Why are the Hamiltonian and the Hamiltonian density not Lorentz scalars? If they are to represent energy and energy density, respectively, does this make sense? (Does the energy of an object or a system have the same value for all observers? Do you measure the same kinetic energy for a plane passing overhead as someone on board the plane would?) Energy is the zeroth component of the four momentum pμ. Does one component of a four vector have the same value for everyone?