{
  "annotation_id": "3fbbd6e8-43ef-4ab2-864d-aa2a82e1ae24",
  "date_created": "2026-03-02T18:02:17.091000Z",
  "date_modified": "2026-03-02T18:02:17.091000Z",
  "file_hash": "4484f12ac09afb259cc96073587998b559e6cdfbf99656d6ab3a3fa88a35efbb",
  "private": false,
  "record": {
    "abstract": "The purpose of this paper is to show that: when a single particle moving\nunder 3-proper time (three-dimensional time), the trajectories of a classical\nparticle are equivalent to a quantum field with spin. Three-proper time models\nare built for spinless particle, particles with integer spin and half-integer\nspin respectively. The models recreate the same physical behavior as quantum\nfield theory of free particles -- by using pure classical methods with three\nproper time. A new interpretation of spin is given. It provides us more evident\nthat it is possible to interpret quantum physics by using multiple dimensional\ntime. In the last part of this paper, Bose-Einstein statistics and Fermi-Dirac\nstatistics are derived under classical method.",
    "arxiv_id": "quant-ph/0506176",
    "authors": [
      "Xiaodong Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Equations of Motion with Multiple Proper Time: A New Interpretation of   Spin",
    "url": "https://arxiv.org/abs/quant-ph/0506176"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "43fb0921-36a7-4bec-9dd0-f2ba31fa3e39",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}