Hydrogen system
The model of
hydrogen system.
The hydrogen system
is a system of two objects held near each other by fundamental forces, with the
ratio of the objects' masses equal to the ratio of the proton mass to the
electron mass. The concept of hydrogen system is used to describe the similarity of matter levels in the Theory
of Infinite Hierarchical Nesting of Matter,
according to which the hydrogen systems characterize the simplest and most
common in the universe systems of two bodies. Each hydrogen system consists of
the primary massive object and the lowmass satellite rotating around it. At
the atomic level the hydrogen system is the hydrogen atom comprising a proton
and an electron. Theoretical definition of specific properties of a hydrogen
system (the mass of the primary object, the distance to the satellite in the
ground state, etc.) is not univocal and depends on additional assumptions.
Uniqueness of a hydrogen atom is that the most total balance between the strong gravitation and electromagnetic
forces is achieved in it. ^{[1]} Table 1 shows the parameters of a
hydrogen atom, which is the standard hydrogen system.
Table 1.
Parameters of a hydrogen atom in the ground state 

Proton mass 
M_{p}_{ }=
1.6726485∙10^{27 }kg 
Electron mass 
M_{e}_{ }= 9.109534∙10^{31
}kg 
Electron's orbital velocity 
V_{e}_{ }= 2.187691∙10^{6
}m/s 
The radius of electron's orbit 
R_{B }=
5.2917706∙10^{11 }m 
As it is shown in the substantial electron model, the electron
in the hydrogen atom in the ground state represents a discoidal cloud, with the
inner edge of the disk and the outer edge . The matter of the
electron disk rotates around the atomic nucleus differentially, that is with
different angular velocities, depending on the distance from the nucleus. Since
the electron bears the electrical charge and the charge's rotation is the
electric current, then the magnetic moment of the electron takes place which is
equal to the Bohr magneton: ^{[2]}
,
where is the elementary charge, is the Dirac constant.
Proton also has
a magnetic moment, exceeding 2.7928456 times the nuclear magneton:
.
The radius of
the electron's orbit specified in Table 1 is the mean radius of the electron
cloud and is called the Bohr radius. The orbital velocity of the electron is
the rotation velocity of the electron matter at the Bohr radius, which is found from the relation:
,
where is the fine structure constant, is the speed of light, is the vacuum permittivity.
The formula for
the Bohr radius is as follows:
.
From this
equation it follows that the orbital angular momentum of the electron in the
ground state is equal to . In the presented formulas for the velocity and the radius of the
electron's orbit small additives are not included which arise when the center
of the electron cloud is shifted relative to the proton. In this case, the
cloud and the proton rotate around the common center of mass, the electron
obtains dynamic spin and loses energy due to electromagnetic emission until it
achieves the stationary state of the matter rotation. In the stationary state there is no emission from the electron
charge due to the axially symmetric shape of the electron cloud.
Stellar and
galactic hydrogen systems
R. Oldershaw
model
R. Oldershaw in
his model assumes that the stars of spectral type M, with the mass of the order
of (where is the Solar mass), are the stellar
analogue of the hydrogen atom with the mass . ^{[3]} Then the
coefficient of similarity in mass equals
. The mass of the object corresponding to the electron can be obtained by
multiplying the electron mass by the coefficient of similarity in mass: kg or 26 Earth masses.
