  Scientific imagination and experimental ingenuity are at the heart of
physics. One of the most known instances where this interplay between theory
(i.e., foundations) and experiments (i.e., technology) occurs is in the
discussion of Bell's inequalities. In this paper, we present a revisitation of
the violation of Bell's inequality in the Clauser-Horne-Shimony-Holt (CHSH)
form with entangled quantum states. First, we begin with a discussion of the
1935 Einstein-Podolski-Rosen (EPR) paradox (i.e., incompleteness of quantum
mechanics) that emerges from putting the emphasis on Einstein's locality and
the absolute character of physical phenomena. Second, we discuss Bell's 1971
derivation of the 1969 CHSH form of the original 1964 Bell inequality in the
context of a realistic local hidden-variable theory (RLHVT). Third, identifying
the quantum-mechanical spin correlation coefficient with the RLHVT one, we
follow Gisin's 1991 analysis to show that quantum mechanics violates Bell's
inequality when systems are in entangled quantum states. For pedagogical
purposes, we show how the extent of this violation depends both on the
orientation of the polarizers and the degree of entanglement of the quantum
states. Fourth, we discuss the basics of the experimental verification of
Bell's inequality in an actual laboratory as presented in the original 1982
Aspect-Grangier-Roger (AGR) experiment. Finally, we provide an outline of some
essential take home messages from this wonderful example of physics at its
best.
