dorsal/arxiv
View SchemaUncertainty principle for proper time and mass II
| Authors | Shoju Kudaka, Shuichi Matsumoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901031 |
| URL | https://arxiv.org/abs/quant-ph/9901031 |
Abstract
When we quantize a system consisting of a single particle, the proper time $\tau $ and the rest mass $m$ are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities are regarded as operators in addition to the position and the momentum. Applying this new rule to a scalar particle and to a particle with spin $ 1/2 $, we analyze the time evolution of the operator $\tau $. In the former case, the evolution of the proper time perfectly matches several well-established classical formulae. In the case of the particle with spin 1/2, our new rule implies that an oscillation appears in the time evolution of the operator $\tau $. This oscillation is similar to Zitterbewegung which is well-known in the ordinary Dirac theory. We formulate one physical effect of this oscillation by considering the interaction with a gravitational field, and estimate how small it is.
{
"annotation_id": "c4a47cfb-589a-4788-8edb-7010f00e2c20",
"date_created": "2026-03-02T18:02:44.983000Z",
"date_modified": "2026-03-02T18:02:44.983000Z",
"file_hash": "dd95b8983154f7cb08a0cca8552f4956a1b23b79743e096397f146e706f110b2",
"private": false,
"record": {
"abstract": "When we quantize a system consisting of a single particle, the proper time\n$\\tau $ and the rest mass $m$ are usually dealt with as parameters. In the\npresent article, however, we introduce a new quantization rule by which these\nquantities are regarded as operators in addition to the position and the\nmomentum. Applying this new rule to a scalar particle and to a particle with\nspin $ 1/2 $, we analyze the time evolution of the operator $\\tau $. In the\nformer case, the evolution of the proper time perfectly matches several\nwell-established classical formulae. In the case of the particle with spin 1/2,\nour new rule implies that an oscillation appears in the time evolution of the\noperator $\\tau $. This oscillation is similar to Zitterbewegung which is\nwell-known in the ordinary Dirac theory. We formulate one physical effect of\nthis oscillation by considering the interaction with a gravitational field, and\nestimate how small it is.",
"arxiv_id": "quant-ph/9901031",
"authors": [
"Shoju Kudaka",
"Shuichi Matsumoto"
],
"categories": [
"quant-ph"
],
"title": "Uncertainty principle for proper time and mass II",
"url": "https://arxiv.org/abs/quant-ph/9901031"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8bdf1ae7-422a-452f-8a92-462194111263",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}