The coefficient
of similarity in sizes (and in time) according to Oldershaw equals to . Multiplying this quantity by the Bohr radius we can estimate the radius
of the stellar hydrogen system: m or 0.039 Solar radii. Since the
dwarf stars of main sequence with the mass have the radius about 0.15 Solar
radii, the Oldershaw's stellar hydrogen system can be located entirely within
the star. Explaining this phenomenon, Oldershaw assumes that as according to
quantum mechanics the electron matter is somehow distributed in the atom, so in case of stars, the matter of the object – the electron's analogue can be distributed in the
spherical shell of the star. The fact that the radius of the star with the mass
exceeds the radius of the stellar
hydrogen system in this case is the consequence of the fact that the stellar matter is in an excited state, and the object – the electron's analogue has
higher energy levels, which in case of more excitation turn into Rydberg
states, in which the object can take the form of separate planets. According to
this picture a star with a planet around it is considered as the analogue of a
negative hydrogen ion, consisting of a proton and two electrons (one electron
corresponds to the planet and the other electron corresponds to the object –
the electron's analogue inside the star). Since negative hydrogen ions are
rare, Oldershaw predicts sharp minimum in the number of planetary systems with
one planet for dwarf stars with the mass around .
In order to
obtain the masses of the hydrogen system's objects at the level of galaxies
according to Oldershaw it is necessary to multiply the masses of the proton and
electron by , which gives kg and kg, respectively. To explain such
large masses and the observed interaction at the level of galaxies Oldershaw
introduces a new gravitational constant of very small value, which can be
found from dimensional equations for this constant. Since the dimension of the
gravitational constant is cubic meter divided by kilogram and squared second,
and the coefficients of similarity in sizes and time, according to Oldershaw,
have equal value, then we obtain:
m^{3} /(kg ∙ s^{2}),
where is the gravitational constant.
However,
introduction of the gravitational constant for galaxies does not solve the
problem completely. Indeed, let the dwarf galaxy with the mass rotate around the galaxy with the
mass . The equality of gravitation and the centripetal force in equilibrium in
an ordinary case and from Oldershaw's point of view is as follows:
,
.
Assuming the
rotation velocity of a dwarf galaxy and the distance from the normal galaxy to be equal in both cases, we obtain:
.
This equality
with reasonable masses of galaxies is not satisfied, that makes the
validity of Oldershaw's galactic hydrogen system parameters questionable.
Oldershaw also
admits that part of the mass is “transformed” in singularities of black holes,
located by him inside of the galaxies. Considering the proton and the electron
as black holes, he determines their radii by Schwarzschild formula, and then
transfers this approach to the level of stars. In this case, another type of
hydrogen systems consists of two black holes, one of which, with the mass and the radius about 400 m,
corresponds to the proton, and the other black hole, with the mass which is
1836 times less and the radius of about 20 cm, is the analogue of the electron.
As a consequence, it is assumed that these black holes are the basis of the
dark matter.
S. Fedosin model
Planetary
systems
Modeling the
hydrogen system consisting of a planet and a main sequence star of minimal
mass, Fedosin predetermined the mass of such star. This was done by comparing
the multitude of all known atomic nuclei and stars of different masses. As a
result discreteness of
stellar parameters was discovered
as similarity between the nuclides of chemical elements and the stars of
corresponding masses, as well as similarity with respect to their abundance in
the Universe and to their magnetic properties. The mass of a main sequence star
of minimum mass is kg, where is the Sun's mass. The mass of the planet – the electron's
analogue is 1836 times less than the mass of the star corresponding to
situation in the hydrogen atom. The mass of such planet is 10.1 Earth masses and
it orbits the star at a distance of the order of 19 a.u.
Table 2. The hydrogen system for planets and main
sequence stars 

The star's mass 
M_{ps} = 1.11∙10^{29} kg 
The planet's mass 
M_{п} = 6.06∙10^{25} kg 
The planet's orbital velocity 
V_{п} = 1.6∙10^{3} m/s 
The planet's orbital radius 
R_{F} = 2.88∙10^{12}
m 
The relation between the masses of the objects of hydrogen systems in Tables 2
and 1 and the relations between the orbital velocities and the orbital radii
are set by the corresponding coefficients of similarity in mass, speed and
size: ^{[4]}
,
,
.
The coefficient
of similarity in time, understood as the ratio of time flow rates between
atomic time and ordinary stellar systems, equals:
.
