dorsal/arxiv
View SchemaThe Minkowski metric in non-inertial observer radar coordinates
| Authors | E. Minguzzi |
|---|---|
| Categories | |
| ArXiv ID | physics/0412024 |
| URL | https://arxiv.org/abs/physics/0412024 |
| DOI | 10.1119/1.2060716 |
| Journal | Am.J.Phys. 73 (2005) 1117-1121 |
Abstract
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform experiments in spacetime without making reference to inertial frames. To clarify the relation between inertial and non-inertial observers the coordinate transformation between radar and inertial coordinates, also is given. We show that every conformally flat coordinate system can be regarded as the radar coordinate system of a suitable observer for a suitable parametrization of the observer worldline. Therefore, the coordinate transformation between arbitrarily moving observers is a conformal transformation and conformally invariant (1+1)-dimensional theories lead to the same physics for all observers, independently of their relative motion.
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"abstract": "We give a closed expression for the Minkowski (1+1)-dimensional metric in the\nradar coordinates of an arbitrary non-inertial observer O in terms of O\u0027s\nproper acceleration. Knowledge of the metric allows the non-inertial observer\nto perform experiments in spacetime without making reference to inertial\nframes. To clarify the relation between inertial and non-inertial observers the\ncoordinate transformation between radar and inertial coordinates, also is\ngiven. We show that every conformally flat coordinate system can be regarded as\nthe radar coordinate system of a suitable observer for a suitable\nparametrization of the observer worldline. Therefore, the coordinate\ntransformation between arbitrarily moving observers is a conformal\ntransformation and conformally invariant (1+1)-dimensional theories lead to the\nsame physics for all observers, independently of their relative motion.",
"arxiv_id": "physics/0412024",
"authors": [
"E. Minguzzi"
],
"categories": [
"physics.class-ph",
"gr-qc",
"physics.gen-ph"
],
"doi": "10.1119/1.2060716",
"journal_ref": "Am.J.Phys. 73 (2005) 1117-1121",
"title": "The Minkowski metric in non-inertial observer radar coordinates",
"url": "https://arxiv.org/abs/physics/0412024"
},
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