{
  "annotation_id": "09a95dcf-4c61-46c0-a9aa-50524035967e",
  "date_created": "2026-03-02T18:00:53.743000Z",
  "date_modified": "2026-03-02T18:00:53.743000Z",
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  "record": {
    "abstract": "It is demonstrated how the right hand sides of the Lorentz Transformation\nequations may be written, in a Lorentz invariant manner, as 4--vector scalar\nproducts. This implies the existence of invariant length intervals analogous to\ninvariant proper time intervals. This formalism, making essential use of the\n4-vector electromagnetic potential concept, provides a short derivation of the\nLorentz force law of classical electrodynamics, the conventional definition of\nthe magnetic field, in terms of spatial derivatives of the 4--vector potential\nand the Faraday-Lenz Law. An important distinction between the physical\nmeanings of the space-time and energy-momentum 4--vectors is pointed out.",
    "arxiv_id": "physics/0409103",
    "authors": [
      "J. H. Field"
    ],
    "categories": [
      "physics.class-ph",
      "physics.ed-ph"
    ],
    "doi": "10.1088/0031-8949/73/6/018",
    "journal_ref": "Phys. Scripta 73 (2006) 639-647",
    "title": "Derivation of the Lorentz Force Law, the Magnetic Field Concept and the   Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation",
    "url": "https://arxiv.org/abs/physics/0409103"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "869c5549-28f1-4ef9-be3f-3689f681282c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}