dorsal/arxiv
View SchemaTrouton-Noble paradox revisited
| Authors | Tomislav Ivezic |
|---|---|
| Categories | |
| ArXiv ID | physics/0606176 |
| URL | https://arxiv.org/abs/physics/0606176 |
| DOI | 10.1007/s10701-007-9116-x |
Abstract
An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment; there is a three-dimensional torque in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque in S', the rest frame of the capacitor. In this paper instead of using 3D quantities and their ``apparent'' transformations we deal with 4D geometric quantities their Lorentz transformations and equations with them. We introduce a new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}. It is shown that in the frame of ``fiducial'' observers, in which the observers who measure N_{s} and N_{t} are at rest, and in the standard basis, only the spatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with components of two 3D torques. In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment without the introduction of any additional torque.
{
"annotation_id": "6c69bded-7512-4c48-882f-af6efc43170f",
"date_created": "2026-03-02T18:01:11.210000Z",
"date_modified": "2026-03-02T18:01:11.210000Z",
"file_hash": "a31467725f027f667649b9f3996171f33d120b2b738edf29b7c9ceef73b0fb28",
"private": false,
"record": {
"abstract": "An apparent paradox is obtained in all previous treatments of the\nTrouton-Noble experiment; there is a three-dimensional torque in an inertial\nframe S in which a thin parallel-plate capacitor is moving, but there is no 3D\ntorque in S\u0027, the rest frame of the capacitor. In this paper instead of using\n3D quantities and their ``apparent\u0027\u0027 transformations we deal with 4D geometric\nquantities their Lorentz transformations and equations with them. We introduce\na new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}.\nIt is shown that in the frame of ``fiducial\u0027\u0027 observers, in which the observers\nwho measure N_{s} and N_{t} are at rest, and in the standard basis, only the\nspatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with\ncomponents of two 3D torques. In such treatment with 4D geometric quantities\nthe mentioned paradox does not appear. The presented explanation is in a\ncomplete agreement with the principle of relativity and with the Trouton-Noble\nexperiment without the introduction of any additional torque.",
"arxiv_id": "physics/0606176",
"authors": [
"Tomislav Ivezic"
],
"categories": [
"physics.gen-ph"
],
"doi": "10.1007/s10701-007-9116-x",
"title": "Trouton-Noble paradox revisited",
"url": "https://arxiv.org/abs/physics/0606176"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "36667c3b-0244-4309-b8c0-af1055ccecc5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}