Lorentz's Galilean-Invariant Form of Maxwell's Equations in Free Space
David M. Drury
Keywords: Lorentz's version of Maxwell's equations, Galilean-invarient interaction, charged particle
A Galilean-invarient interaction Lagrangian of a charged particle moving in an electromagnetic field in free space is obtained assuming that a natural (i.e., preferred) reference frame exists for the field and that all uniformly moving observers can determine their velocities with respect to this frame. From this Lagrangian, a Lorentz force law is derived. From this Lorentz force law, Poisson's equation, and the principle of conservation of electric charge, Lorentz's version of Maxwell's equations in free space for an observer moving uniformly through the ether is obtained. These modified Maxwell's equations, the field quantities they contain, and the wave equations derivable from them are shown to be Galilean invariant. They predict experimentally-obtained electromagnetic forces on charged particles in free space if the natural frame (i.e., ether) is entrained by the earth.
