In special relativity , Maxwell 's equations for the vacuum are written in terms of four-vectors and tensors in the `` manifestly covariant '' form . This has been done to show more clearly the fact that Maxwell 's equations ( in vacuum ) take the same form in any inertial coordinate system . In special relativity , in order to more clearly express the fact that Maxwell 's ( ` microscopic ' ) equations take the same form in any inertial coordinate system , Maxwell 's equations are written in terms of four-vectors and tensors in the `` manifestly covariant '' form .