Components of general field
General field is a physical field, the components of
which are the electromagnetic and gravitational fields, acceleration field, pressure field, dissipation field, strong interaction
field, weak interaction field, and other vector fields acting on the matter and
its particles. Thus, the general field is manifested through its components and
it is not equal to zero, as long as at least one of these components exists.
Fundamental interactions, which include electromagnetic, gravitational, strong
and weak interactions, that occur in the matter, are part of the interactions
described by the general field.
The concept of the general field appeared within the
framework of the metric
theory of relativity and covariant
theory of gravitation as a generalization of the procedure for finding the
stressenergy tensor and equations of a vector field of any kind. ^{[1]} With the help of this procedure, based on the
principle of least action the gravitational field equations were first derived,
^{[2]} ^{[3]} ^{[4]} then the equations of acceleration and pressure
fields, ^{[5]} and then the equations of the field of
energy dissipation due to viscosity. ^{[6]} All
these equations are similar in form to the Maxwell equations. This means that
the nature of every vector field has something in common, which unites it with
other fields. This implies the idea of a general field, which is described in
articles by Sergey Fedosin. ^{[7] [8]}
The general field theory represents one of the variants of
the nonquantum unified field theory and is one of the Grand Unified theories
as well.
Table 1 shows notation for all the fields, which are the components of
the general field.
Table 1. Notation
of field functions 

Field function 
Electromagnetic field 
Gravitational field 
Acceleration field 
Pressure field 
Dissipation field 
Strong interaction field 
Weak interaction field 
General field 
4potential









Scalar
potential 








Vector
potential 








Field
strength 








Solenoidal
vector 








Field
tensor 








Stressenergy
tensor 








Energymomentum
flux vector 








Field
constant 








In Table 1, the vector is the Poynting vector, the vector is the Heaviside
vector.
In the covariant theory of
gravitation the main representative of any vector field is its 4potential,
with the help of which all other field functions are expressed. Since the
general field exists due to its components in the form of particular fields,
the 4potential of the general field is the sum of the 4potentials of
particular fields, in accordance with the
superposition principle for the fields:
By its meaning the
4potential is a generalized 4velocity. ^{[9]}
Since the 4potential of any
field consists of the scalar and vector potentials, the scalar potential of the
general field is the sum of the scalar potentials of particular fields, and the
same applies to the vector potentials:
The tensor of the general field
is calculated as the 4curl of the 4potential. If we assume that the ratio of
the charge density to the mass density in
each considered matter unit is constant as the ratio of the charge to the
mass of the unit, the tensor of the general field turns out to be
the sum of tensors of particular fields:
The components of field tensors
are their strengths and solenoidal vectors. Consequently, the general field
strength in each matter unit (volume unit) is the sum of
strengths of particular fields and the same applies to solenoidal vector of the
general field:
Within the covariant
theory of gravitation the matter is characterized by the mass 4current , where is the 4velocity. While the charge
4current is obtained with the help of the mass 4current from the following relation:
Consequently, the energy density
of interaction of the general field and the matter is given by the product of
the 4potential of the general field and the mass 4current: . Another tensor
invariant, in the form , is up to
a constant factor proportional to the energy density of the general field. The
action function containing the scalar curvature and the cosmological constant , is given by the
expression:
where is the Lagrange function or Lagrangian; is the time differential of the coordinate
reference frame; and are the constants to be determined; is the speed of light as a measure of the
propagation speed of electromagnetic and gravitational interactions; is the invariant 4volume expressed in terms
of the time coordinate differential , the product of space coordinates’ differentials and
the square root of the determinant of the metric tensor, taken with a
negative sign.
The variation of the action function consists of the sum of
terms, including:
1) the variation of the 4potential of the general field;
2) the variation of coordinates , which creates
the variation of the mass 4current;
3) the variation of the metric tensor.
Due to the principle of least
action, the variation must vanish. This leads to the vanishing of
the sums of all the terms, standing before the variations , and , respectively. As a consequence, the equations
of the general field, the fourdimensional equation of motion and the equation
for the metric follow from this.
