Probability Theory with Superposition Events: A Classical Generalization in the Direction of Quantum Mechanics
Abstract
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the density matrices induced by the experiments or `measurements' is the Luders mixture operation as in QM. And finally by moving the machinery into the ndimensional vector space over Z_2, different basis sets become different outcome sets. That `noncommutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over Z_2 that can model many characteristic nonclassical results of QM.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.09918
 Bibcode:
 2020arXiv200609918E
 Keywords:

 Quantum Physics;
 Mathematics  Probability;
 03B48;
 46L53
 EPrint:
 4 figures