Photon and Electron Interactions from Moving Photon Sources in an Inertial and non-Inertial Frames of Reference

In 2016, for the first time to the author’s knowledge, the conservation of energy and momentum was balanced for an emission and absorption of a photon that results in motion of an atom or molecule [1]. This balancing was performed by reasoning and algebra. In this paper a formal balancing of the conservation laws is presented. This includes a new operator that allows a photon to be separated between an observed value of the photon, and a value that is the difference between the observed and the emitted value of the photon at the source, for a single atom in space and a single photon source. A new method for applying the conservation of momentum to an absorption and emission of a photon is also presented, where the coordinate system, for the emitted photon, is shifted so the emitted photon is moving in the same direction as the absorbed photon.