The Modified Electromagnetism and the Emergent Longitudinal Wave

The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca, Vlaenderen & Waser and Arbab theories are investigated. The different approaches are compared to each other and the relevant equations are combined. The telegrapher’s equation can be obtained and with a specific choice of the function a Klein-Gordon equation of massive scalar field can be obtained. When the Lorentz gauge is violated by introducing the first order time derivative the emergence of the photon mass and the relevant longitudinal wave for the electromagnetic wave is apparnt.