Gudder’s Theorem and the Born Rule
AbstractWe 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
Share & Cite This Article
De Zela, F. Gudder’s Theorem and the Born Rule. Entropy 2018, 20, 158.
De Zela F. Gudder’s Theorem and the Born Rule. Entropy. 2018; 20(3):158.Chicago/Turabian Style
De Zela, Francisco. 2018. "Gudder’s Theorem and the Born Rule." Entropy 20, no. 3: 158.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.