By definition, the integral of action should be the sum of the integrals
over the 4volume on all the elements of matter, and the entire volume occupied
by fields. In many cases, the physical system contains elements of matter, in
which the ratio of is different from the average. In this case,
the equation for the field, the motion of matter and the metric will depend not
only on local ratio , but also on the ratio of charge to
mass in other matter elements that is implemented through a total field of
these elements.
The Lagrangian is a volume
integral of the sum of terms with the dimension of the energy density and it is
similar by its components to the Hamiltonian, which determines the system’s
energy. Actually, the Hamiltonian is obtained from the Lagrangian by means of
the Legendre transformation for a system of particles. As we know, the energy
is determined up to a constant that means the energy is subject to gauge. For
example, the energy of the electromagnetic field is gauged so that at infinity
with respect to the charge the electromagnetic field energy density is equal to
zero. Similarly, the system’s energy in the form of the Hamiltonian can be
gauged. In the covariant theory of gravitation it is assumed that the
cosmological constant is a gauge term. By its meaning it up to a
constant factor represents the energy density, that the system has after all
the system’s matter is divided into separate particles and scattered to
infinity. In this case, the energy of the particles’ interaction with each
other by means of the fields disappears, and only the proper energy of the
particles remains as the energy of their proper fields at zero temperature. The
gauge condition of the cosmological constant has the following form:
When the gauge conditions of the
cosmological constant is met, the system’s energy ceases to depend on the term
with the scalar curvature and becomes uniquely defined:
where and denote the time components of the
4vectors and
.
The 4momentum of the system is
determined by the formula:
where and denote the system’s momentum and the
velocity of motion of the center of mass.
The general field equations have the following form:
Thus, the only
source of the general field is assumed to be the mass 4current . The latter
equation can be written more concisely using the LeviCivita symbol or a
totally antisymmetric unit tensor:
Substituting (1), we can express
the general field equations in terms of the tensors of particular fields:
At equilibrium state, we can
assume that equation (5) is satisfied separately for the tensor of each field,
and not only for the entire sum of tensors of particular fields. Similarly,
under the condition equation (4) can be divided into seven
separate equations, in which the mass 4current is the source of one or another particular
field.
The gauge condition of the
4potential of the general field:
The continuity equation in the
curved spacetime is written with the Ricci tensor :
In Minkowski space of the special
theory of relativity the left side of this equation becomes equal to zero,
since the Ricci tensor becomes zero. Besides, the covariant derivative is transformed into the 4gradient so that the continuity equation is
simplified:
The equation of motion of the
matter unit in the general field is given by the formula:
.
Since , and the general field tensor is expressed in
terms of the tensors of particular fields, then the equation of motion can be
presented using these tensors:
Here is the acceleration
tensor, is the electromagnetic tensor, is the gravitational
tensor, is the pressure
field tensor, is the dissipation
field tensor, is the tensor of the strong interaction
field, is the tensor of the weak interaction field.
The stressenergy tensor of the general field is
determined from the principle of least action with the expression
With this tensor the equation of
motion is written in a very simple form, as the equality to zero of the
divergence of the tensor:
.
The stressenergy tensor of the
general field is included into the equation for the metric:
where is the gravitational
constant, is a certain constant and the gauge condition
of the cosmological constant is used.
The general field tensor has such components as the strength and solenoidal vector of the
general field. The vector , according to
(2), is the sum of the strengths of particular fields, and the vector , according to (3), consists of the solenoidal
vectors of particular fields. The stressenergy tensor of the general field includes the tensor product , so that the
tensor contains the squared vectors and
. Substituting these vectors with the sums of the
respective vectors of particular fields, we obtain the following:
where are some coefficients, is the electromagnetic stressenergy tensor, is the gravitational
stressenergy tensor, is the acceleration
stressenergy tensor, is the pressure
stressenergy tensor, is the dissipation
stressenergy tensor, is the stressenergy tensor of the strong
interaction field, is the stressenergy tensor of the weak
interaction field.
As we can see, the stressenergy
tensor of the general field contains not only stressenergy tensors of
particular fields, but also the crossterms with the products of strengths and
solenoidal vectors of particular fields.
For example, if we consider only
the gravitational field and the acceleration field, for the stressenergy
tensor of the general field we obtain the following:
where is a constant, which is part of the
definition of the acceleration stressenergy tensor.
