Arnold Neumaier
Published 2025-02-12Version 1
Details of the contents, and formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. Based to a large extent on little known results from the recent books 'Coherent Quantum Physics' by Neumaier and 'Algebraic Quantum Physics', Vol. 1 by Neumaier and Westra, this paper traces the early history 100 years ago, its generalization (essential for today's quantum optics and quantum information theory) to POVMs 50 year ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when applied outside this domain.
Quantum Interval-Valued Probability: Contextuality and the Born Rule
Derivation of the Born rule based on the minimal set of assumptions
Origin of which-way information and generalization of the Born rule
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