Between the
parameters of the stellar hydrogen system there is a relationship, resulting
from the balance of gravitational force and centripetal force on a circular
orbit:
Based on this
relation we determine the radius of the planet's orbit using the known velocity . In turn, the orbital velocity, as
in the hydrogen atom, is given by:
,
where is the fine structure constant, km/s is the stellar speed, which is the characteristic
speed of the matter of the star
with the mass .
The speed is found based on similarity with
the proton, for which the rest energy equals . From the point of view of the principle of mass–energy equivalence, this
energy is equal to the binding energy in the field of strong gravitation. For
the mainsequence star with minimum mass the corresponding binding energy
will equal . The total energies of stars as their binding energies were studied by
many authors, which allowed us to determine the speed and the parameters of the stellar
hydrogen system. ^{[4]}
The
characteristic angular momentum for planetary systems is the orbital angular
momentum of the planet – the electron's analogue J∙s. The fine structure constant has the same
value in the atomic hydrogen system and in the analogous system for planetary
systems, and it can be expressed not only by electromagnetic but also by
gravitational quantities:
,
where is the strong gravitational constant.
Systems with
neutron stars
From the point
of view of the density of energy and matter, neutron stars
are much closer to nucleons than mainsequence stars. Therefore, the similarity
between atoms and neutron stars is more exact. Most of the known masses of
neutron stars are close to the value , and this mass is taken as the mass
of the star – the proton's analogue. ^{[1]} Dividing this mass by 1836
(this number is the ratio of the proton's mass to the electron's mass) we
estimate the mass of the object – the electron's analogue. It is equal to 250
Earth masses or 0.78 Jupiter masses.
Table 3. The hydrogen system for a neutron star 

The star's mass 
M' _{ps}
= 2.7∙10^{30} kg 
The mass of the object – the
electron's analogue 
M' _{п} = 1.5∙10^{27}
kg 
The orbital velocity 
V' _{п} = 4.96∙10^{5}
m/s 
The orbital radius 
R' _{F} = 7.4∙10^{8}
m 
Using the expression for the binding energy of the neutron star as the absolute
value of its total energy in the form:
where , is the star's radius, Fedosin estimates the characteristic speed of the
stellar matter m/s. From this using the fine structure constant, the orbital velocity of
the object – the electron's analogue in Table 3 is determined, and using
relation (1) he determines the orbital radius:
,
.
As the objects
– the electron's analogues we assume magnetized disks with a high content of
iron, which are discovered near the Xray pulsars – which are the main
candidates to magnetars. ^{[5]} The mean radii of the disks are close
to the radius , as well as to the Roche radius, at
which the planets are disintegrated due to strong star's gravitation. If we
compare with the Solar system, in which the Sun's mass is 1.35 times less than
the mass of a neutron star, than the radius turns out larger than the Solar
radius and less than the orbital radius of Mercury.
The ratios of
objects' parameters in Table 3 and Table 1 give the coefficients of similarity
between atoms and neutron stars:
,
,
.
For the
coefficient of similarity in time and the characteristic angular momentum for
neutron stars we obtain: ^{[4]}
,
J∙s.
The quantity sets the stellar Dirac constant for compact stars.
Using the coefficients of similarity and the dimensional relations for physical
quantities we determine the electric charge and the magnetic moment of the
magnetar, which is the proton's analogue:
C,
J/T,
where and are the elementary charge and the magnetic moment of the proton ,
respectively.
Similarity
relations also lead to the following formula:
.
Due to
electrical neutrality of the hydrogen system, the disks near the positively
charged magnetars must have a charge, opposite in sign and equal in magnitude
to . Rotation of disks as well as rotation of the electron in the atom,
creates a magnetic moment, which is found by the formula:
J/T,
where is the magnetic moment of the
electron.
Galactic systems
Estimating the parameters
of the hydrogen system at the level of galaxies, Fedosin takes into account the
discreteness of similarity coefficients, arising from the similarity of matter levels and the existence of basic and intermediate levels of matter. Atoms and
stars belong to the basic levels of matter, while galaxies belong to the
intermediate level of matter.