Dividing into two components
In the article ^{[8]} the
general field was divided into two main components. One of them is the mass
component of the general field, the source of which is the mass
fourcurrent . The source of the second one – the charge component
of the general field – is the charge fourcurrent . The mass component of the general field contains the
gravitational field, acceleration field, pressure field, dissipation field,
fields of strong and weak interaction, and other vector fields. The charge
component of the general field represents the electromagnetic field. As a
result of dividing the general field into two components the field equations
have become more independent of each other, since the invariability condition
of the ratio of the invariant charge density to the invariant mass density is no longer
required. To denote the field functions of the mass component of the general
field, the same notation is used further, which are specified in Table 1 for
the general field itself.
The fourpotential of the charge
component of the general field is the electromagnetic fourpotential . The 4potential of the mass component of the general field is equal to
the sum of the fourpotentials of the corresponding fields:
Similarly, the scalar and vector
potentials of the mass component of the general field will equal:
Instead of (1), (2) and (3) for the
tensor, field strength and solenoidal vector of the mass component of the
general field, we will obtain the following:
The tensor of the charge component
of the general field is the electromagnetic tensor :
consisting of the components of the
electromagnetic field strength and the
components of the magnetic field .
The potentials, field strengths and
solenoidal vectors of the particular fields for a spherical body were
calculated in the article ^{[10]} and in other articles. ^{[6]}
^{[11]} ^{[12]} ^{[13]}
The action function and the system’s
energy are determined as follows:
The equations for the tensors of the
mass and charge components of the general field will be as follows:
The gauge conditions of the fourpotentials
of the general field components are as follows:
The continuity equations for the
corresponding fourcurrents in the curved spacetime are as follows:
The equation of motion of the matter
under the action of the fields is as follows:
The equation of motion can also be
written using the stressenergy tensor of the electromagnetic field and the
stressenergy tensor of the mass component of the general field :
These tensors with contravariant
indices are defined as follows:
The equation for the metric:
In the article ^{[14]} it was
shown that for the coefficients of the fields, which are part of the mass
component of the general field, the following relation should hold:
where is the
acceleration field constant, is the
pressure field constant, is the
gravitational constant, is the
dissipation field constant, ^{[6] } is the
constant of the macroscopic strong interaction field, ^{[7]} is the
constant of the macroscopic weak interaction field.
For the case of the relativistic
uniform system, the tensors of the fields, which are part
of the mass component of the general field, are proportional to each other. ^{[15]}
^{[10]} With this in mind, the stressenergy tensor of the mass
component of the general field is expressed in terms of the stressenergy
tensors of the particular fields, while the cross terms disappear:
In a stationary case we can assume that the energy in the
system is distributed in accordance with the equipartition theorem. According
to this theorem, for systems in thermal equilibrium under conditions, when
quantum effects do not play a big role yet, any degree of freedom of a particle, which is part of the energy as
the power function , at the average
has the same energy , where is the Boltzmann constant, is the temperature. The particles of the
ideal gas have only three degrees of freedom of this kind – they are three
components of velocity, which are a squared term of the kinetic energy (), therefore the
average energy of the particle is .
In general case, the particles
have their proper fields, and the strengths and solenoidal vectors of these
fields are squared terms of the corresponding stressenergy tensors. With this
in mind, it is assumed, ^{[7]} that the
equipartition theorem also holds for the field energy in the sense that the
energy of the system in equilibrium tends to be distributed proportionally also
between all the existing fields in the system. In equilibrium, we can expect
that the particular fields as the components of the general field become
relatively independent of each other. In this case, for each field their own
field equations must hold, and the equations of the general field (4) and (5)
are divided into sets of equations for each particular field. All these
equations have a form similar to the Maxwell's equations.
The following solutions were
calculated assuming that the crossterms in (7) are equal to zero. This implies
complete independence of particular fields so that not only the equations of
particular fields are independent of each other, but also the way how the
general field energy simply equals the sum of energies of particular fields.
Since the particular fields do influence each other, these solutions can be
considered as a first approximation to the real picture.
Outside the bodies there are only the
electromagnetic and gravitational fields. The tensors of these fields only will
contribute to the equation for the metric (8), while the scalar curvature is zeroed. ^{[16]}
The metric around an isolated
spherical body was calculated in the article. ^{[1}^{7}^{]} For the time component of the metric tensor
there is obtained the following:
where is the distance from the center of the body
to the point where the metric is defined;
is
the energy of the gravitational field inside and outside of the body; is the energy of the electric field; , and are the mass, charge and radius of the body, is the electric
constant; are the coefficients to be determined; are the numerical coefficients of the order
of unity, in case of the uniform density of mass and charge of the body they
are the same and equal approximately the value 5/3.
