{
  "annotation_id": "11cae345-35fe-42ae-b6d1-223355d3a9cf",
  "date_created": "2026-03-02T18:01:07.016000Z",
  "date_modified": "2026-03-02T18:01:07.016000Z",
  "file_hash": "134eb3af0855af643fb8db52996a6aed4c37822eb144d1a6d0f679ec4d73be78",
  "private": false,
  "record": {
    "abstract": "In this paper we present definitions of different four-dimensional (4D)\ngeometric quantities (Clifford multivectors). New decompositions of the torque\nN and the angular momentum M (bivectors) into 1-vectors N_{s}, N_{t} and M_{s},\nM_{t} respectively are given. The torques N_{s}, N_{t} (the angular momentums\nM_{s}, M_{t}), taken together, contain the same physical information as the\nbivector N (the bivector M). The usual approaches that deal with the 3D\nquantities $\\mathbf{E}$, $\\mathbf{B}$, $\\mathbf{F}$, $\\mathbf{L}$,\n$\\mathbf{N}$, etc. and their transformations are objected from the viewpoint of\nthe invariant special relativity (ISR). In the ISR it is considered that 4D\ngeometric quantities are well-defined both theoretically and\n\\emph{experimentally} in the 4D spacetime. This is not the case with the usual\n3D quantities. It is shown that there is no apparent electrodynamic paradox\nwith the torque, and that the principle of relativity is naturally satisfied,\nwhen the 4D geometric quantities are used instead of the 3D quantities.",
    "arxiv_id": "physics/0602105",
    "authors": [
      "Tomislav Ivezic"
    ],
    "categories": [
      "physics.gen-ph"
    ],
    "doi": "10.1007/s10701-006-9071-y",
    "title": "The 4D geometric quantities versus the usual 3D quantities. The   resolution of Jackson\u0027s paradox",
    "url": "https://arxiv.org/abs/physics/0602105"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d9aa75c1-9572-47c0-b69b-5ab60d737e9f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}