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An Assessment of Evans’ Unified Field Theory I

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Abstract

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ αβ. These two potentials yield the field strengths torsion T α and curvature R αβ. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic potentials \(\mathcal{A}^{\alpha }\) ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.

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  1. Institute for Theoretical Physics, University at Cologne, 50923, Köln, Germany

    Friedrich W. Hehl

  2. Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, MO, 65211, USA

    Friedrich W. Hehl

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Hehl, F.W. An Assessment of Evans’ Unified Field Theory I. Found Phys 38, 7–37 (2008). https://doi.org/10.1007/s10701-007-9190-0

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