QUANTUM GRAVITATION.

The certificate of the copyright ¹ 8493 – 30.09.2003ã.

The state department of the intellectual property.

(has translated daughter Olga)

 

             For the first time the concept of gravitation of classical laws of gravitation has been determined by Newton. After creation of the Special Theory of the Relativity, classical relativistic gravitation of the General Theory of the Relativity has been created.

             Within the framework of the Quantum Theory of the Relativity, in technology of dynamical axioms, Quantum Gravitation is created.

             In Euclid’s axiomatic as a special case of technology of dynamical axioms, Quantum Gravitation in mathematical trues, passes in classical relativistic gravitation of the General Theory of the Relativity. Its not relativistic limit gives classical gravitation of Newton.

                                    1. PROBLEMS OF THEORIES OF GRAVITATION.

             Now gravitational interaction is well investigated, submitted in mathematical models, and laws of gravitation are used in practical calculations.

             Problems of gravitation begin at definition of mathematical true of laws of classical gravitation of Newton and classical relativistic gravitation of the General Theory of the Relativity of Einstein.

             In classical gravitation of Newton,

F=GMm/R2,                            F=gm,

at overlapping the centers of cooperating weights (R→0), forces of gravitation (F → ∞), and acceleration of " free falling » (g→ ∞)  weights (m) is equal also, in a gravitational field grow indefinitely.

             On the one hand laws of gravitation are valid and reflect real gravitational interaction of weights. On the other hand in the nature there are no infinite forces and is accelerated. 

             This fundamental problem of mathematical true, in real laws of classical gravitation of Newton, the decision has no. The same problem of mathematical true takes place for radial force of interaction of charges in real law of Kulon.

             Infinite growth of acceleration of weight  in a gravitational field, gives indefinitely big speeds of this weight. However after creation of the Special Theory of the Relativity it was found out, that speed of weight  cannot exceed speed of light . For Einstein imperfection of classical gravitation of Newton was obvious. Einstein the first has decided to connect classical gravitation of Newton to relativistic dynamics in space of speeds but so that they followed from more General Theory of the Relativity. It and has named it. 

             Already in the General Theory of the Relativity dynamics of Criteria of Evolution in space of speeds had relativistic limits. The classical law of gravitation of Newton was investigation of not relativistic limit of the equation,

 

                                   F=GMm / R2(1-GM / Rc2),                 (GM / R)<<c2 .

 

             This equation follows from the equation of relativistic dynamics existential a component already in a gravitational field.

 

            1).c2 – (1/2)(cx2 = GM/R) = (cY2 = Ï ≠ 0);                 2). c2(1 –  GM/2R c2) = ( ÏY ≠ 0) = c2;          3). (X2/T2)(1 – GM/2R c2) = (ÏY ≠ 0) = c4/c2,

4). X2(1 –  GM/2R c2) = ( ÏY ≠ 0) = c4/b2 = (F=Ï2)/(F/m)2,   5). F= m2/X2(1 –  GM/2R c2),             6). m2 = GM2, (G)1/2 = cosαX

7). F= GM1M2 / X2(1 –  GM/2R c2),

 

             Such equation in turn, follows from the law of preservation of full energy (E = mc2), which Einstein has taken for a basis. With high accuracy of calculations, such equation gives a real deviation of rays of light in a gravitational field of the Sun. In strict mathematical trues it passes in òåíçîð Einstein in Riemann’s space,

 

PKT – (1/2)PgKT = kTKT

 

as the equation of the General Theory of the Relativity.

Already distances of the centers of weights could not approach up to zero (R≠0). And the space of speeds in a gravitational field, with nonzero gravitational ( Ï ≠ 0)  potential, could not exceed speed of light

cx2 << c2 .

             Problems of classical gravitation of Newton have been solved by Einstein in strict mathematical trues of the General Theory of the Relativity.

