Probability Theory with Superposition Events: A Classical Generalization in the Direction of Quantum Mechanics

11 Pages Posted: 13 Jul 2020

Date Written: June 19, 2020

Abstract

In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional 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 Lüders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over ℤ₂, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over ℤ₂ that can model many characteristic non-classical results of QM.

Keywords: Probability theory, quantum mechanics, objective indefiniteness, superposition

Suggested Citation

Ellerman, David, Probability Theory with Superposition Events: A Classical Generalization in the Direction of Quantum Mechanics (June 19, 2020). Available at SSRN: https://ssrn.com/abstract=3631026 or http://dx.doi.org/10.2139/ssrn.3631026

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA
Slovenia

HOME PAGE: http://www.ellerman.org

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