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Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

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Special Relativity

Part of the book series: Lecture Notes in Physics ((LNP,volume 702))

Abstract

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral matter. Electric charge and magnetic flux are postulated to be conserved. As a consequence, the inhomogeneous and the homogeneous Maxwell equations emerge expressed in terms of the excitation H = (H,D) and the field strength F = (E,B), respectively. H and F are assumed to fulfill a local and linear “spacetime relation” with 36 constitutive functions. The propagation of electromagnetic waves is considered under such circumstances in the geometric optics limit. We forbid birefringence in vacuum and find the light cone including its Lorentzian signature. Thus the conformally invariant part of the metric is recovered. If one sets a scale, one finds the pseudo-Riemannian metric of spacetime.

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Author information

Authors and Affiliations

  1. Inst. Theor. Physics, University of Cologne, Köln, 50923, Germany

    F.W. Hehl

  2. Dept. Physics Astron., Univ. of Missouri-Columbia, Columbia, MO, 65211, USA

    F.W. Hehl

  3. Inst. Theor. Physics, University of Cologne, Köln, 50923, Germany

    Y.N. Obukhov

  4. Dept. Theor. Physics, Moscow State University, Moscow, 117234, Russia

    Y.N. Obukhov

Authors
  1. F.W. Hehl
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  2. Y.N. Obukhov
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Editors and Affiliations

  1. Albert-Einstein-Institut MPl Gravitationsphysik, Am Mühlenberg 1, Golm, 14476, Germany

    Jürgen Ehlers

  2. ZARM, Universität Bremen Am Fallturm, Bremen, 28359, Germany

    Claus Lämmerzahl

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Hehl, F., Obukhov, Y. (2006). Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme. In: Ehlers, J., Lämmerzahl, C. (eds) Special Relativity. Lecture Notes in Physics, vol 702. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34523-X_7

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