dorsal/arxiv
View SchemaJackson's paradox and its resolution by the four-dimensional geometric quantities
| Authors | Tomislav Ivezic |
|---|---|
| Categories | |
| ArXiv ID | physics/0608054 |
| URL | https://arxiv.org/abs/physics/0608054 |
Abstract
In this paper it is shown that the real cause of Jackson's paradox is the use of three-dimensional (3D) quantities, e.g., $\mathbf{E}$, $% \mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{T}$, their transformations and equations with them. The principle of relativity is naturally satisfied and there is no paradox when the physical reality is attributed to the 4D geometric quantities, e.g., to the 4D torque $N$ (bivector) or, equivalently, to the 4D torques $N_{s}$ and $N_{t}$ (1-vectors), which together contain the same physical information as the bivector $N$.
{
"annotation_id": "46856d26-dc0d-41b8-a6b5-7b76764c34dc",
"date_created": "2026-03-02T18:01:10.740000Z",
"date_modified": "2026-03-02T18:01:10.740000Z",
"file_hash": "6b798554c0a47d27d1b949e9634910a84e7956e2767919194f987bf57ba4a473",
"private": false,
"record": {
"abstract": "In this paper it is shown that the real cause of Jackson\u0027s paradox is the use\nof three-dimensional (3D) quantities, e.g., $\\mathbf{E}$, $% \\mathbf{B}$,\n$\\mathbf{F}$, $\\mathbf{L}$, $\\mathbf{T}$, their transformations and equations\nwith them. The principle of relativity is naturally satisfied and there is no\nparadox when the physical reality is attributed to the 4D geometric quantities,\ne.g., to the 4D torque $N$ (bivector) or, equivalently, to the 4D torques\n$N_{s}$ and $N_{t}$ (1-vectors), which together contain the same physical\ninformation as the bivector $N$.",
"arxiv_id": "physics/0608054",
"authors": [
"Tomislav Ivezic"
],
"categories": [
"physics.gen-ph"
],
"title": "Jackson\u0027s paradox and its resolution by the four-dimensional geometric quantities",
"url": "https://arxiv.org/abs/physics/0608054"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "11ed4eba-0666-483a-b307-dc55a63d2f8e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}