In this case it appears that the
metric depends both on the ratio of the body radius to the radius vector to the
observation point, and on the ratio of the total field energy to the rest
energy of the body.
The energy of the system of particles with regard to the
electromagnetic and gravitational fields, acceleration field and pressure field
is calculated in the article. ^{[1}^{5}^{]} It is shown that
in the center of mass frame the total energy and momentum of all the fields are
equal to zero, and the system’s energy is formed only of the energy of
particles under influence of these particular fields. Five mass values can be
introduced for the system: the inertial mass ; the gravitational
mass ; the total mass of all the particles of the body scattered at
infinity; the mass obtained by integrating over the volume the
density of the matter moving within the system; the
auxiliary mass obtained by integrating over the volume the
density of the matter, calculated in the reference
frame associated with each particle. For these masses we obtain the relation:
From the equality it follows that ideal spherical collapse is
possible when the system’s energy does not change when the matter is
compressed. In addition, the gravitational mass appears to be larger than the system’s mass . This is due to
the fact that the particles are moving inside the system and their energy is
greater than if the particles were motionless at infinity and would not
interact with each other.
Calculation shows that the energy
of the electromagnetic field reduces the gravitational mass. Therefore, adding
a number of charges to a certain body could lead to a situation when the
gravitational mass of the body would begin to decrease, despite the additional
mass of the introduced charges. This follows from the fact that the mass of the
charges increases proportionally to their number, and the massenergy of the
electromagnetic field increases quadratically to the number of charges. We can
calculate that if a body with the mass of 1 kg and the radius of 1 meter is charged
up to the potential of 5 Megavolt, it would decrease the gravitational mass of
the body (excluding the mass of the added charges) at weighing in the gravity
field by mass fraction, which is close to the modern
accuracy of mass measurement.
If we take
into account a more accurate relation for the field coefficients, we obtain for
the masses another expression: ^{[18]}
Here, the
gauge mass is related to the cosmological constant and represents the massenergy
of the matter’s particles in the fourpotentials of the system’s fields; the
inertial mass ; the auxiliary mass is equal to the product of the
particles’ mass density by the volume of the system; the mass is the sum of the invariant
masses (rest masses) of the system’s particles, which is equal in value to the
gravitational mass .
The
conclusion that as the electric charge increases the system’s mass may decrease
remains valid, however this applies not to the gravitational mass , but to the inertial mass of the system.
The 4/3 problem, according to
which the field mass found through the field energy is not equal to the field
mass determined through the field momentum, and the problem of neutrino energy
in an ideal spherical collapse of a supernova were
considered in the article. ^{[1}^{0}^{]} It was shown that in a
moving body the excess massenergy of the gravitational and electromagnetic
fields is compensated by a lack of the massenergy of the acceleration field and pressure field. The
result is achieved by integrating the equation of motion and by calculating the
conserved integral 4vector of the energymomentum of the system. Since this
integral 4vector must be equal to zero, in contrast to the ordinary 4vector
of the energymomentum of the system, it imposes restrictions on the constant , located in the acceleration stressenergy tensor, and the
constant in the pressure
stressenergy tensor. For these constants in case of the massive
gravitationally bound system of particles and fields the relation is found
which connects them with the gravitational constant and electric constant:
,
where and are the charge and mass of the system, and
their ratio within the assumptions made can be interpreted as the ratio of the
charge density to mass density.
The solution of the wave equation
for the acceleration field inside the system results in temperature
distribution according to the formula:
where is the temperature in the center; is the particle mass, for which the mass of
the proton is assumed (for the systems the basis of which is hydrogen or
nucleons in atomic nuclei); is the mass of the system within the current
radius ; is the Boltzmann constant.
Similarly, for the pressure
distribution inside the system we obtain:
where is the pressure in the center; is the mass density in the comoving frame of a
particle; is the Lorentz factor in the center.
These formulas are well satisfied
for various space objects, including gas clouds and Bok globules, the Earth,
the Sun and neutron stars. The only significant discrepancy (58 times) has been
found for the pressure in the center of the Sun. However, if we take into
account the presence of thermonuclear reactions in the Solar core, which can be
described by introducing the strong and weak interaction fields, then the
increased pressure in the center of the Sun can be explained by the influence
of these fields. ^{[7]} In this case, for the
constant in the stressenergy tensor of the strong
interaction field we obtain the estimate: , which coincides
with the coefficients and for the acceleration field and pressure
field, respectively. In all cases the scalar potentials of particular fields
inside the bodies change proportionally to the square of the radius, as it
happens in case of the gravitational field.
