375
D. Special Relativity: Invariance and Covariance
convince the reader of the power of the 4-vector notation for this purpose:
compare the ‘by inspection’ covariance of (2.18) with the job of verifying
Lorentz covariance starting from the original Maxwell equations (2.1), (2.2),
(2.3) and (2.8)! The latter involves establishing the rather complicated transformation law for the fields E and B (which, of course, form parts of the
tensor F
μν ). One can indeed show in this way that the Maxwell equations
are covariant under Lorentz transformations, but they are not manifestly (i.e.
without doing any work) so, whereas in the form (2.18) they are.
D. Special Relativity: Invariance and Covariance
convince the reader of the power of the 4-vector notation for this purpose:
compare the ‘by inspection’ covariance of (2.18) with the job of verifying
Lorentz covariance starting from the original Maxwell equations (2.1), (2.2),
(2.3) and (2.8)! The latter involves establishing the rather complicated transformation law for the fields E and B (which, of course, form parts of the
tensor F
μν ). One can indeed show in this way that the Maxwell equations
are covariant under Lorentz transformations, but they are not manifestly (i.e.
without doing any work) so, whereas in the form (2.18) they are.