{
  "id": "2502.08545",
  "version": "v1",
  "published": "2025-02-12T16:28:49.000Z",
  "updated": "2025-02-12T16:28:49.000Z",
  "title": "The Born rule -- 100 years ago and today",
  "authors": [
    "Arnold Neumaier"
  ],
  "comment": "32 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-12T16:28:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81-03",
      "81P10",
      "81P15"
    ],
    "keywords": [
      "born rule",
      "books coherent quantum physics",
      "todays quantum optics",
      "algebraic quantum physics",
      "quantum information theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}