In the article ^{[14]} the
4/3 problem was explained using the generalized Poynting theorem. This theorem
is applied to the fourtensors of the fields, which are part of the general
field components. These tensors consist of the components of the strengths and
solenoidal vectors of the corresponding fields, with the help of which the
energy and momentum of these fields are found. As a result, we obtain a more
exact relation between the coefficients of the fields inside the matter of
massive bodies: ^{[14]} ^{[19]}
which allows estimating the internal
temperature, pressure and other parameters of cosmic bodies for the case of
nonuniform density.
Due to the Poynting theorem, both
the sum of the energy densities of all the fields inside the body and the sum
of the vectors of the energy fluxes of all the fields inside this body become
equal to zero. Outside the body, the energy flux of the gravitational or
electromagnetic field accurately compensates for the change in the energy of
the corresponding field in each selected volume. As a result, the 4/3 problem
disappears inside the body, but it remains for fields outside the body. The
solution of the 4/3 problem with the example of the electromagnetic field is
reduced to the following: the requirement of the equality of the massenergy
associated with the time component of the
stressenergy tensor of the field and the massenergy of the energy flux of
this field in the tensor components , is wrongful. The point is that these tensor
components do not constitute a fourvector and therefore cannot contain the
same massenergy, as it occurs in the fourmomentum.
One of the general field components is the dissipation
field, it describes the energy, momentum and energy flux, which are associated
with the processes of energy conversion of particular fields into thermal
energy. In the real substance the interaction of the substance fluxes moving at
different speeds can take place under the influence of the internal friction
and viscosity. In such processes the velocities of the substance fluxes are
equalized, their kinetic energy decreases, but the thermal energy increases and
the total energy of the system does not change. It turns out that if we
introduce the dissipation field as a vector field, similarly to all the other
particular fields, then in case of appropriate choice of the scalar potential
of the dissipation field, it allows us to obtain the NavierStokes equation in
hydrodynamics and to describe the motion of viscous compressible and charged
fluid. ^{[6]}
If we assume the local
equilibrium condition and the validity of the theorem of energy equipartition,
then for each particular field it is possible to use with sufficient accuracy
their own field equations. As a result, for the pressure, for which its field
equations were previously not known, we obtain specific wave equations for the
scalar and vector potentials of the pressure field and the equations for the
strength and solenoidal vectors of the pressure field. Similar equations are
valid for the dissipation field, electromagnetic and gravitational fields,
acceleration field, etc. This allows us to close the system of equations for
the moving fluid with the fields existing in this fluid and to make this
system of equations basically solvable.
Virial theorem
According to this theorem, in each
stationary physical system there is a relationship between the kinetic energy
of the particles and the energy, associated with the acting forces from all the
existing fields that together make up the general field. In case when in the
physical system the pressure field, the acceleration field of particles, the electromagnetic
and gravitational fields are taken into account, the virial theorem is expressed in the relativistic form as follows: ^{[20]}
where denotes the
radiusvector of the th particle, is the force
acting on this particle, and the value exceeds the
kinetic energy of the particles by a factor
equal to the Lorentz factor of the
particles at the center of the system.
In the weak fields, we can assume that , and then we can see that in the virial theorem the kinetic energy is related to the energy of the forces on the righthand side of the equation not by the coefficient 0.5 as in the classical case, but rather by the coefficient close to 0.6. The difference from the classical case arises due to considering the pressure field and the acceleration field of particles inside the system. The expression for the scalar virial function is found:
where is the
momentum of the th particle, and it is shown that the derivative of
this function is not equal to zero and should be considered as the material
derivative. In addition, it is found out that, in contrast to the conclusions
of classical mechanics, the energy associated with the acting forces from all
the existing fields and included in the righthand side of the virial theorem
does not equal the potential energy of the system. ^{[21]}
An analysis of the integral theorem of
generalized virial makes it possible to find, on the basis of field theory, a
formula for the rootmeansquare speed of typical particles of a system without
using the notion of temperature: ^{[22]}
where is the
speed of light, is the acceleration
field constant, is the
mass density of particles, is the
current radius.