             It is necessary to note, that tensor of  Einstein it is mathematical true of Riemann’s space in Einstein's conditions, as the multiplication table. To change if it is impossible. And with physical interpretation in a gravitational field, Einstein could think up this mathematical true only. It is possible to argue on physical ideas or conditions applications òåíçîðà Einstein. But nobody can already change this mathematical true of "multiplication table", a potential field in Riemann’s space.

             In a basis of mathematical true òåíçîðà Einstein Einstein's deep physical idea – a difference of relativistic dynamics in two points of a potential field submitted Riemann’s tensor lays. And on Einstein's (g KT)1/2 = 1  conditions, one of them is resulted to Euclid’s spac. In not relativistic limit the second point too is resulted to Euclid’s space, and the theory passes in classical gravitation of Newton.

In it essence of classical relativistic gravitation. And classical gravitation of Newton, and classical relativistic gravitation of the General Theory of the Relativity of Einstein, are confirmed with experiment and there correspond realities.

However this, not last in Euclid’s axiomatic mathematical true of classical relativistic gravitation, too has a problem of gravitational radius of any weight,

 

RG = GM / c2.

 

In a surface of such sphere R = RG  which have named « a black hole », forces and acceleration of weight (m) in a gravitational field of such sphere, again increase is boundless. Such forces are not present in the nature. If force of gravitation indefinitely big, our planet already would be in the nearest to " a black hole ». However we sit and we read further. 

Einstein has devoted this problem whole clause (Å.t.2, page 514, 1939 year.). It has noted in particular: « …Shvarcshuldovsky’s singularity at  r = 2GM / c2 , are absent in the nature as the substance cannot be concentrated arbitrarily, otherwise particles it is achieved speeds of light ». So the founder of classical relativistic gravitation of the General Theory of the Relativity has told. In technology of dynamical axioms, the mathematical true of such statement consists that

RG/K = cosαX = (G)1/2 ,            RG < K ,    K = (Y2/Y0) ,      RG  = Y0 ,

 

at presence of a constant(G), gravitational interaction in this case, the radius of curvature of a trajectory K, always is more than radius of sphere of gravitational radius RG. From here impossibility of radial speed limit of light in a potential field   of mass trajectories, in mathematical trues.

             Such problems of mathematical true R = RG in Einstein's classical relativistic gravitation, and (R=0)in classical gravitation of Newton – decisions have no mathematical true. These are fundamental and insoluble in Euclid’s axiomatic of a problem of theories of gravitation. However in the nature of real gravitation of such problems is not present.

Question, what laws of real gravitation, without problems?

             Presence of the specified problems in mathematical trues of theories of gravitation defines areas and conditions in which these theories of gravitation are void. In this connection there is a set of the questions which are not having answers. For example:

             - that such the center of weights (R=0)?

             - what gravitation in the center of weights or on a surface of sphere of gravitational radius if forces of gravitation are not infinite? What laws of these forces of interaction in the center of weights?

             - that such gravitation in general? What relationships of cause and effect of gravitation with other fundamental forces of interaction, in uniform spaces - matters?

             As a matter of fact, after creation of classical gravitation of Newton and classical relativistic gravitation of the General Theory of the Relativity of Einstein, there were fundamental problems of theories of gravitation. They have no decisions in mathematical trues. 

1. A question of unity of quantum relativistic dynamics existential a component of an electro(Y+ = X-) magnetic field of a photon (Y+ = γ)  and its  (Y- = X+)  mass trajectory. The question is a reality of a deviation of its trajectory in a gravitational (X+) field of the Sun - star.

 

c2 – (1/2)cx2 = (cY2 = Ï = gR),

 

This question has remained open, and not solved in the theory.

             2. The question quantum potential (Ï = gKT), fields of gravitation « outside of a powerful matter », has remained open.

             3. Program of Maxwell  « … descriptions (the author - uniform) a physical reality by means of fields », has remained not executed.

