The operational meaning of total energy in general relativity

The ADM and Bondi energies are key examples of observables in general relativity. They have played a crucial role to clarify the meaning of gravitational energy, and by Noether's theorem, to understand (boundary) symmetries. In spite of their conceptual importance, they are not directly measurable: their reconstructed values from gravitational waveforms are only inferred quantities. In this talk I will present thought experiments that provide an operational meaning to both ADM and Bondi energies. I will then argue that the equivalence principle allows us to go one step further than the Bondi energy, and define a energy density of gravitational waves at null infinity, that is completely local in space, with non-locality confined to time. Finally, I will comment on a possible quantization of the Bondi energy inspired by results in loop quantum gravity.