(Here is a PDF version for printing.)

Some Angles From Physics
And Their Geometry
Part 3

It is interesting that these 2 cone angles occur in the same geometry, having the same cone vertex point, and are limits (min and max) of the Jitterbug dynamics.

Here we have both tetrahedra rotating together.

(Alternative Animation Mode)

Defining their cones.

(Alternative Animation Mode)

We now need to know a little bit more about FCC lattices.

Note that an orientation axis system (x-, y-, z-axis) can be defined for the Face Centered Cubic (FCC) lattice (the lattice of closest packing of spheres) such that all the vertices can be given integer valued (x, y, z) coordinates.

Further, the axes can be so oriented that the "logical even/odd sum" of the x, y, z coordinates is always even (or alternatively always odd, see below). The even/odd summation operation is summarized in the following table ("e"=even, "o"=odd):

(x, y, z) Logical Sum
(e, e, e) even
(e, e, o) odd
(e, o, e) odd
(e, o, o) even
(o, e, e) odd
(o, e, o) even
(o, o, e) even
(o, o, o) odd

The FCC lattice for which all the vertex corrdinates are "logically summed" even includes the coordinate (0, 0, 0). That is, a lattice vertex will be located at (0, 0, 0).

An example of this is the yellow lattice shown previously. The Cuboctahedron (VE) was taken as a small part of the FCC lattice. Note that it has a vertex at its center of volume. We used this center of volume vertex (corrdinate (0,0,0)) as the apex point of the cones.

Another FCC lattice can be defined in which the vertex coordinates (x, y, z) are all integers and "logically summed" odd. For this (pink) "odd" FCC lattice, there is no vertex at the coordinate origin (0,0,0). Note that in this case, the coordinate origin (0,0,0) occurs at the center of volume of an Octahedron.

(Alternative Animation Mode)

The Jitterbug motion occures between these two "even" (yellow) and "odd" (pink) FCC lattices.

(Alternative Animation Mode)

In the Electrodynamic theory of Myron Evans, as used by Tom Bearden to explain how his group's Motionless Electrical Generator (MEG) device can produce more energy out than is put in, it is shown that the applied voltage induces a dipole moment in the material. The dipoles act as gates allowing energy to flow into the device.

Could it be that Universe consists of 2 different spaces, represented here as 2 different FCC lattices? Could it be that the induced dipoles allows the energy of one space to be transduced into energy in the other space? Is the Jitterbug the dynamics which allows this to happen?

Perhaps these 2 lattices are the space and anti-space of particle physics. Particles consist of some dynamic system of the yellow lattice while antiparticles are the same dynamic system only of the pink lattice.


The Quantum Mechanical angular momentum, space quantization is described in any introductory Modern Physics or Introduction to Quantum Mechanics text. For example:

And many others....

For Ampere's force equation between 2 Ampere current elements see

These references also describe why an Amperian current element is not to be considered to be the same as electron drift currents.

These authors also point out that the Ampere force equation was not liked by some researchers of that time because there was no reason for the seemingly arbitrary angular arrangement resulting in a zero radial force. This is the 35.264389...° angle illustrated above. I wonder why researchers of that time complained about this angle but not the corresponding zero force angle in the dipole force equation.

For the dipole force equation, see any of the "standard" Electrodynamic texts. For example:

Curiously, and as the Graneau references point out, Ampere's force equation is not to be found in these or other "standard" Electrodynamic texts, yet Ampere's force equation is known to be experimentaly valid.

An introduction to Tom Bearden, et. al. Motionless Electric Generator can be found in the following references:

Myron Evans has published many papers on higher guage symmetry electrodynamics. Here are just a couple of references.

Most of this material, with different graphics was originally presented on my web page here.

Go To: Home Page
Part 1 Part 2

Usage Note: My work is copyrighted. You may use my work but you may not include my work, or parts of it, in any for-profit project without my consent.