The relation between the theorem and
the cosmological constant, characterizing the physical system under
consideration, is shown. The difference is explained between the kinetic energy
and the energy of motion, the value of which is equal to half the sum of the
Lagrangian and the Hamiltonian.
Binding energy of macroscopic bodies
The relativistic energy, total
energy, binding energy, fields’ energy, pressure energy and the potential
energy of the system of particles and four fields (the general field components)
are calculated in the relativistic uniform model, ^{[21]} and then are
compared with the kinetic energy of particles and with the total energy of the
gravitational and electromagnetic fields outside the system. Another result is
the fact that the inertial mass of the system is less than the gravitational
mass, which is equal to the total invariant mass of the particles that make up
the system. It is also proved that as increasingly massive relativistic uniform
systems are formed, the average density of these systems decreases in
comparison with the average density of the particles or bodies making up these
systems.
The model allows us to
estimate the particles’ velocity at the center of the sphere, the
corresponding Lorentz factor , the scalar potential of the pressure field; to find the
relationship between the field coefficients; to express the dependences of the
scalar curvature and the cosmological constant in the matter as functions of
the parameters of typical particles and field potentials. ^{[16]} Besides, comparison of the cosmological
constants inside a proton, a neutron star and in the observable Universe allows
us to explain the problem of the cosmological constant arising in the
LambdaCDM model.
The general field is assumed to be the main source of the
acting forces, energy and momentum, as well as the basis for calculating the
metric of the system from the standpoint of nonquantum classical field theory.
Among all the fields unified by
the general field, two fields – the electromagnetic and gravitational fields –
act at a distance, while the rest fields act locally, at the pave of location
of one or another matter unit. The proper vector potential of any
field for one particle is proportional to the scalar potential of this field
and the particle velocity, if the vector potential of this particle is zero in
the reference system that accompanies the particle. For the
electromagnetic and gravitational fields in the system with a number of
particles the superposition principle holds, according to which the scalar
potential at an arbitrary point equals the sum of scalar potentials of all the
particles and the same is assumed to apply to the vector potential. Due to the
different rules of the vector and scalar summation, the vector potential of the
system ceases to depend on the scalar potential of the system of particles. The
same situation should take place for other fields. For example, the pressure
near the particle depends not only on the scalar potential of the pressure
field in the comoving frame and the particle velocity, but also on the total
pressure from other particles in the system.
The scalar potentials of
particular fields are proportional to the energy, appearing in the system
during one or another interaction per unit mass (charge) of the matter, and
have a dimension of the squared velocity. The vector potentials of particular
fields have a dimension of velocity and allow us to take into account the additional
energy, which appears due to motion. Since the 4potential of a particular
field consists of the scalar and vector potentials, then the sum of the
4potentials of particular fields gives the 4potential of the general field,
which describes the total energy of all interactions in the system of particles
and fields. This is why the general field exists as long as there is at least
one of its components in the form of the particular field. From a philosophical
point of view, the existence of only one particular field is impossible
particular – there should always be other fields. For example, if there is a
particle, whose motion is described by the acceleration field, then this
particle must also have at least the gravitational field and a full set of proper
internal fields inside the particle.
The most natural method of describing the emergence of the general field is
provided by the FatioLe Sage's theory of gravitation. This theory provides a
clear physical mechanism of emergence of the gravitational force, ^{[}^{23}^{]} ^{[2}^{4}^{]} ^{[2}^{5}^{] [2}^{6}^{]} as a consequence of the influence of
ubiquitous fluxes of gravitons, in the form of tiny particles like neutrinos or
photons, on the bodies. The same mechanism can explain the electromagnetic
interaction, if we assume the presence of praons – tiny charged particles in the
fluxes of gravitons. ^{[3]} ^{[2}^{7}^{]} Praons and neutral particles such as field quanta form a vacuum field contained in an electrogravitational vacuum. The fluxes
of the particles of the vacuum field permeate all bodies and carry out
electromagnetic and gravitational interaction by means of the field even
between the bodies, which are distant from each other. The bodies can also
exert direct mechanical action on each other, which can be represented by the
pressure field. An inevitable consequence of the action of these fields is the
deceleration of fast matter particles and bodies in the surrounding medium,
which is described by the dissipation field. At last, the acceleration field is introduced for the
kinematic description of the motion of particles and bodies, the forces acting
on them, the energy and momentum of the motion.
