{
  "annotation_id": "2c416678-78a9-487e-a923-fa699e94965d",
  "date_created": "2026-03-02T18:02:47.316000Z",
  "date_modified": "2026-03-02T18:02:47.316000Z",
  "file_hash": "49e390d49e5ec63e267e8281a420c20305067eed591e82ffbb14887285a94bff",
  "private": false,
  "record": {
    "abstract": "Given a state on an algebra of bounded quantum-mechanical observables (the\nself-adjoint part of a C*-algebra), we investigate those subalgebras that are\nmaximal with respect to the property that the given state\u0027s restriction to the\nsubalgebra is a mixture of dispersion-free states---what we call maximal\n\"beable\" subalgebras (borrowing a terminology due to J. S. Bell). We also\nextend our investigation to the theory of algebras of unbounded observables (as\ndeveloped by R. Kadison), and show how our results articulate a solid\nmathematical foundation for central tenets of the orthodox Copenhagen\ninterpretation of quantum theory (such as the joint indeterminacy of\ncanonically conjugate observables, and Bohr\u0027s defense of the completeness of\nquantum theory against the argument of Einstein, Podolsky, and Rosen).",
    "arxiv_id": "quant-ph/9905042",
    "authors": [
      "Hans Halvorson",
      "Rob Clifton"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "journal_ref": "Int.J.Theor.Phys. 38 (1999) 2441-2484",
    "title": "Maximal Beable Subalgebras of Quantum-Mechanical Observables",
    "url": "https://arxiv.org/abs/quant-ph/9905042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a275535b-17b7-41ec-ae89-009b3dd12e2a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}