Interaction-Free Energy Transmission

A gedanken experiment generalizing the Elitzur-Vaidman bomb-tester is discussed, in which energy is transferred from a photon to an atom without the photon ever going near the atom.  The photon passes through a Mach-Zender interferometer with the atom initially in its ground state, which partly overlaps the arm, and with photon tuned to be absorbed perfectly by the atom.  Detecting the photon at the dark port of the interferometer collapses the atom into the beam path, increasing its energy, but the photon could not have taken that path or it would have been absorbed by the atom.  This paradoxical effect only obtains under a specific post-selection, and thus the choice of measurement settings is crucial, and reveals a strongly contextual effect in the experiment, which also has close connection to the Hardy paradox and the 3-box paradox.  The weak values of the atom-photon system are also examined, revealing anomalous values, and an interesting narrative in which the atom gains energy by emitting a pair of virtual photons with negative energy.