For bodies of a spherical shape, the chaotically moving particles of
their matter can be characterized by a certain average radial velocity and an
average tangential velocity perpendicular to it, the values of which depend on
the current radius. It can be assumed that the radial velocity gradient leads
to the radial acceleration described with the help of the pressure field. The
tangential velocity of the particles also causes the radial acceleration due to
the centripetal force, which can be taken into account by the acceleration
field. These radial accelerations with addition of the acceleration from the
electric forces in the charged matter resist the acceleration from the
gravitational forces that compress the matter of massive cosmic bodies.
As a result, the
general field can be represented as a field, in which the neutral and charged
bodies, under the action of the fluxes of neutral and charged particles of vacuum field, exchange energy and momentum with each
other and with vacuum field. The energy and momentum of the general field can
be associated with the energy and momentum acquired by the vacuum field during
interaction with the matter, and in order to take into account the energy and
momentum of the system we need to add the energy and momentum of the matter,
arising from its interaction with vacuum field.
In the model of quark quasiparticles it is
emphasized that quarks are not real particles but quasiparticles. In this
regard, it is assumed that the strong interaction can be reduced to strong gravitation, acting at the level of
atoms and elementary particles, with replacement of the gravitational constant by the strong gravitational constant. ^{[3]} ^{[4]} Based on the
strong gravitation and the gravitational
torsion field the gravitational model of
strong interaction is substantiated. One of the consequences of this is
that the gravitational and electromagnetic fields are represented as
fundamental fields, acting at different levels of matter by means of the field
quanta with different values of their spin and energy and with different
penetrating ability in the matter.
The abovementioned approach
allowed calculating the proton radius in the selfconsistent model and
explaining the de Broglie wavelength. ^{[2}^{8}^{]} As for the weak
interaction, from the standpoint of the theory of Infinite Hierarchical Nesting of Matter,
it is reduced to the processes of matter transformation, which is under action
of the fundamental fields, with regard to the action of strong gravitation.
Similarly, the pressure and dissipation fields in principle could be reduced to
the fundamental fields, if all the details of interatomic and intermolecular
interactions were known. Due to the difficulties with such details, we have to
attribute the existence of proper 4potentials to the pressure field, energy
dissipation field, strong interaction field and weak interaction field, and to
approximate the influence of these fields in the matter with the help of these
4potentials.
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equations of any form. Advanced Studies in Theoretical
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S.G. The Principle of Least Action in
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3570 (2012). http://dx.doi.org/10.5281/zenodo.889804.
3. ^{3.0} ^{3.1} ^{3.2} Fedosin
S.G. Fizicheskie teorii i beskonechnaia
vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289.
ISBN 9785990195110. (in Russian).
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5.
Fedosin S.G. About
the cosmological constant, acceleration field, pressure field and energy. Jordan Journal of Physics. Vol. 9, No. 1, pp. 130 (2016). http://dx.doi.org/10.5281/zenodo.889304.
6.
^{6.0} ^{6.1}
^{6.2} ^{6.3} Fedosin S.G. FourDimensional
Equation of Motion for Viscous Compressible and Charged Fluid with Regard to
the Acceleration Field, Pressure Field and Dissipation Field. International Journal
of Thermodynamics. Vol. 18, No. 1, pp. 1324 (2015). http://dx.doi.org/10.5541/ijot.5000034003
.
7. ^{7.0} ^{7.1} ^{7.2 7.3} Fedosin S.G. The Concept of the General Force Vector Field. OALib Journal, Vol. 3, pp. 115 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459.
8.
^{8.0} ^{8.1}
Fedosin S.G. Two components of the macroscopic general field. Reports in Advances of Physical
Sciences, Vol. 1, No. 2, 1750002, 9 pages (2017). http://dx.doi.org/10.1142/S2424942417500025.
9. Fedosin
S.G. The Hamiltonian in Covariant
Theory of Gravitation. Advances in Natural Science, Vol. 5, No. 4, pp.
5575 (2012). http://dx.doi.org/10.3968%2Fj.ans.1715787020120504.2023.
10. ^{10.0} ^{10.1}
^{10.2} Fedosin S.G. The Integral EnergyMomentum 4Vector and
Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.
American Journal of Modern Physics. Vol. 3, No. 4, pp. 152167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12
.
