Next Article in Journal
IBVis: Interactive Visual Analytics for Information Bottleneck Based Trajectory Clustering
Next Article in Special Issue
Quantization and Bifurcation beyond Square-Integrable Wavefunctions
Previous Article in Journal
Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations
Previous Article in Special Issue
Uncertainty Relation Based on Wigner–Yanase–Dyson Skew Information with Quantum Memory
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(3), 158;

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)
Full-Text   |   PDF [254 KB, uploaded 2 March 2018]


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).

Share & Cite This Article

MDPI and ACS Style

De Zela, F. Gudder’s Theorem and the Born Rule. Entropy 2018, 20, 158.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top