Canadian Journal of Pure and Applied
Sciences, Vol. 15, No. 1, pp. 5125-5131 (2021). http://doi.org/10.5281/zenodo.4515206
On the structure of the force
field in electro gravitational vacuum
Sergey Grigorievich Fedosin
PO box
614088, Sviazeva
str. 22-79, Perm, Perm Krai, Russia
E-mail: fedosin@hotmail.com
Analysis of the field equations for the tensors of the mass and charge
components of the general field shows that their source is the charge
four-current. In this connection, an assumption is made that it is the charge
component of the force field of the electrogravitational vacuum in the form of
fluxes of charged particles within the framework of Le Sage's theory of
gravitation, which is mainly responsible for both electromagnetic and
gravitational interactions, as well as for the action of other fields inside
bodies. The parameters of the vacuum’s charged particles can be determined quite
accurately using the theory of similarity within the theory of infinite nesting
of matter, so that the description of the cause of emergence of electromagnetic
and gravitational forces is filled with specific content.
Keywords: force field; electromagnetic interaction; gravitational interaction; electrogravitational
vacuum.
1. Introduction
The concept of a force vacuum field takes its origin from the appearance
of the Fatio-Le Sage’s model in the 17th and 18th centuries, in which numerous
rapidly moving tiny particles filling the entire space penetrate all bodies and
lead to gravitation between bodies [1-4]. The modernized Fatio-Le Sage’s
model does not only describe the emergence of gravitational forces [5], but
also explains the origin of electromagnetic forces [6]. In addition, this
model, in combination with the theory of infinite nesting of matter, provides
specific parameters of particles, many of which make up the force field of the
electrogravitational vacuum. In particular, the energy density and energy flux
density, the Lorentz factor, the limiting density of the transferred electric
current and the cross-section of interaction between the particles and matter
are calculated for the particles like praons. In [7], the Lorentz factor at the
center of the proton is determined, and the subsequent use of the similarity
theory allows us to estimate the praon charge, mass and dimensions, and the
gravitational constant, Dirac constant and Boltzmann constant acting at the
praon level of matter.
As a result of the force vacuum field’s action on the matter, such
phenomena as electromagnetism and gravitation arise, which are described in
modern physics by the field theory. One of the first scientists who pointed out
the analogy of the equations of electromagnetic and gravitational fields is
Oliver Heaviside [8]. As a result, the gravitational field
must have two components, just as the electromagnetic field, which contains the
electric and magnetic components [9]. With this in mind, in [10] the theory of
acoustic waves is considered, which depend simultaneously on the potentials of
both the electromagnetic and gravitational fields and which propagate in solid
bodies. The theory
of gravitation, constructed similarly to the theory of the electromagnetic
field, is presented in [11-13].
In the general theory of relativity, the gravitational field is considered
as a tensor metric field and is actually replaced with the spacetime metric, so
that the physics of phenomena is “hidden in the shadow” of geometry. In a weak field, the equations of
general relativity can be represented as equations of gravitoelectromagnetism,
in which the gravitational field is indeed described in terms of two components
[14-18].
Contrastingly, in the covariant theory of gravitation, the gravitational
field is a physically acting vector field that exists independently of the
metric. As a result, the gravitational field is described by its own four-potential
and the gravitational field tensor, while the field’s stress-energy tensor is
derived from the principle of least action in a covariant form [19].
For brevity, we will further consider only four main fields: the
gravitational and electromagnetic fields, acceleration field and pressure field.
All these fields are vector fields, and, if necessary, other vector fields can
be added to them, for example, dissipation field [20], weak and strong
interaction fields. All these fields can be combined into one general field [21].
A relativistic uniform system, which has a spherical shape and is in
equilibrium under the action of its own gravitation and the other three fields,
will be used as a physical model describing the matter.
Our goal will be to analyze the general field theory and then to define
the main active component of the force field of the electrogravitational vacuum. This may
be important for development of projects for obtaining energy from the vacuum
and manufacturing of electrogravitational engines [22-24].
