The electromagnetic wave equation being of the same form in all intertial frames is because Newton's force is a vector quantity? I mean, if the wave equation changes its form from a intertial frame to another one, would the electromagnetic force be different in the two frames? I know that one of the Eintein's postulates is that laws of nature are invariant under change of intertial frames. Also, I know that one can argue that it should be this way independently from Newton's theory. (e.g. by guessing the Eintein's elevator). But would conservation of Newtonian force be another way to say that the electromagnetic wave equation should be the same?