Recall that a covariant 4-vector is obtained from a contravariant one by changing the si...

Recall that a covariant 4-vector is obtained from a contravariant one by changing the sign of the zeroth component. The same goes for tensors: When you “lower an index” to make it covariant, you change the sign if that index is zero. Compute the tensor invariants

in terms of E and B. Compare Prob. 12.47.

Reference prob 12.47

(a) Show that (E . B) is relativistically invariant.

(b) Show that (E² − c²B²) is relativistically invariant.

(c) Suppose that in one inertial system B = 0 but E ≠ 0 (at some point P). Is it possible to find another system in which the electric field is zero at P?