{
  "annotation_id": "77b4ee66-0aca-4f8b-a318-69893b564e1c",
  "date_created": "2026-03-02T18:00:56.927000Z",
  "date_modified": "2026-03-02T18:00:56.927000Z",
  "file_hash": "bcabfcba8d6cc4a377e10e09e5953903460e91c21f80b2d14fe37ce1db3afec4",
  "private": false,
  "record": {
    "abstract": "The equation of the Doppler shift of two bodies in inertial motion in a\nreference frame at rest (i.e., stationary reference frame) is derived. In this\nderivation, the wave-particle duality of photons in the theory of special\nrelativity is considered. The dilation of time of a moving clock, which is\nderived from the Lorentz transformation that depends on the velocity of the\nmoving clock in the reference frame at rest, and wavefront counting by\ngeometrical drawing are used to describe the longitudinal Doppler shift. We\nshow that the equation of the Doppler shift depends on the velocities of the\ntwo bodies in the reference frame at rest.",
    "arxiv_id": "physics/0502151",
    "authors": [
      "Masanori Sato"
    ],
    "categories": [
      "physics.gen-ph"
    ],
    "title": "Derivation of longitudinal Doppler shift equation between two moving   bodies in a reference frame at rest using the particle property of photons",
    "url": "https://arxiv.org/abs/physics/0502151"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "83c16d1a-3708-4f7b-bee1-fcff287ea014",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}