http://arxiv.org/abs/1508.06910
Maxwell’s equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge Maxwell’s equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell’s equations need to be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both of which can address the paradoxes. One is the Proca-type equation, which contains a photon mass term, i.e., a term proportional to the vector potential of the electromagnetic field. We show that this term can naturally arise if the electromagnetic field is coupled to a complex scalar field. If the complex scalar field is interpreted as describing charged pion particles, the mean mass density of charged pions in the universe gives rise to an effective photon mass with a Compton wavelength comparable to the Hubble radius of the universe. The other type of modified Maxwell equations contains a term with the electromagnetic field potential vector coupled to the spacetime curvature tensor. We show that this term can naturally arise if the Maxwell equation in a flat spacetime is written in terms of a symmetric tensor instead of the anti-symmetric tensor and then extended to a curved spacetime through the “minimal substitution rule”. Some consequences of the modified Maxwell equations are investigated. The results show that for reasonable parameters the modification does not affect existing experiments and observations. However, we argue that, the modified equations may be testable in appropriate astrophysical and cosmological environments.
L. Li
Fri, 28 Aug 15
14/49
Comments: 19 pages, including 1 figure
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