All of the mathematical formulations of quantum mechanics describe the interaction between radiation
and atoms, but we show here that only Einstein has been able to establish a solid logical connection
with classical theory. His methods are used to interpret the other mathematical models by requiring
that observables be described in a physically-defined coordinate system and that there be strict
adherence to the conservation of momentum. The properties of momentum exchange are included in a
quantum oscillator, or clock, by replacing the non-relativistic Hamiltonian model with a relativistically
correct Lagrangian model. Equal contributions are assigned to photon, electron, and nucleus; and
field boundaries are defined that coincide with the electron shells. The fields of the particles superpose
linearly, but otherwise their physical integrity is maintained throughout. The Lagrangian model
accounts for the 720 degree rotation of a wave function as an initial 360 degree electromagnetic wave
cycle (photon absorption) followed by a second wave cycle (photon emission), yielding two wave cycles
to correspond with one complete electron cycle. The abstract space of quantum mechanics is replaced
by a real classical space.
