3.3  The Law of Motion for Sources

We shall save all designations and definitions of the previous item (3.2), but we shall replace identifications (3.2.18.E) on following:

Then

and the law of motion of charged sources (ONs) in a field of electron will be following:

Here the impulse of source p and Lagrangian L are referred to charge unit, but it should remember, that the speech goes about motion of the infinitely small charged source (ON). In an equation (4.a) δq is simply reduced. The top mark concerns to positively charged sources, and bottom mark – to negatively charged ones. The complete absence of empirical constants is the large advantage of a equation of motion.

The vector of speed satisfies to kinetic equation (3.2.3). The impulse, which is received by multiplication of vector of speed on scalar function of distance up to electron symmetry centre satisfies to a dynamic equation (3). This procedure of p determination is defined by law of a impulse moment conservation along a global line of a moving source – integral of a motion equation.

For apical speeds (vertex velocities), satisfying to condition k=1, we shall get:

At the same time following equations are fair:

We shall omit a procedure of a electron individualisation from all collection of two charge marks FM-field driven sources and decomposition of all quantities on own (individual) and portable (external), which is coming to develop yet. Before gaining a result, we shall choose the top minus mark in (6), (7) and multiply both components by some positive factors, which for real distances in atom (r>>1) we shall consider as constants. The received equation will describe an electron motion in a field of a hydrogen atom nuclear.

It by a surprising image reminds a Joseph John Thomson procedure of the Planck's constant obtaining by selection of constants for Coulomb attraction to a centre of atom and repulsion from it which is proportional to a third index of reverse radius. This mechanism, by the idea of electron discoverer, should define stability of atom in his model and allowed to combine it with a Max Planck hypothesis.

For the thousandth time we are convinced in necessity of careful and close relation to gold fund of physical ideas of the predecessors.

In the remarkable book «The Science and the Life of Albert Einstein» Abraham Pais pays attention on the James Clerk Maxwell remarks regarding to difficulty, concerning with vector gravitation theory negative energy in a fundamental level. And in particular – «dense bodies presence influences on environment in the direction of [internal] energy reduction, where the resulting gravitation is only presenting. As far as I can not realise, how environment can have such properties, I can not go further in this direction in searches of the gravitation reasons», citing from milestone work «The Dynamic Theory of Electromagnetic Field», completed in 1864.

This is a brightest sample of the genius intuition, which is not tolerant to «obvious» facts.

Hendrik Antoon Lorentz «in one of few articles, constructed on purely speculative reasons, written a 1900 year» has made a pioneer attempt to deduce residual Newton's gravitation between electric neutral pairs (+e, –e). For this purpose the repulsion force between particles of a identical charge mark was assumed as «a little» smaller, than attraction force between opposite charged particles of electric neutral pairs.

The Lorentz genius has found necessary to publish this article, in spite of understanding of its being incomplete, but at the same time felt perspective…

It is good to add the vector interaction to scalar one in accordance with (3), to work on the electron and hydrogen atom nuclear individualisation procedure, and we shall be awarded by obtaining of Isaac Newton gravitation residual force between electrically neutral atoms with the appropriate amendments.

So the constructed field of gravitation in case of rotation electrically neutral mass should create a magnetic field, necessary for the whole system impulse moment conservation. Formally it is stipulated by the fact, that at equation (3) recalculation in a rotated readout system, the vector and scalar fields are mixed similarly to that occurs to 4th vector components at the Lorentz transformation.

This phenomenon, co-ordinated with Samuel Barnett effect, attracted Einstein's fixed attention. He persistently searched for an opportunity to elevate it in a managing PRINCIPLE for construction of the uniform field theory. It should only remember, that fundamental seeding magnetic field of space bodies as snow ball reels up ferromagnetic inclusions' fields on itself and the resulting field, observable by our devices, can be essentially bigger.

The field theory of electron will be firm, when scalar function Φ will be formally co-ordinated with subgroup of the scale conforming transformations, preserving ML-equation and co-ordinated with the electron spherical symmetry group. This scale invariance in connection with a equation (3.2.3) should determine a structure of the configuring space with conservation of a impulse moment for driven sources of FM-fields.

The first step in this direction may be Gunnar Nordström first uniform 5-theory formalism of first analysis, uniting electromagnetic field with scalar gravitation and offered by him in 1914. This theory (after replacement of empirical factor at a scalar field) should be applied to FM-fields sources (to ONs), but not to particles (electrons), as it was made originally.

There is more known Theodor Kaluza 5-theory, offered to Einstein in 1919, but published only in 1921. Thanking to Oscar Klein merits in development of this field, now it is named as the Kaluza–Klein theory.

Nordström's 4th-theory (1912, 1913) is individual case of the Einstein's General Relativity by virtue of additional condition of light speed constancy, but more general, than Special Relativity. It was well known to the participants of «gravitational competition» and was precisely formulated in Einstein–Fokker article (1914). This enclosure is present in 5-theories as well.

«Superfluous», «unacceptable» components appeared in many uniform theories, applied to particles. In 5-theories it is «Superfluous» scalar field and «superfluous» equation. As to Arthur Stanley Eddington uniform theory and its development in Einstein articles (1923) – there are «superfluous» currents, rigidly connected with electromagnetic field. As a consequence, it is impossible to obtain Maxwell equations for field without sources. «Faulty» variants, causing to «antigravitation» are less known.

All these «superfluous» components were precursors of motion laws of the ON-currents – sources of FM-field. A problem of reinterpretation of these formalisms on a fundamental ON-level is urgent.

For physicists of a quantum epoch the reinterpretation of quantum representations and Dirac–Feynman electron-positron field doctrine is more close and exiting. It is hard to pass conformity between a role of an additional scalar field in (3) and quantum potential in de Broglie–Bohm causative interpretation. Electron-positron field in Richard Feynman interpretation corresponds to a field of opposite charged pairs of ON-currents.

The decision of equations (3.2.3) and (3) in the form of a pair of two-parametrical families of vectors in each point has natural spinor representation. It is outstanding, that impulse vector has other form of record as well:

In a course of undressed electron dressing the replacement of electron-positron pairs

to pairs of differential ON-currents with cancellation of the local law of charge conservation in formation of a differential virtual pair is fruitful. As far as there are only Fourier's components, global law of charge conservation for all pairs in whole the space is sufficient. The local law of conservation was imposed by interpretation, not by formalism. It may be possible on this way to close quantum electrodynamics and to get rid from electron own charge and weight infinite values.

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