According to the French philosopher Michel Bitbol, the "deep-lying connection between the contextual character of observables, and the wave-like form of probability distributions was demonstrated mathematically by P. Destouches-Février [1956]" (See page 7 of this article). Unfortunately I cannot find the 1956's book cited in the article.
Does any of you know this result (or a similar one)? Isn't it too good to be true?
Here is an article (in french--abstract in english) from Bitbol on Destouches: https://www.google.fr/url?q=http://michel.bitbol.pagesperso-orange.fr/destouches_long.pdf&sa=U&ei=wSuhVLHtDsLTaLKEgoAK&ved=0CA0QFjAB&sig2=Fxqr_4Nfxsr2mZsz5_WkWw&usg=AFQjCNGdtnDyYkjrAlaqidWozObZtVdZFA
The most notorious result on contextuality in QM is Kochen-Specker theorem. See this entry: http://plato.stanford.edu/entries/kochen-specker/ The theorem says roughly that one cannot assign non-contextual, definite values to all observables of a system in pain of contradiction. Some interpretations solve the problem by selecting a priviledged observable (generally the position as in bohmian mechanics and GRW), other by assuming the contextuality of measurement results (Everett-like interpretations).
Concerning the link between contextuality and wave-like behaviour, I don't know Destouches' contribution on the subject. The closest I can think of is this article which explains intuitively why QM can be seen as a generalization of a probability theory (with complex numbers as probabilities) and how this is related to some fundamental aspects of QM http://www.scottaaronson.com/democritus/lec9.html A complex number can be represented as a positive coefficient and a phase. If you impose continuity constraints over space-time, you get something pretty much like a wave (sorry this is not a rigorous proof).
