My discussions of quantum foundations with John Stewart Bell

In 1976, I met John Bell several times in CERN and we talked about a possible violation of optical theorem, purity tests, EPR paradox, Bell inequalities and their violation. I review our discussions, and explain how they were related to my earlier research. I also reproduce handwritten notes, which I gave to Bell during our first meeting and a handwritten letter he sent to me in 1982. We have never met again, but I have continued to discuss BI-CHSH inequalities and their violation in several papers. The research stimulated by Bell papers and experiments performed to check his inequalities led to several important applications of quantum entanglement in quantum information and quantum technologies. Unfortunately, it led also to extraordinary metaphysical claims and speculations about quantum nonlocality and retro-causality, which in our opinion John Bell would not endorse today. BI-CHSH inequalities are violated in physics and in cognitive science, but it neither proved the completeness of quantum mechanics nor its nonlocality. Quantum computing advantage is not due to some magical instantaneous influences between distant physical systems. Therefore one has to be cautious in drawing far-reaching philosophical conclusions from Bell inequalities.