             4. The question internal spaces - matters of sphere of gravitational radius R<RG of a powerful matter, as well as a sphere - point of an individual, indivisible charge, has remained open.

             5. A question of Newton about « … the strongest interaction » in the center of weight, and it is equal and in the center of an indivisible charge   (R → 0), both in the law of Newton, and in law of Kulon, in uniform mathematical model of radial forces, has remained open. There is no even a basic idea of its decision. The charge appeared fractional in quarks. But the charge of an electron  does not contain (positron) of quarks. Then that such a charge in general? Any of theories of answers to such questions does not give. There are no even basic ideas. And it not a unique problem in physical theories.

             However the physical reality uniform spaces - matters nevertheless comprises decisions of all these questions and problems.

             With finding-out of laws of quantum relativistic dynamics in « the Quantum Theory of the Relativity », there is an opportunity to define mathematical trues of quantum potential fields. As the component, speech about quantum potential fields with existential components of Electromagnetic (Y+ = X-)  and mass (Y- = X+) fields of interaction separately, in uniform Y+ = X-), (Y- = X+)  spaces - matters the question is quantum relativistic dynamics existential. Thus there are conditions of transition from one potential fields  to another’s.

             Equations of Maxwell are mathematical true of a special case of the integrated equations of Electro strong Interaction of nucleons of a nucleus. (« Electro strong interaction of a nucleus »). Then quantum relativistic gravitation should comprise mathematical trues:

             - classical and quantum relativistic dynamics with conditions of transitions,

             - electro strong interaction of nucleons of a nucleus,

             mathematical true of Einstein’s tensor in the General Theory of the Relativity, as special case fixed  (gKT = const), (gKTC = 0),   conditions in variable (quantum) gravitational potentials   (gKT ≠ const), (gKTC ≠ 0)  

             mathematical trues of laws of classical gravitation,

Except for it mathematical trues of quantum potential   fields of gravitation, should contain conditions of transition to quantum potential   fields of electric charges without mutual exception in uniform spaces - matters. For example, the indivisible quantum of a space - matter of a proton has weight which forms a potential   field of gravitation, and a charge which is consequence of its potential electric   field. And mathematical trues of quantum potential fields should solve:

             Problems of infinity and uncertainty laws of classical gravitation (R → 0),  in the center of weights or charges, and relativistic gravitation (in a surface of sphere R → RG).

             problems of sources of a potential field of gravitation and a charge,

             quantum character and properties of such potential fields,

             - conditions of transition to classical potential gravitational and electric fields.

The decision of such problems and tasks opens new prospects. These problems are solved behind frameworks of the modern theories created in Euclid’s axiomatic, as a special case of dynamical axioms.

 

2. QUANTUM GRAVITATION.

 In dynamical axioms uniform spaces - matters, covariant dynamics vector a component of charging and mass fields is considered in allocated directions of Euclid’s space.

For each of them in conditions of Global and Local Invariancy, the uniform mathematical true of classical and quantum relativistic dynamics is submitted.

In uniform consideration relativistic of covariant dynamics vector a component of charging and mass fields in allocated directions of Euclid’s space (in conditions of turns with displacement within the limits of a dynamical corner of parallelism of trajectories), the mathematical true of deformation of Euclid’s space is submitted. Thus appears quantum a potential field, as consequence.

The fixed difference of such quantum relativistic dynamics in two points (1 and 2) gives the fixed potential field in mathematical true òåíçîðà Einstein. However the internal maintenance of such quantum or fixed potential field, and physical essence of relativistic gravitation, as against of Einstein’s tensor, it is opened in a full kind, including charging and mass fields of substance as a whole. Causes and effects of such quantum or fixed potential field are opened. In the General Theory of the Relativity the fixed points of a potential field of large-scale quantums of a space - matter of planets, stars, galaxies are considered.