Since masses
and sizes of objects increase exponentially from one level to another, it
allows to estimate masses and sizes of carriers at any level of matter by means
of respective multiplication by the factors and . Between atoms and stars there are nine more intermediate levels of
matter. Hence the coefficient of similarity in mass between the adjacent
intermediate levels is found as the tenth root of the coefficient of similarity
in mass between atoms and mainsequence stars:
.
On the other
hand, between atoms and stars there are eleven scale levels, nine of which are
associated with the sizes of the objects of intermediate levels, and two
additional levels take place during transition from the sizes of atomic nuclei
to the sizes of atoms. As a result, the coefficient of similarity in size
between the adjacent intermediate levels is determined as the twelfth root of
the coefficient of similarity in size between atoms and planetary systems of
mainsequence stars:
.
In terms of
masses, galaxies are located two levels higher than stars, but in terms of
sizes they are six levels higher. This results in the following relations for
the masses of galaxies and the orbital radius of a dwarf galaxy in Table
4 :
,
,
,
where is the mass of the main sequence
stars of minimum mass, and are the planet's mass and its orbital radius in Table 2 .
Table 4. The hydrogen system for galactic systems 

The mass of a normal galaxy 
M_{pg} = 8.15∙10^{9} M_{c} 
The mass of a dwarf galaxy 
M_{gd} = 4.43∙10^{6} M_{c} 
The orbital velocity 
V_{gd} = 1.3∙10^{3} m/s 
The orbital radius 
R_{gd} = 6.7∙10^{23} m 
The orbital speed of a dwarf galaxy is estimated with the help of the orbital
radius and the mass of the galaxy from the relation similar to (1):
.
Table 4 shows
that Mpc, which
is much more than the ordinary distances between galaxies. At the same time the
velocity of orbital rotation of a dwarf galaxy is too little compared with the
ordinary velocities of galaxies.
Estimation of
the characteristic speed of stars in a normal galaxy of minimum mass is made
with the help of formula (2) with :
,
where the
volumeaveraged radius of the galaxy is determined by multiplying the radius of
the main sequence star of minimum mass Solar radii by the sixth degree of
discrete coefficient of similarity in size : m = 520 pc. From here the
characteristic speed of stars in the galaxy is km/s. In the hydrogen system
obtained in Table 4, the ratio of the orbital velocity of a dwarf galaxy to the characteristic speed of the stars in a normal galaxy is
approximately equal to the fine structure constant, just as it is in the
hydrogen atom and in planetary systems.
In reality the
systems containing normal and dwarf galaxies are closer to each other and
rotate faster near each other. One explanation of this situation lies in the
fact that galaxies do not belong to the basic matter level. A neutron star
contains about nucleons, and the same number of
particles is supposed in a proton. Meanwhile, in a normal galaxy of minimum
mass, usually it is a galaxy of the spiral type, the number of stars does not
exceed the value . This number is much less than the number of nucleons in a star. From the
point of view of similarity, galaxies contain the same number of stars, as the
number of atoms in microscopic dust particles. In contrast to ordinary solid
dust particles, the concentration of stars in galaxies is of such kind, that
they are similar to strongly rarefied gas clouds, only in the center of which there
is solid substance. ^{[4]} If in the hydrogen atom in the ground state
the electron's orbital angular momentum is
, and the proton's quantum spin has the value , then the orbital angular momentum of a dwarf galaxy can be significantly
less than the spin of a normal galaxy. This leads to increase in the orbital
velocity of the dwarf galaxy and to a smaller radius of its orbital rotation
around the normal galaxy. Probably the loss of the orbital angular momentum by
dwarf galaxies is associated with the evolution of galaxies and their formation
from large hydrogen clouds, in which the angular momentum is lost due to the
friction between the adjacent clouds.
Source: http://sergf.ru/vsen.htm