Gudder's theorem and the born rule

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3 Scopus citations


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.

Original languageEnglish
Article number158
Issue number3
StatePublished - 1 Mar 2018


  • Born probability rule
  • Quantum-classical relationship
  • Spinors in quantum and classical physics


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