David, Here <http://arxiv.org/abs/math-ph/0508006>'s an arXiv reference for the "cottage industry" i was referring to. Best wishes, --greg On Wed, May 13, 2009 at 12:59 PM, Greg Meredith < lgreg.meredith@biosimilarity.com> wrote:
David,
To my mind there are three presentations of a "theory" of probability. Two arrive at essentially the same theory by somewhat different means; these are frequentist and Bayesian presentations of "standard" probability theory. The third comes from a completely different direction: quantum mechanics. i remember when i first encountered the Dirac presentation of QM and the interpretation of <a| M |b> as a probability amplitude. My first thought was -- hang on, doesn't that come with an obligation to prove that this aligns with (satisfies the axioms of) a theory of probability. In attempting to work that out for myself, i realized that it didn't; discovered a whole cottage industry of people who had made a similar observation; and argued to myself that of the various notions of probability put forward, this one enjoyed being rigourously employed in physical calculations verified to many decimal places.
Best wishes,