Abstract:
From a theory of an abstract quantum information the theory of general relativity can be deduced by means of few and physically good founded reasons. "Abstract" quantum information means that primarily no special meaning is connected with it. Therefore it is named with a new denotation: Protyposis. From the Protyposis and by using group-theoretical methods follows a cosmological model, which has an isotropic and homogeneous metric and solves the so-called cosmological problems. The Protyposis is subject to an equation of states for energy density and pressure that fulfils all the energy conditions and that also gives an explanation for the "dark energy". If it is demanded that the relations between spacetime structure and the material content should remain valid for variations from this ideal cosmology, then general relativity results from this quantum theoretical considerations as a description for local inhomogenities.

Abstract:
There are now at least eight experiments extending over more than 100 years that have detected the anisotropy of the speed of light, implying the absolute motion of the detecting apparatus through a dynamical space. This light-speed anisotropy is consistent with relativistic effects and Lorentz symmetry, contrary to prevailing beliefs in physics. The theoretical and experimental evidence implies that physics has failed to realise the existence of a dynamical 3-space, and that motion relative to that space is the cause of various relativistic effects, as proposed by Lorentz in 1899. This has resulted in a necessary generalisation of the Maxwell, Schrodinger and Dirac equations, which then provide an explanation for gravity as an emergent phenomenon within the new physics. From the generalised Dirac equation we show that the spacetime formalism is derivable, but as merely a mathematical construct whose geodesics arise from the trajectories of quantum wavepackets in the 3-space. However the metric of this spacetime is shown not to satisfy the Hilbert-Einstein equations, except in the special case of the Schwarzschild metric. Hence we demonstrate that the successes of the General Relativity formalism have been more illusory than real, that its successes are in fact quite limited, which explains why it failed to account for the bore hole anomaly, the so-called `dark matter' spiral galaxy rotation anomaly, the systematics of black hole masses and so on. It also failed in that the dynamics of the 3-space is determined by two fundamental constants, namely G and the fine structure constant alpha.

Abstract:
In this work we present a study of a new method to prove the equation of the gravitational red shift of spec-tral lines. That’s according to the generalized special relativity theory. The equation of the gravitational red shift of spectral lines has been studied in many different works, using different methods depending on the Newtonian mechanics, and other theories. Although attention was drawn to the fact that the well-known ex-pression of the gravitational Red-Shift of spectral lines may be derived with no recourse to the general rela-tivity theory! In this study a unique derivation has been done using the Generalized Special Relativity (GSR) and the same result obtained.

Abstract:
Einstein relativity theory shows its high capability of promoting itself to solve the long stand physical problems. The so-called generalized special relativity (GSR) was derived later, using the beautiful Einstein relation between field and space-time curvature. In this work we re-derive (GSR) expression of time by incorporating the field effect in it, and by using mirror clock and Lorentz transformations. This expression reduces to that of (GSR) the previous conventional one, besides reducing to special relativistic expression. It also shows that the speed of light is constant inside the field and is equal to C. This means that the observed decrease of light in matter and field is attributed to the strong interaction of photons with particles and mediates which causes successive absorption and reemission processes that lead to time delay. This absorption process makes some particles appear to move faster than light within the field or medium. This new expression, unlike that of GSR, can describe time and coordinate relativistic expressions for strong as well as weak fields at constant acceleration.

Abstract:
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.

Abstract:
Transfinite graphs have been defined and examined in a variety of prior works, but transfinite digraphs had not as yet been investigated. The present work embarks upon such a task. As with the ordinals, transfinite digraphs appear in a hierarchy of ranks indexed by the countable ordinals. The digraphs of rank 0 are the conventional digraphs. Those of rank 1 are constructed by defining certain extremities of 0-ranked digraphs, and then partitioning those extremities to obtain vertices of rank 1. Then, digraphs of rank 0 are connected together at those vertices of rank 1 to obtain a digraph of rank 1. This process can be continued through the natural-number ranks. However, to achieve a digraph whose rank is the first infinite ordinal $\omega$ (i.e., the first limit ordinal), a special kind of transfinite digraph, which we call a digraph with an "arrow rank" must first be constructed in a way different from those of natural-number rank. Then, digraphs of still higher ranks can be constructed in a way similar to that for the natural-number ranked digraphs. However, just before each limit-ordinal rank, a digraph of arrow rank must be set up.

Abstract:
It is shown that Ohm’s law is not only the main electrical engineering law, but also a generally scientific worldview law of the extreme significance, as in the interpretation of Steinmetz it proves physical reality of imaginary numbers theoretically and experimentally in the most indisputable way. Thus, it refutes the principle of light speed non-exceedance, which is fundamental in the special theory of relativity. Moreover, unlike the MINOS and OPERA experiments recognized by physical com-munity as not enough reliable, which were conducted for the same purpose, alternative experiments were performed during the research of oscillation processes in linear electric circuits. Therefore, they are absolutely reliable and conclusive as can be repeated and verified in any electrical engineering laboratory. The principle of phy-sical reality of imaginary numbers proven by the electrical engineering experiments is generally scientific, since mathematics is the universal language of the exact sciences. Therefore, all scientific theories and hypotheses in quantum mechanics, relativity theory, geo-physics, cosmology, optics, radio electronics and other sciences should be adjusted accordingly, given the principle of physical reality of imaginary numbers. There is an example of how this can be done in the special theory of relativity and astrophysics. This approach allowed explanation of dark matter and dark energy, which correspond to the invisible parallel universes existing in extra dimensions.

Abstract:
An ordinal-valued metric taking its values in the set of all countable ordinals can be assigned to a metrizable set of nodes in a transfinite graph. Then, a variety of results concerning nodal eccentricities, radii, diameters, centers, peripheries, and blocks can be extended to transfinite graphs.

Abstract:
Nonstandard digraphs and transfinite digraphs have been defined and examined in two prior technical reports. The present work examines digraphs that are both nonstandard and transfinite. This requires a combination in certain ways of the techniques used in the prior two works. We first construct herein nonstandard transfinite digraphs for all the natural-number ranks. Then, a special kind of nonstandard transfinite digraph having the "arrow rank" $\vec{\omega}$ needs to be constructed. Once this is done, the first limit-ordinal rank $\omega$ can be attained. This procedure can be continued on to still higher ranks.