Galilean Non-invariance of Maxwell Equations Revisited

Abstract

It is universally accepted that Maxwell equations do not remain invariant under the Galilean transformation. This conflicts the principle of relativity which states that the physical law must remain invariant in the mathematical form in all inertial frames of reference. For this reason, the Lorentz transformation is invented, and the Galilean transformation is nowadays superseded by the Lorentz transformation. However, this paper challenges this widely held belief that the Maxwell equations are not invariant under the Galilean transformation. By applying the Galilean transformation to Lienard-Wiechert electromagnetic fields it is mathematically proven that the Maxwell equations indeed remain invariant under the Galilean transformation. In addition, the critical error in Lorentz's proof of Galilean non-invariance of Maxwell equations is pointed out, and it turns out that Lorentz's conclusion that Maxwell equations are not invariant under the Galilean transformation is the result of a mathematical error.