As I noted in a comment to the original posting, the work of Chris Fuchs and his collaborators gives intriguing ways out from the apparent contradiction between conditional probability and quantum mechanics. Fuchs's latest paper on the subject is Quantum-Bayesian Coherence.
Saturday, September 12, 2009
The laws of conditional probability are false
The laws of conditional probability are false: This is all standard physics. Consider the two-slit experiment [...] In standard probability theory, the whole idea of conditioning is that you have a single joint distribution sitting out there--possibly there are parts that are unobserved or even unobservable (as in much of psychometrics)--but you can treat it as a fixed object that you can observe through conditioning (the six blind men and the elephant). Once you abandon the idea of a single joint distribution, I think you've moved beyond conditional probability as we usually know it.