Whereas I am using quaternions to model a "rotationally distributed scalar motion," as Larson describes it, some interesting things have happened, particularly after I realized that the progression of the natural reference system is just the "clock" concept, and it is this "clock" that forms the

*projective plane*of our interpretation of reality. That is why we normalize homogeneous coordinates to unity--bring them in sync with clock time, and normalize rotation to the unit quaternion--bring them in sync with clock space, for a consistent perspective of "reality."

When it comes to atomic rotation, there are two types: magnetic (2D) and electric (1D), as Larson describes in detail. Larson also describes that they two types are interchangeable, 1 magnetic = 8 electric, and vice versa. Larson has his geometric explanation for this, but the work of Miles Mathis opened up another perspective... quantum π, where π = 4 in a "discrete" (quantized) circle, such as you

*have*in the Reciprocal System. What that translates to is that the electric field is just a "circumference" based on a radius: circumference = 2 π radius, so c = 8r when quantized, and electric = 8 x magnetic.

The other radial measure we use is for the area of a circle, π r

^{2}, which quantizes to 4r

^{2}, which is the equation Larson uses to create the magnetic rotations for the elements. If you consider the "rotational vibration" as a circular motion, then the area =

*magnetic rotation*and the circumference =

*electric rotation*. They are NOT two, separate things, but just two

*perspectives*of the

*same*motion.

When it came to using quaternions to model this, it was easy... model the electric as a single rotation, i, j or k (does not matter which one), and the magnetic as a double rotation, ij, jk, or ki. Looked good, until I realized:

ij = k

jk = i

ki = j

Which states that electric motion and magnetic motion are the

**... if I do a "double rotation" from X to Y, then from Y to Z, I get the same result as doing a "single rotation" from X to Z. That is where I realized that you had to**

*same thing**normalize*the rotation to unity, the projective plane and "clock", which meant the full equation would have to include

*all three*rotations, so the net result was unity.

If you have a double-rotation of "i j" that was the same as a single rotation of "k", then to get back to unity, all you had to do was to multiply "i j" by (-k)... and lo and behold, all the

*inductive*(jωL) and

*capacitive*(-jωC) relations popped into existence.

That means if you have a

*magnetic*field, the

*dielectric*field forms in the opposite direction from that necessity, to balance out to unity. If you have an electric field, the magnetic field forms to balance to unity, because of the 3D structure of the universe.

Because this system normalizes to concurrent positive and negative rotations, you end up with a

*birotation*that appears mechanically as a vibration: a

*rotational vibration*.