Maxwell electromagnetic equations in the uniform medium. An alternative to the Minkowski theory of special relativity
2014jcx | Balan V., Ovsiyuk E.M., Red’kov V.M., Veko O.V.  // Mozyr State Pedagogical University, Mozyr, Belarus; University Politehnica of Bucharest, Bucharest, Romania; B.I. Stepanov Institute of Physics, NAS of Belarus, vladimir.balan@upb.ro; e.ovsiyuk@mail.ru; redkov@dragon.bas-net.by; vekoolga@mail.ru

Two known, alternative to each other, forms of presenting the Maxwell electromagnetic equations in a moving uniform medium are discussed. The commonly used Minkowski approach is based on two tensors; the relationships between them change their form under Lorentz transformations and take the shape of Minkowski equations, depending upon the 4-velocity of the moving particle in an inertial reference frame. In this approach, the wave equation for the electromagnetic 4-potential has a form which explicitly involves this 4-velocity vector of the reference frame. Hence, the Minkowski electrodynamics implies the absolute nature of mechanical motion. An alternative formalism (proposed by Rosen & al.) may be constructed in new variables, when the Maxwell equations are written in terms of a single tensor. This form of Maxwell equations exhibits symmetry under modified Lorentz transformations in which, everywhere, instead of the vacuum speed of light cone uses the medium speed of light c*c. Due to this symmetry, the formulation of Maxwell theory in this medium can be considered as invariant under the mechanical motion of the reference frame, while the transition must follow modified Lorentz formulas. The transition of the Maxwell equations to 4-potential leads to a simple wave equation which does not contain any additional 4-velocity parameter, so this form of the electrodynamics presumes a relative nature of the mechanical motion; also, this equation describes waves which propagate in space with light velocity kc, which is invariant under the modified Lorentz formulas. In connection with these two theoretical alternative schemes, an essential issue must be stressed: it seems reasonable to perform the Poincar´e-Einstein clock synchronization in uniform media with the help of real light signals influenced by the medium, which leads us to modified Lorentz symmetry. A similar approach is developed for a spin 1/2 particle obeying the Dirac equation in a uniform medium.

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