1. The problem statement, all variables and given/known data Under what conditions is the quantity [tex]E^2+B^2[/tex] relativistically invariant? 2. Relevant equations [tex]E\cdot B[/tex] and [tex]E^2-c^2B^2[/tex] are invariant. (Also Lorentz transformation laws for E and B which I won't type here.) 3. The attempt at a solution I think you can just subtract multiples [tex]E^2-c^2B^2[/tex] from the given quantity to show that [tex]E^2[/tex] and [tex]B^2[/tex] must also be separately invariant if the given quantity is invariant, which I think happens only if E and B are both zero. But I have been told this is wrong by someone.