Appendix B
In the first-order spacetime del operator, 
, a gradient in time serves to exchange information between the real and imaginary components of the two field vectors, 
and 
. “Imaginary”, in this context, desigates those time-like properties of processes occurring orthogonal to the plane which represents the real component. Both planes are defined within the limited atmospheric spacetime domain. In the second-order spacetime del operator, 
, a time rate of change of the temporal gradient serves to exchange information between the real and imaginary components of the same two field quantities. In the second case, the imaginary component carries information (spin) to both the horizontal and vertical planes, which are defined within the embedding domain.
To generate the wave equations descriptive of the first component of information exchange, we employ the first-order temporal derivative and expand to separate the spatial and temporal components:
to the imaginary (
) component of the temporal derivative of , weighted by +c-1. Wave Eq. (21b) is generated by exchanging the two field quantities within the complex determinant, then solving for the 
of the temporal derivative of , weighted by -c-1:
, in place of ±c plus ¶/¶t 
above, yields wave Eqs. (22a) and (22b), respectively.