11. Fedosin
S.G. The electromagnetic field in the relativistic uniform model. International
Journal of Pure and Applied Sciences, Vol. 4, Issue. 2, pp. 110116 (2018). http://dx.doi.org/10.29132/ijpas.430614.
12. Fedosin S.G. The gravitational field in
the relativistic uniform model within the framework of the covariant theory of
gravitation. 5th Ulyanovsk International SchoolSeminar “Problems of
Theoretical and Observational Cosmology” (UISS
2016), Ulyanovsk, Russia, September 1930, 2016, Abstracts, p. 23, ISBN
9785860458727.
13. Fedosin S.G.
The Gravitational Field in the Relativistic Uniform Model within the Framework
of the Covariant Theory of Gravitation. International Letters of Chemistry,
Physics and Astronomy, Vol. 78, pp. 3950 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.
14.
^{1}^{4}^{.0} ^{1}^{4}^{.1} ^{1}^{4}^{.2} Fedosin
S.G. The generalized Poynting theorem for the general field and solution of the
4/3 problem. International Frontier Science Letters, Vol. 14, pp. 1940
(2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19.
15. ^{15.0} ^{15.1} Fedosin S.G. Relativistic Energy
and Mass in the Weak Field Limit. Jordan Journal of Physics. Vol. 8, No. 1,
pp. 116 (2015). http://dx.doi.org/10.5281/zenodo.889210.
16. ^{16.0} ^{16.1} Fedosin
S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray
University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127143
(2018). http://dx.doi.org/10.29002/asujse.433947.
17.
Fedosin S.G. The Metric Outside a Fixed Charged Body
in the Covariant Theory of Gravitation. International Frontier Science
Letters, ISSN: 2349 – 4484, Vol. 1, No. I, pp. 4146 (2014). http://dx.doi.org/10.18052/www.scipress.com/ifsl.1.41.
18.
Федосин
С.Г. Иерархия масс в релятивистской однородной системе. Препринт, 2018.
19. Fedosin S.G. Estimation
of the physical parameters of planets and stars in the gravitational
equilibrium model. Canadian Journal of Physics, Vol. 94, No. 4, pp. 370379
(2016). http://dx.doi.org/10.1139/cjp20150593.
20. Fedosin S.G. The
virial theorem and the kinetic energy of particles of a macroscopic system in
the general field concept. Continuum Mechanics and Thermodynamics, Vol. 29,
Issue 2, pp. 361371 (2017). https://dx.doi.org/10.1007/s0016101605368.
21.
^{21}^{.0} ^{21}^{.1} Fedosin S.G.
The binding energy and the total energy of a macroscopic body in the relativistic
uniform model. Preprint, June 2016.
22. Fedosin S.G. The
integral theorem of generalized virial in the relativistic uniform model.
Continuum Mechanics and Thermodynamics (2018). https://dx.doi.org/10.1007/s001610180715x.
23. Fedosin
S.G. Model of Gravitational Interaction in
the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4, No. 1, pp. 124 (2009). http://dx.doi.org/10.5281/zenodo.890886.
24.
Michelini M. A flux of
Microquanta explains Relativistic Mechanics and the Gravitational Interaction.
Apeiron Journal, Vol.14, pp. 6594 (2007).
25. Fedosin S.G. The graviton field as the source of mass
and gravitational force in the modernized Le Sage’s model. Physical Science
International Journal, ISSN: 23480130, Vol. 8, Issue 4, pp. 118 (2015).
http://dx.doi.org/10.9734/PSIJ/2015/22197.
26. Fedosin
S.G. The Force Vacuum Field as an Alternative to the
Ether and Quantum Vacuum. WSEAS Transactions
on Applied and Theoretical Mechanics, ISSN / EISSN: 1991‒8747 / 2224‒3429, Volume 10, Art. #3, pp. 3138 (2015). http://dx.doi.org/10.5281/zenodo.888979.
27.
Fedosin S.G. The charged component of the vacuum
field as the source of electric force in the modernized Le Sage’s model. Journal
of Fundamental and Applied Sciences, Vol. 8, No. 3, pp. 9711020 (2016). http://dx.doi.org/10.4314/jfas.v8i3.18, https://dx.doi.org/10.5281/zenodo.845357.
28. Fedosin
S.G. The radius of the proton in the
selfconsistent model. Hadronic Journal, Vol. 35, No. 4, pp. 349363
(2012). http://dx.doi.org/10.5281/zenodo.889451.
Source:
http://sergf.ru/gfen.htm