2. Relationships between the four-currents,
field tensors and vacuum field components
The equation of the matter’s motion in a two-component general field is
written in a covariant form as follows [25]:
. (1)
Here 
is the electromagnetic field tensor,
considered as the tensor of the charge component of the general field; 
is the four-vector
of charge current; 
is the charge density of a typical particle
of the matter in the particle’s comoving reference frame; 
is the particle’s four-velocity; 
is the tensor
of the mass component of the general field; 
is the four-vector
of mass current; 
is the mass density of a typical
particle of the matter in the particle’s comoving reference frame; 
is the stress-energy tensor of the
electromagnetic field; 
is the stress-energy tensor of the
mass component of the general field.
The tensor is expressed in terms of the sum of tensors of
all vector fields acting in the system, except for the electromagnetic field
tensor .
If we denote the gravitational field tensor as 
,
the acceleration field tensor as 
,
the pressure field tensor as 
,
then we can write:
.
In the equation of the matter’s motion (1) all the tensors are taken in the
volume occupied by the matter.
Outside the matter, the four-currents 
and 
vanish, and as
a result the left-hand side of (1) vanishes too. But the electromagnetic and
gravitational fields also exist outside the charged matter, and here neither
the tensors and , nor the tensor , nor the stress-energy tensor of the gravitational
field 
are equal to zero. In addition, the
equalities 
, 
become true, and then (1) can be
written as follows [26]:
. (2)
If we take the index 
in (1) and (2),
then we will obtain relations describing the generalized Poynting theorem.
Tensor expression (2) represents the relationship between the energy densities,
energy flux densities and field tensions at each point in space outside the
matter, and it is an equation of motion written for the electromagnetic and
gravitational fields without taking into account the matter. Similar equalities
involving divergence are known for four-vectors, for example, continuity equations
for the four-currents of the form 
, 
. From the mathematical point of view, equality to zero of the divergence
of a four-vector or tensor is an appropriate gauge condition that specifies
certain relationships between the components of this four-vector or tensor.
Thus, the gauging of the electromagnetic field according to Lorentz implies
that the relation 
holds true for
the electromagnetic four-potential 
.
The stress-energy tensors , and in (1) and (2) are expressed in terms of the field tensors , and , respectively, and in the notation with contravariant
indices have the following form:
,
,
,
where 
is the electric constant, 
is the speed of light, 
is the metric tensor, 
is the coefficient of the mass
component of the general field, 
is the gravitational constant.
In turn, the field tensors , and are determined
from the corresponding field equations derived from the principle of least
action:
, 
. (3)
, 
. (4)
, 
. (5)
Here 
is the Levi-Civita symbol. It was found in [26] that
. (6)
When deriving (6), we used the condition
, (7)
where 
is the acceleration field
coefficient, 
is the pressure field coefficient.
Condition (7) implies that a relativistic uniform system is considered,
in which the acceleration field and the pressure field are also taken into
account in addition to the gravitational and electromagnetic fields. The
relation between the field coefficients in (7) is a consequence of the balance
of forces in the equation of motion [27] and the balance of energies in the
generalized Poynting theorem [26], and it was used in [28] in formulation of
the virial theorem.
Equations (3) and (5) were solved in [29-30] for a uniform relativistic
system. In this case, similarity of expressions for the field tensors was
found:
. (8)
Relation (8) was used to derive (6) along with (7).
The components of the tensor 
are the gravitational field strength
divided by the
speed of light and the torsion field 
. Similarly, the components of the tensor are the electric
field strength 
divided by the
speed of light and the magnetic field 
. In a generally motionless uniform relativistic
system, the vectors and become equal to zero, and then we
can assume that 
. Let us suppose now that we are modeling a proton
using the relativistic uniform system. Then the density of the electric force
acting in the proton matter will equal 
, and the density of the gravitational force will be 
. In view of (8), for the relation of the magnitudes
of the force densities we can write the following:
. (9)
Here 
is the elementary charge, 
is the proton mass. According to
(9), the electric interaction in the proton exceeds the gravitational
interaction by about a factor of 
. The same will happen if we divide the constant of
electromagnetic interaction (fine structure constant) 
by the constant
of gravitational interaction 
. The ratio 
defines the ratio of the energy of the electrical interaction of two
protons to the absolute value of the energy of their gravitational interaction,
without taking into account the energies associated with the torsion fields and
magnetic fields. The provided example shows that (8) is valid even when applied
to the proton.
