{
  "annotation_id": "6ee44c81-fa6a-4175-bf9a-fbad9647b98b",
  "date_created": "2026-03-02T18:02:41.238000Z",
  "date_modified": "2026-03-02T18:02:41.238000Z",
  "file_hash": "c346b350b0830ed826367673de556b7d69540de5526a8797606f38610bbfd123",
  "private": false,
  "record": {
    "abstract": "John Bell once argued that one ought to select, out of the \u0027observables\u0027 of\nquantum theory, some subset of \u0027beables\u0027 that can be consistently ascribed\ndeterminate values. Moreover, this subset should be selected so as to guarantee\n(among other things) that we can dispense with the orthodox interpretation\u0027s\nloose talk about \u0027measurement values\u0027: \"...the probability of a beable being a\nparticular value would be calculated just as was formerly calculated the\nprobability of observing that value\". Working in the framework of C*-algebras\n(in particular, Segal algebras), I propose an algebraic characterization of\nthose subsets of bounded observables of a quantum system that can have beable\nstatus with respect to any (fixed) state of the system. It turns out that\nobservables with beable status in a state need not all commute (a possibility\nBell himself does not consider), but they must at least form a certain kind of\n\u0027quasicommutative\u0027 subalgebra determined by the state. A virtue of the analysis\nis that it applies to beables with continuous spectra, usually neglected in\ndiscussions of the no-hidden-variables theorems. In the (very) special case\nwhere the algebra of observables for a system is representable on a\nfinite-dimensional Hilbert space, I give a complete characterization of the\nmaximal beable subalgebras determined by any state of the system; the\ninfinite-dimensional case remains open. These results are discussed in relation\nto previous results of a similar nature, to \u0027no-collapse\u0027 interpretations of\nquantum mechanics, and to algebraic relativistic quantum field theory.",
    "arxiv_id": "quant-ph/9711009",
    "authors": [
      "Rob Clifton"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Beables in Algebraic Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9711009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b10d8861-e4bc-4fb5-932b-ef265924a190",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}