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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?

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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).

  • I read the lecture by Scott Aaronson. This is indeed closely related. Starting from this lecture I found other related papers but none of them cite Destouches. If however the report by Bitbol is right, the results by Destouches are much deeper. Is it that Bitbol overerates the results by Destouches? No doubt your next blog post will clarify the matter, right? ;) – Bob Dec 29 '14 at 21:49
  • It's difficult to say since I don't know Destouches' result, but note that Bitbol statement is rather vague (a "deep connection"?)... Thanks for reading my blog ;-) – Quentin Ruyant Dec 30 '14 at 0:13

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