A Mathematician ’ s Viewpoint to Bell ’ s theorem : In Memory of Walter Philipp Andrei Khrennikov

In this paper dedicated to the memory of Walter Philipp, we formalize the rules of classical→ quantum correspondence and perform a rigorous mathematical analysis of the assumptions in Bell’s NO-GO arguments. I met Walter Philipp on many occasions — mostly during the Växjö conferences and during my visits to the University of Illinois in UrbanaChampaign — and I always enjoyed social and scientific contacts with him. It was impressive that he always behaved as if he had just moved recently from Vienna (which in fact he had left as early as the 60th to move to Illinois): he was a man of great European cultural level, with a deep sense of humor, and he exhibited them both through uncountable stories about writers, poets, artists and scientists from Vienna. Our common scientific interest was the mathematical formalization of Bell’s arguments [1] which are widely known as Bell’s NO-GO theorem. Contacts with Walter were very attractive for me, because we both had the same background: a specialization in probability theory. I was really happy to find in Walter a fellow mathematician with whom discussions on Bell’s theorem could be made in the language of mathematically rigorous statements. Walter and I shared the common viewpoint — one that I have been trying to