This was a project thesis for the mathematical logic course (2016) at Beijing Normal University. It is notorious that quantum mechanics is full of counterintuitive ideas. Sometimes one needs a philosophical ground to make an idea easier to accept. There are alternative theories based on different philosophical viewpoints that can be as good as the orthodox in predictions. One of them is quantum Bayesianism, another one is Bohmian mechanics. Here I outline a case where a generalisation of a classical probability formula lacking interpretation as probability.
This thesis introduces some basic concepts in quantum logic. Then I outline the connection between Gleason’s Theorem and the density matrices. I point out one problem in the alternative formalism of quantum Bayesianism. The meaning of making noncommutative generalisation of the classical Bayesian rule is unclear. Since the space of events is non-boolean, the term interpreting the intersection of events doesn’t have proper meaning in the quantum cases. Such generalisation of probability is just formal but doesn’t have a clear interpretation of probability.
Warning: The file is in a draft state containing errors and typos (I have lost the latex file for it and this is the only draft I can find).
This article doesn’t address any important issue and it’s no longer of any interest for me. The reason I wrote such nonsense is due to my quest for an interpretation of quantum mechanics, for which I explain on my page Thoughts on Physics, Maths and Reality