I didn't do much
in 2014 on my independent research topics, as I was busy days and nights
with my work. Atmosphere in the company was still stormy, and many
people lost their jobs. I was fully dedicated to my work
of software engineer. I also enjoyed my new wife, as I got married in
march. But you can't stop ideas they are coming all the time! Therefore late in 2014 and mainly in summer 2015 I really made a breakthrough. In the autumn 2014, something
reminded me that in 2013, just before I left Prague, in a
flash of intuition I wrote on paper very simple quaternion equation. As I
suspected that equation, contained all electromagnetism on one single line,
and had barely 3 symbols besides equal and minus signs. Here is the summary in it's full beauty: (TODO
 CHECK FOR ALTERNATIVE DERIVATION WITH OPPOSITE SIGNUM OF SPACE
ELEMENT, NOTE +/ CORRESPONDS TO CHANGE OF SPACE DIRECTION, OR TIME !!!
DIRECTION. IN SECOND CASE THE WHOLE EXPRESSION IS NEGATIVE THOUGH)
The biquaternion eight intensity E8 is generalized version of electrical intensity, known from Maxwell equations. The subscript "8" I added later, to emphasize, that this intensity has up to 8 real dimensions (or four complex). As expected this simple equation could be expanded to more complex expression, which shows relation to electromagnetic quantities E,B (these are written as purely imaginary quaternions with real components). Purely imaginary quaternion means, that it contains only vector part, therefore neither E or B has scalar component in the following equation. Immediately I have also realized, that the mysterious indwelling subexpression, that I started call G, is indeed equal to expression from Lorenz gauge condition (LGC), but it's not equal to 0 here anymore! Instead G it's on the left side of equation (and thus can have any value): I
knew already in Prague, that this magical and simple expression
represents complete theory of electromagnetic field. This includes both
field components B and E as well as all Maxwell
equations. Some quantities like charge
density or vectors of current densities are a bit obscured
in this equation, but they are inherently still there. E.g. if we
calculate quaternion Laplacian (note there are even 2 versions or
components of
this operator which differ in sign at space components), we clearly see
current densities Ji. To see this immediately, either knowledge of wave equation for
vector potential is needed (which have been derived based on LGC
assumption e.g. G=0, or we can see this also in other way.
Let's also set G=0 i.e. LGC, for which this wave equation was
derived, and then we apply appropriate quaternion gradient (also has 2
variants which differ in sign at space components ) also on E8. Because of LGC precondition, E8 has
now zero scalar component, and is a purely imaginary quaternion
according to quaternion terminology. By expression of components of
quaternion gradient of E8 we can immediately
see that the real part of the equation express rot(B) vector operator i.e. Ji. The similar is valid for imaginary part of E8, i.e. electrical intensity. When G=0 and quaternion gradient is applied on E8,
we get div(E), and on right side free charge density divided by c.
(Note: but there is also one more element related to divergence of
vector potential  this should be checked, why is there this extra component?).
From the above explanation, it is clear, that even though obscured, the current density and charge density, is there inherently in the one line equation of electromagnetism. Why I call the new element G? Well simply G stands for gradient or gauge. Gradient because it can be generated by 4dimensional gradient of vector 4potential. Space components have much higher influence, in this case. But we can call G also gauge, and in electromagnetism generally this gauge can be any (see e.g. Lorentz gauge, Coulomb gauge or Weyl gauge on wikipedia). But there are infinitely many possibilities how to select gauge. And any gauge can be converted to Lorentz gauge (or LGC or G=0). This is very similar to selection of inertial frame in classical Newton dynamics or even theory of relativity. Therefore I started to hypothesize, that this similarity is not random, but G corresponds to acceleration or in other words to GRAVITY!!! I other words, if G=0 (LGC) there is no acceleration or gravity. If G<>0 then there is some acceleration or gravity in the frame of reference. This connection I anticipated even earlier, but I got closer to that conclusion only on the beginning of year 2016 when I was in Richmond. Here I'm going to show also another indication to this conclusion. Let's start with energy calculation of generalized electromagnetic field. I have calculated the energy density & flow W as:
Note that except of 3 standard electromagnetic elements, which are
exactly equal to elements from standard electromagnetic theory (magnetic
energy, electrical energy and flowing
electromagnetic energy i.e. Poynting vector) there are also other two
elements containing G. First element has scalar and the second one
vector character. Please note, that about formula is valid only for real G, and in this case there is no magnetoscalar energy. For complex G, you must use full formula, which can be found in Theory of everything.

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