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Entropy 2018, 20(3), 158; https://doi.org/10.3390/e20030158

Gudder’s Theorem and the Born Rule

Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, Peru
Received: 23 December 2017 / Revised: 29 January 2018 / Accepted: 6 February 2018 / Published: 2 March 2018
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
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Abstract

We derive the Born probability rule from Gudder’s theorem—a theorem that addresses orthogonally-additive functions. These functions are shown to be tightly connected to the functions that enter the definition of a signed measure. By imposing some additional requirements besides orthogonal additivity, the addressed functions are proved to be linear, so they can be given in terms of an inner product. By further restricting them to act on projectors, Gudder’s functions are proved to act as probability measures obeying Born’s rule. The procedure does not invoke any property that fully lies within the quantum framework, so Born’s rule is shown to apply within both the classical and the quantum domains. View Full-Text
Keywords: Born probability rule; quantum-classical relationship; spinors in quantum and classical physics Born probability rule; quantum-classical relationship; spinors in quantum and classical physics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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De Zela, F. Gudder’s Theorem and the Born Rule. Entropy 2018, 20, 158.

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