This matrix determines in which dimension we end up when multiplying vector components.
The result of multiplying vectors and can obviously be written as a 4x4 matrix!
We honor this finding by defining
Looking rigorously at Eq. 2 yields
We can therefore write
This also gives us the following sums and differences:
With our new algebra we can square this equation without producing ambiguities.
This turns out to be the well known cosinus relationship for arbitrary triangles.
Let's look at Eq. 7 first.
Our model for an electron is two pretonic charges rotating around each other with speed . This gives us the following for Eq. 7.
In the special case of the two pretonic charges constituting an electron and are parallel with opposite direction and perpendicular to at all times. We can therefore simplify to
So Eq. 7 gives us Coulombs law if we look at two pretonic charges rotating with around each other. In the general case (two arbitrary charges with arbitrary velocities) we end up with an additional term
Let's look at Eq. 8 and Eq. 9 now.
A moving charge generates a field at distance. A target charge feels a force if this field (at the location of ) changes. The field at the location may change due to a change of (limited propagation speed) but the more probable reason is that moved to another location with a different .
Equations Eq. 10, Eq. 11 and Eq. 12 describe all known electromagnetic phenomena (Lorentz Force, Biot-Savat, Lenz Law,...).
Source: Robert Distinti (www.distinti.com)
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