The direction in the 4D Space-Time continuum is lost in the scalar product.
This equation describes only Bosons – for example: photons
(It is the wave equation obtained from Maxwell’s equations of electrodynamics.)
The expansion separates space from time in the 4D Space-Time continuum.
This allows a coordinate separation among radial, angular, and time coordinates
Y(r,q,f,t) = R(r)Y(q,f)T(t)
This permits the spin to be treated as an angular coordinate, and combined with the spatial rotations
Y(q,f) ® Y(q,f)c(spin)
And here the orbital and spin angular momentum of many electrons can be combined.
Here the 4D Space-Time continuum causes spin to be an intrinsic dynamic quantity, associated with its 4D nature (and NOT angular variable).
It is bound individually to the electron (up/down) and positron (up/down) solutions.
Thus, the result is relativistically correct for a single electron charge-coupled to a nucleus.
Virtual photon exchange with all other electrons in the universe are neglected.
It includes only the connection of the spin-own-orbit interaction, and cannot include spin-other-orbit or orbit-other-orbit interactions.