{
  "annotation_id": "dfd4dd62-d1f9-4d32-a2e2-0599e024b6e5",
  "date_created": "2026-03-02T18:02:19.837000Z",
  "date_modified": "2026-03-02T18:02:19.837000Z",
  "file_hash": "446d2e368147a656cca4d8b0b55de68311fddb623cc0105f1befa337e13a2334",
  "private": false,
  "record": {
    "abstract": "We find a quantum mechanical formulation of proper time for spin 1/2\nparticles within the framework of the Dirac theory. It is shown that the rate\nof proper time can be represented by an operator called the ` ` tempo\noperator\u0027\u0027, and that the proper time itself be given by the integral of the\nexpectation value of the operator. The tempo operator has some terms involving\nthe Pauli spin matrices, and the evolution of the proper time is influenced by\nthe spin state via these terms. The relation between the tempo operator and the\nmetric tensor is elucidated.",
    "arxiv_id": "quant-ph/0508046",
    "authors": [
      "Shoju Kudaka",
      "Shuichi Matsumoto"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Proper Time for Spin 1/2 Particles",
    "url": "https://arxiv.org/abs/quant-ph/0508046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1ca9fa06-fa6d-4187-b275-d51f4cd24cce",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}