  When a well-localized photon is incident on a spatially superposed absorber
but is not absorbed, the photon can still deliver energy to the absorber. It is
shown that when the transferred energy is small relative to the energy
uncertainty of the photon, this constitutes an unusual type of weak measurement
of the absorber's energy, where the energy distribution of the unabsorbed
photon acts as the measurement device, and the strongly disturbed state of the
absorber becomes the effective pre-selection. Treating the final state of the
absorber as the post-selection, it is shown that the absorber's energy increase
is the weak value of its translational Hamiltonian, and the energy distribution
of the photon shifts by the opposite amount. The basic case of non-scattering
is examined, followed by the case of interaction-free energy transfer. Details
and interpretations of the results are discussed.
