Hidden in Plain View: The Material Invariance of Maxwell-Hertz-Lorentz Electrodynamics
نویسنده
چکیده
Maxwell accounted for the apparent elastic behavior of the electromagnetic field through augmenting Ampere’s law by the so-called displacement current much in the same way that he treated the viscoelasticity of gases. Original Maxwell constitutive relations for both electrodynamics and fluid dynamics were not material invariant, while combining Faraday’s law and the Lorentz force makes the first of Maxwell’s equation material invariant. Later on, Oldroyd showed how to make a viscoelastic constitutive law material invariant. The main assumption was that the proper description of a constitutive law must be material invariant. Assuming that the electromagnetic field is a material field, we show here that if the upper convected Oldroyd derivative (related to Lie derivative) is used, the displacement current becomes material invariant.
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