In separate consideration of charging fields, in same mathematical true, the submitted transformations pass in electromagnetic dynamics with mathematical true of equations of Maxwell. Such equations give an induction of mass fields and an induction of relativistic weights in variable fields of Strong and Gravitational Interaction. They are similar to the equations of an induction of a magnetic field in a variable electric field. Speech about the equations of the gravitational waves similar to electromagnetic waves.

In both cases in a full kind, the component uniform the spaces - matters, submitted in the theory of " Electro strong interaction of a nucleus », with precisely certain conditions of dynamics of electromagnetic and gravitationally-mass fields of interaction in uniform spaces - matters the question is mathematical true the integrated equations of dynamics vector.

Both conditions of the integrated equations of dynamics, are submitted in a uniform case Globally invariant uniform to a space - matter. Dynamics of such trajectories in the closed contour, within the limits of dynamical corners of parallelism of trajectories with quantum relativistic dynamics , gives quantum charging and mass potential fields within the limits of corresponding constants of interaction.

In technology of dynamical axioms, Locally invariant conditions of quantum relativistic dynamics in quantum charging and mass fields of interaction separately are determined. By the example of quantums of a space - matter of indivisible protons and an electrons, Locally invariant conditions of quantum relativistic dynamics are considered. These are conditions of the closed contours of trajectories, with a dynamical corner of parallelism, within the limits of corresponding constants of interaction. Such conditions in mathematical trues give a quantum field of Strong Interaction of a proton and a quantum electric field of an electron. In the same mathematical trues conditions of formation of the charged and neutral quantums of Strong Interaction of nucleons of a nucleus in electro strong Interaction are considered. Levels of quantum gravitational fields, since a nucleus of atoms are submitted.

Quantums of Strong Interaction of a nucleus of planets, stars, the galaxies corresponding to their nuclear matter are submitted. Already in the center  any weight or a charge, (in conditions of Local Invariancy, in technology of dynamical axioms) the closed contours accordingly charging or mass trajectories (with quantum relativistic dynamics take place within the limits of dynamical corners of parallelism). The nonzero radius   of these closed contours, in mathematical trues, passes in quantum dynamical "surface" of «a black hole ».

Thus, in strict mathematical trues solve fundamental problems of classical gravitation of Newton, with the same problem of law of Kulon, and classical relativistic gravitation of the General Theory of the Relativity of Einstein. Opportunities of such mathematical trues in creation of indivisible quantums of a space - matter of new power substance 15,3TeV,  on counter positrons, and 17,6TeV,  on counter antiprotons are shown. An electron-positron and a proton – antiproton of reaction give unstable particles of these energies.

The law of return squares of distances follows from ratio in mathematical trues of quantum relativistic dynamics for radial forces. It used by Newton and Kulon in the laws of classical gravitational and charging interaction.

In technology of dynamical axioms limiting (hc) radiuses of action of such radial gravitational forces of usual substance of atoms are submitted. Radial forces deformed Euclid’s  spaces in levels of physical vacuum, have dependence on own space of speeds. In technology of dynamical axioms calculations of limiting   radiuses of action of radial gravitational forces, substances of a nuclear matter of planets, stars, galaxies, in own levels of singularity of physical vacuum are shown.

Such forces in mathematical trues, pass on the strength of classical gravitation of Newton and relativistic gravitation of the General Theory of the Relativity, as to special cases.

             Thus:

- the submitted mathematical trues of a space - matter in the dynamical axioms - facts, solve the specified problems as tasks. These decisions have the coordinated models of all types of fundamental interaction and their relationships of cause and effect.

- in these mathematical trues conditions of transition between types of fundamental interactions are shown.

             - classical and relativistic forces of gravitational fields are a special case of the general quantum radial forces in power levels of physical vacuum.

             - in mathematical trues problems of infinity and uncertainties of classical and relativistic theories of gravitation are solved. 

             - power levels of physical vacuum, with potential fields of radial forces of interaction in these levels, on extremely big and extremely small distances Are submitted.