Invariance Definition and 454 Threads

I am asked to prove that the d'Alembertian operator (the 4 dimensional Laplacian operator) |_|^2 is a lorentz invariant operator. Do I just multiply the Lorentz transformation matrix by the second partial derivatives with respect to four space?

If I were to attempt to prove that the dot product of an electric and magnetic field is invariant under the conditions of Einstein's Special Theory of Relativity, how would I do this? Would the proof be very involved and complicated? Or should I just use hypothetical magnetic and electric fields...

If I were to attempt to prove that the dot product of an electric and magnetic field is invariant under the conditions of Einstein's Special Theory of Relativity, how would I do this? Would the proof be very involved and complicated? Or should I just use hypothetical magnetic and electric fields...

maybe someone else can clarify; these recent papers suggest a surprising turnaround in the quantization of General Relativity, contrary to some earlier papers by other people, they predict no quantum gravity dispersion in longrange transmission of light: On low energy quantum gravity induced...