{
  "annotation_id": "f41e94fa-402c-43cf-919b-0ba20f46126d",
  "date_created": "2026-03-02T18:02:20.631000Z",
  "date_modified": "2026-03-02T18:02:20.631000Z",
  "file_hash": "1d881c06877ceead425376926f2ccfd31e8f2507f1a50caece445bbdd7dc5b81",
  "private": false,
  "record": {
    "abstract": "Quantum mechanics is considered to arise from an underlying classical\nstructure (``hidden variable theory\u0027\u0027, ``sub-quantum mechanics\u0027\u0027), where\nquantum fluctuations follow from a physical noise mechanism. The stability of\nthe hydrogen ground state can then arise from a balance between Lorentz damping\nand energy absorption from the noise. Since the damping is weak, the ground\nstate phase space density should predominantly be a function of the conserved\nquantities, energy and angular momentum.\n  A candidate for this phase space density is constructed for ground state of\nthe relativistic hydrogen problem of a spinless particle. The first excited\nstates and their spherical harmonics are also considered in this framework. The\nanalytic expression of the ground state energy can be reproduced, provided\naverages of certain products are replaced by products of averages. This\nanalysis puts forward that quantum mechanics may arise from an underlying\nclassical level as a slow variable theory, where each new quantum operator\nrelates to a new, well separated time interval.",
    "arxiv_id": "quant-ph/0511144",
    "authors": [
      "Th. M. Nieuwenhuizen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.2158722",
    "title": "Classical Phase Space Density for the Relativistic Hydrogen Atom",
    "url": "https://arxiv.org/abs/quant-ph/0511144"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2f44a02c-dad3-403c-b851-c741b5b9a7c1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}