{
  "annotation_id": "628b2188-5bc7-40e2-9d92-433749e4a686",
  "date_created": "2026-03-02T18:02:41.659000Z",
  "date_modified": "2026-03-02T18:02:41.659000Z",
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  "record": {
    "abstract": "Quantum theory is formulated as the only consistent way to manipulate\nprobability amplitudes. The crucial ingredient is a consistency constraint: if\nthere are two different ways to compute an amplitude the two answers must\nagree. This constraint is expressed in the form of functional equations the\nsolution of which leads to the usual sum and product rules for amplitudes. A\nconsequence is that the Schrodinger equation must be linear: non-linear\nvariants of quantum mechanics are inconsistent. The physical interpretation of\nthe theory is given in terms of a single natural rule. This rule, which does\nnot itself involve probabilities, is used to obtain a proof of Born\u0027s\nstatistical postulate. Thus, consistency leads to indeterminism.\n  PACS: 03.65.Bz, 03.65.Ca.",
    "arxiv_id": "quant-ph/9804012",
    "authors": [
      "Ariel Caticha"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "gr-qc"
    ],
    "doi": "10.1103/PhysRevA.57.1572",
    "journal_ref": "Phys.Rev. A57 (1998) 1572",
    "title": "Consistency, Amplitudes and Probabilities in Quantum Theory",
    "url": "https://arxiv.org/abs/quant-ph/9804012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
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    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}