John Bell and the right question

Adan Cabello

Universidad de Sevilla

Bell will be remembered for being the first who realize that, in quantum theory, correlations between outcomes of jointly measurable observables violate certain inequalities satisfied by local (and noncontextual) hidden variables theories. Then, Tsirelson has to be remembered as the first who realize that violations of Bell inequalities are themselves upper bounded in nature. Similarly, Popescu and Rohrlich have to be remembered for being the first ones who asked the "right" question: Why? What reasons or physical principles enforce the violation of Bell inequalities up, but not beyond, certain limits? We will report some recent results related to this question. Specifically, we will identify which Bell and noncontextuality inequalities are violated in nature, which violations are possible and which principle explains that higher violations cannot occur.