experimentalist
  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. 
Alain Aspect