Theory of everything

This page is going to describe how I derived theory of everything. First I will try to explain what theory of everything is. Theory of everything (or unified theory of field or grand theory), is theory, that should combine electromagnetic theory with gravity theory. In other words it should explain, how the gravity is caused by the same fundamental principle as electromagnetism. Such theory was a missing piece in puzzle of knowledge of modern physics since last century, and many scientists are desperately looking for it.

But recently, I have derived my version of this theory! My theory is based on biquaternions and can be formulated also in octonions. This theory also enables us to see conceptual  origin of dark matter and dark energy, which drives  expansion of whole universe. At the moment theory doesn't explain which particles are directly responsible for these effect, but quantization of this theory should be an easy mathematical task. Let's introduce the new theory, surprisingly the derivation is extremely simple.

First assume that Einstein theory of relativity and Maxwell theory of electromagnetism are valid, but not complete theories. If we start to look at theory of relativity (let's consider the special theory of relativity first), we will soon realize, that there have been already introduced biquaternion formulations of this theory.

Let's start with writing relativistics  electromagnetic 4-potential A in a biquaternion format (1.1):

Then define in similar manner biquaternion gradient operator (1.2) :

Now try to apply biquaternion gradient operator on biquaternion of vector potential , and let's define biquaternion of generalized electromagnetic intensity, which extends classical vector of electrical intensity E (1.3):

Expressed in components we get for the right side (up to minus sign) (1.4):

With knowledge of Maxwell equations (expression of E vector using A)  and definition of vector potential as rotation of B, we can immediately identify all the components of generalized electromagnetic intensity and write (1.5):

The scalar component G, can be written as (1.6):

 As we can see, G is indeed exactly equal to right side of expression called Lorenz gauge condition (LGC), but  surprisingly it's not equal to 0 here any more! Btw why it should be equal to zero at all?  By simple logic G is on the left side of equation, and therefore it's value can be arbitrary, resp. depends on what is on the right side of the equation.  If we look at the problem in more details, we will realize, that field G can be really choosen arbitrarily, and the selection process is called gauge fixing. It can be easily proven, that any vector potential (expressed in any gauge) can be also expressed as another vector potential with G=0 by simply adding divergence of properly time dependent scalar field to it. Similar prove that every vector potential can be transformed to that one with Coulomb gauge (i.e. G≠0), can be  found for example  in reference [1].

Isn't this gauge fixing problem similar to selection of frame of reference (not inertial unless G=0) in Newton mechanics and also in general relativity? In reality this problem is very consistent with selection of frame of reference, and I assume, that case G=0 is equal to the case of free falling objects or in other words the case of zero acceleration. In all other cases, where there is a non-zero acceleration present (incl. gravitational) G  is not equal to 0. Let's look on the energy in order to understand this hypothesis better.

Let's use slightly heuristic approach and calculate biquaternion energy density W as (1.7):

Finally we get equation for biquaternion of energy density W  (1.8)                                    

Please note, that the vector of magneto-scalar energy is equal to zero, if G is a real number. The electro-scalar energy vector is equal to zero if G is an imaginary number. Otherwise both vectors are non-zero  and yield to completely new waves, so called electro-scalar and magneto-scalar waves. Also note the negative |G|^2 part of energy density scalar. This is very interesting, because negative energy density is related to gravity [2]. Moreover the absolute value |G| means, that even scalar energy from frames unreachable from our frame of reference (due to complex shift of axes) adds regularly to overall gravity. Complex phase of given G is in this case irrelevant.  This would simply explain origin of dark matter [3] and it's gravitational effect on regular matter, which is  the same as gravitational effect of the regular matter. This is regardless complex shift in axes (t,x,y,z) e.g. x'=x*exp(i*fi)  etc., and therefore my assumption is that dark matter is regular matter in frames where complex shift fi is present (e.g. due to their FTL velocity - will explain in article about Hyperspace waves (FTL)).

Also note, that the energy density is in reality equation of energy continuity (or conservation) for generalized electromagnetic energy. Thus energy contained in every volume element is decreased by outgoing electromagnetic and magneto-scalar energy (if Im(G)>0) over the time, and in the same time it's refilled by incoming vector of electro-scalar energy (if Re(G)>0). This centripetal energy would eventually conceptually explain origin of dark energy. If signature of G changes, than also direction of electro-scalar and magneto-scalar energy flows changes. Also note, that I could define G with opposite signature, and in reality I will probably redefine it so in future, because now G is the only component having minus sign in the front of it in E8 equation. In this case electro-scalar and magneto-scalar energy vector would have opposite signatures in energy continuity equation, but the direction of both energy vectors won't change, as G has opposite signature now.