This is viewed as an elastic collision between a photon and a free electron. However, the appearance of the magnetic field at the electron identifies a partially elastic or totally inelastic field coupling at the Compton wavelength, and the subsequent emission of radiation. If the "mass" of the electron is increased as in tightly bound orbital states, or the photon’s energy is decreased, the recoil approaches a Rayleigh scattering. The dependency on frequency in the photoelectric effect is consistent with the quantized states of the Bohr orbits. Collisions of photons and free particles fall between. This suggests the Compton effect may apply to the total spectrum of sub-atomic particle and field interactions including Coulomb forces.

A classical one-dimensional elastic collision between an electron [m_o] and a mass-equivalent photon [h/l c = m_x = m_o] would result in a Newtonian velocity [v_n] of,

2m_xc/(m_o + m_x) = v_n = c (1)

A similar configuration in a Compton collision gives, [cv_m = v_k²], where [v_m] and [v_k] are the relativistic momentum and kinetic energy velocities. If the mass ratio is modified and/or a two-dimensional collision is introduced,

2m_xcv_mCos f /(m_x + m_o ) = v_nv_m = v_k² (2)

where f is the recoil angle of the electron.
Substituting into the relativistic equation, v_m² = v_k² - (v_k⁴/4c² ) (2a) (See: A New Basis for Relativistic Dynamics) ,

(v_m/v_n = (1 – v_k²/4c²) (3)

Equation (2a) and [3] conform to Dirac's relativistic treatment of the energy levels of the hydrogen atom and more importantly, provide an ontological basis for fine structure splitting of spectral lines based on the dual states of Section [4] of the main paper.

The speed [v_n] is implicit in the relativistic equations. It would appear that classical mechanics has not been supplanted, but obscured. The parabolic configuration is again confirmed in (2). Furthermore, the velocity associated with kinetic energy is explicitly defined in the square of the angular velocity [v_k²]. Since this is equal to the combined linear velocities, an immediate explanation for its scalar attribute is also identified.

The Compton formula may be expressed in terms of mass,

l ’ = l + h (1 - cos f ) /m_oc º l ’/hc = l /hc + (1/ m_oc²) – (cos f )/m_oc² º (1/m_x’) = (1/m_x) + (1/ m_o) – (cos f /m_o )(4)

where l , l ’ are the initial and recoil wavelengths, f is the photon angle of recoil and m_{x ,} m_x’ are "mass" equivalents.

By setting the photon scattering to 90 degrees, its "mass equivalence" is equal to the reduced mass [m_xm_o/(m_x + m_o)] of an electron-photon pairing.

With a wavelength equal to the ground state of a hydrogen atom, the mass equivalence of the photon, or in this case the equivalent Coulomb field, would be m_oa (fine line constant). Solving the Compton equations, and adjusting the momentum of the electron by [cos f ] to maintain a perpendicular configuration provides the following,

h/mv_m = h/m_ov (5)

The equivalence is due to conservation of momentum but the scattering and the initial distribution of momentum between "mass" and velocity also identifies a field coupling and a re-established balance between material and anti-material states (electromagnetic and mechanical). The inference is also that in any interaction, the energy loss (radiation) in coupling is that of potential (magnetic) and the magnitude is in all instances equal to the reduced "mass" rather than a relativistic conversion of rest mass to energy.

As the electron approaches the nucleus, the Compton effect shows that the induced electric field approaches the magnitude of the primary field. The "scattered" radiation approaches the reduced mass of the electron. Of specific interest is where the field strength is equivalent to the proton mass, which occurs at the classical electron radius. The result is that it precisely parallels the total energies of the atom. The electron assumes the "mass" of a proton, [v_m] equals the sum of the speeds of the electron and proton, the "scattered" radiation equals the reduced mass of the electron and its speed is that of the first Bohr hydrogen orbit. The reverse inversion from proton to electron is not entirely clear and requires further study.

However, it is clear that an inversion of space, time and mass takes place at this point. It is also clear that the proton and electron are both aspects of the same fundamental particle. The inversion also applies electrostatically, since the proton charge is positive. Furthermore, by logical extension it may be stated that if penetration is greater than that allowed for the release of the electron, it will result in the creation of a neutron. This cannot be considered stable particle unless it is under the constraints of an energetic nucleus, or decays to a proton with the ejection of the electron. The decay into neutrinos, pions and muons accounts for their electrical neutrality. The sum of the masses of the muon and pion are ½ the mass of the proton divided by the "anomalous" factor in the magnetic moment of the neutron. This confirms the "mass defect" of capture (or the energy required for release) is equal to the reduced mass.