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The usual approaches to the definition of energy give an ambiguous result forthe energy of fields in the radiating regime. We show that for a masslessscalar field in Minkowski space-time the definition may be rendered unambiguousby adding the requirement that the energy cannot increase in retarded time. Wepresent a similar theorem for the gravitational field, proved elsewhere, whichestablishes that the Trautman-Bondi energy is the unique (up to amultiplicative factor) functional, within a natural class, which is monotonicin time for all solutions of the vacuum Einstein equations admitting a smooth``piece'' of conformal null infinity Scri.Comment: 8 pages, revte

Uniqueness of Scalar Field Energy and Gravitational Energy in the Radiating Regime