(October 13, 2022 at 9:02 am)Jehanne Wrote:(October 13, 2022 at 8:36 am)polymath257 Wrote: I could also discuss probability measures and whether they serve as good models of probability in quantum mechanics (they do not).
Bell's Inequality?
Precisely. Probability measures produce the inequalities that Bell discovered. Those inequalities are violated in quantum mechanics (because they are violated by operators on a Hilbert space). In a sense, quantum mechanics is a non-commutative version of probability while measure theory is the commutative version. The uncertainty principle does not happen in the commutative case.