To Consider the Electromagnetic Field as Fundamental,and the Metric Only as a Subsidiary Field |
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Authors: | Email author" target="_blank">Friedrich?W?HehlEmail author Yuri?N?Obukhov |
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Institution: | 1.Inst. Theor. Physics,University of Cologne,K?ln,Germany;2.Department of Physics & Astron,University of Missouri-Columbia,Columbia,USA;3.Inst. Theor. Physics,University of Cologne,K?ln,Germany;4.Department of Theor. Physics,Moscow State University,Moscow,Russia |
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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
and the field strength F = (E,B). Additionally, a local and linear “spacetime relation” is assumed between H and F, namely H ~ κ F, with the constitutive tensor κ. 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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Keywords: | Classical electrodynamics premetric axiomatics differential forms electric/magnetic reciprocity light cone metric |
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