Lorentz transformation in Maxwell equations for slowly moving media

Abstract

We use the method of field decomposition, a technique widely used in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The "deformed" Maxwell equations derived under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame even in the SVA, not just the position and current density as in the Galilean transformation. This marks the essential difference of the Lorentz transformation from the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation the covariant integral form in which the electromotive force can be defined as a Lorentz scalar independent of the observer's frame. No evidences exist to support an extension or modification of Maxwell equations.

arXiv comment16 pages, 1 figure, 3 tables. Section VI is added about integral forms of Faraday and Ampere laws for moving surfaces. Part of Section IV and V are rewitten

References in corpus (5)

• The Exact Solution of the Riemann Problem in Relativistic MHD
• Kubo formulas for relativistic fluids in strong magnetic fields
• Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
• Non-resistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation
• Comments on the expanded Maxwell's equations for moving charged media system

Cited by in corpus (2)

• The expanded Maxwell's equations for a mechano-driven media system that moves with acceleration
• Maxwell's equations for a mechano-driven, shape-deformable, charged-media system, slowly moving at an arbitrary velocity field v(r,t)