dorsal/arxiv
View SchemaTo consider the electromagnetic field as fundamental, and the metric only as a subsidiary field
| Authors | Friedrich W. Hehl, Yuri N. Obukhov |
|---|---|
| Categories | |
| ArXiv ID | physics/0404101 |
| URL | https://arxiv.org/abs/physics/0404101 |
| DOI | 10.1007/s10701-005-8659-y |
| Journal | Found.Phys. 35 (2005) 2007-2025 |
Abstract
In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant and metric-independent way. The electromagnetic field is then given in terms of the excitation $H=(H,D)$ and the field strength $F=(E,B)$. Additionally, a local and linear ``spacetime relation'' is assumed between $H$ and $F$, namely $H \sim \kappa F$, with the constitutive tensor $\kappa$. The propagation is studied of electromagnetic wave fronts (surfaces of discontinuity) with a method of Hadamard. We find a generalized Fresnel equation that is quartic in the wave covector of the wave front. We discuss under which conditions the waves propagate along the light cone. Thereby we derive the metric of spacetime, up to a conformal factor, by purely electromagnetic methods.
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"abstract": "In accordance with an old suggestion of Asher Peres (1962), we consider the\nelectromagnetic field as fundamental and the metric as a subsidiary field. In\nfollowing up this thought, we formulate Maxwell\u0027s theory in a diffeomorphism\ninvariant and metric-independent way. The electromagnetic field is then given\nin terms of the excitation $H=(H,D)$ and the field strength $F=(E,B)$.\nAdditionally, a local and linear ``spacetime relation\u0027\u0027 is assumed between $H$\nand $F$, namely $H \\sim \\kappa F$, with the constitutive tensor $\\kappa$. The\npropagation is studied of electromagnetic wave fronts (surfaces of\ndiscontinuity) with a method of Hadamard. We find a generalized Fresnel\nequation that is quartic in the wave covector of the wave front. We discuss\nunder which conditions the waves propagate along the light cone. Thereby we\nderive the metric of spacetime, up to a conformal factor, by purely\nelectromagnetic methods.",
"arxiv_id": "physics/0404101",
"authors": [
"Friedrich W. Hehl",
"Yuri N. Obukhov"
],
"categories": [
"physics.class-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1007/s10701-005-8659-y",
"journal_ref": "Found.Phys. 35 (2005) 2007-2025",
"title": "To consider the electromagnetic field as fundamental, and the metric only as a subsidiary field",
"url": "https://arxiv.org/abs/physics/0404101"
},
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