2010/08/02 by Jiri Soucek, Soucek, Jiri
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1008.0295
47 pages, second version, small changes in Sect. 2
arxiv created 2010/08/26 · arxiv updated 2010/08/27
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of Ωis replaced with the concept of an event as a partition. The partition is any set of disjoint non-empty subsets of Ω(i.e. partition=subset+its decomposition). Interpretation: elements inside certain part are indistinguishable, while elements from different parts are distinguishable. There are incompatible events, e.g e1,e2 and e1,e2. This is logical incompatibility analogical to the impossibility to have and simultaneously not to have the which-way information in the given experiment. The context is the maximal set of mutually compatible events. Each experiment has associated its context. In each context the extended probability is reduced to classical probability. Then the quadratic representation of events, partitions and probability measures is developed. At the end the central concept of quadratic probability spaces (which extend Kolmogorov probability spaces) is defined and studied. In the next paper it will be shown that quantum mechanics can be represented as the theory of Markov processes in the extended probability theory (Einstein's vision of QM).