Owing to the Hamiltonian constraint in general relativity, the total energy is zero. (To avoid ambiguity, here energy is DEFINED as the corresponding part of the ADM Hamiltonian.) Since matter has positive energy, it implies that gravitational field has negative energy. Does it mean that gravitational waves also have negative ADM energy? If no, then why not? If yes, then does it mean that detection of gravitational waves should manifest as a REDUCTION of the detector energy?