Reference: Moore, Thomas A., *A General Relativity Workbook*, University Science Books (2013) – Chapter 7; Problem 7.7.

We’ve worked out earlier the scalar quantity . We can check this for the case of a Lorentz transformation in flat space-time. We found there that

Calculating the invariant in the new system we get

since . All the cross terms involving the product of a component of and one of cancel out between lines 2/3 and 4.

DanIsn’t the problem supposed to prove that the quantity =2(B^2-E^2)?

gwrowePost authorI had already worked out earlier that , so Moore’s problem 7.7 in effect duplicates his problems 4.8 and 4.9. Here I was just verifying that is actually invariant under a Lorentz transformation.