If we substitute (6) into (4), and take into account that 
, 
, we will obtain the following:
, 
. (10)
From the equations for 
in (10) and for
in (3) it
follows that the main source for the tensors of the mass and charge components
of the general field is the charge four-current 
. In [25], the mass and charge components of the general
field were related to the corresponding components of the force vacuum field in
such a way that the vacuum field generates the general field at the macroscopic
level by acting on the corresponding four-currents of the matter. We can also
take into account the results obtained in [5-6] regarding the vacuum field
components. Hence we arrive at the following hypothesis:
In the framework of the modernized Fatio-Le Sage’s model, the force vacuum
field has two components – the field of gravitons and the field of charged
particles. Among these charged particles we can distinguish praons, which are
identified as the main objects of the underlying level of matter that make up all
elementary particles. Similarly, stars, planets and ordinary matter at the
stellar level of matter are made up of nucleons, which are the main objects of
the nucleon level of matter. The fluxes of charged praons can be similar in their properties
to high-energy cosmic rays, these fluxes emerge near nucleons and, when
interacting with the charged four-current of the matter, lead to
electromagnetic interaction. Photons, neutrinos and praons are assumed as particles
of the graviton field, which generates ordinary gravitation. Since in (10) we related
the tensor of the mass component of the general field 
to the charge
four-current , it is logical to assume that the fluxes of charged
praons are the main component of the vacuum field. These fluxes in the neutral matter
create gravitational forces, as well as interactions of all those fields
(acceleration field, pressure field, dissipation field, etc.), in the equations
of which the source is the mass four-current 
. If there are uncompensated charges in the matter,
then the fluxes of charged praons also generate electromagnetic interaction of
these charges with each other.
3. Additional notes
Analysis of the dependence of the electromagnetic and gravitational interactions
on the fluxes of charged particles of the vacuum field shows that this
dependence is not linear. This can be seen from the fact that during transition
between the matter levels the electric constant 
does not change,
while during transition from the macroscopic level of stars to the level of
nucleons the gravitational constant 
must be replaced
with the strong gravitational constant 
, as indicated in [30-32]. At the same time, according to [6],
the cross-section of interaction of gravitons with the matter, leading to
strong gravitation, coincides with the cross-section of interaction of praons
with the matter, leading to electromagnetic interaction, and is approximately
equal to the proton cross-section. The equality of the interaction cross-sections
substantiates the fact that charged particles, which can differ from each other
and have different origins, are responsible both for strong gravitation and for
electromagnetic phenomena at the level of nucleons.
In particular, the level of graons is the matter level that lies below
the level of the praons, and by induction it is assumed that praons consist of
graons, and the fluxes of charged graons act similarly to the fluxes of charged
praons and are a separate component of the vacuum field that generates strong gravitation.
From the foregoing it follows that the electromagnetic field is primary
relative to the gravitational field in the sense that the fluxes of charged
particles at different levels of matter form a multicomponent vacuum field and
are the source of electromagnetic and gravitational interactions. In turn, primacy
of the gravitational field relative to the electromagnetic field is seen in the
fact that it is gravitation that forms the main objects at the matter levels,
such as neutron stars, nucleons, praons, graons, etc. Each main object has
strong electric, magnetic and gravitational fields, is made up of the main
objects of the underlying levels of matter, and when interacting with them it
generates fluxes of charged particles. These fluxes of particles from numerous
main objects are added together and generate a force vacuum field that fills the
entire space and imparts inertia and mass to bodies [5].
Electromagnetic waves are usually considered as fluxes of photons, which
is best of all proved by the phenomenon of photoeffect. The substantial photon model
assumes that a photon is produced by an excited atom due to the action of fields
of the nucleus and electrons on the charged particles of the vacuum field
(praons) crossing the atomic volume [33]. In
this case, strong gravitation is responsible for the integrity of the emerging
photon, which holds praons together, similarly to the action of strong gravitation
on the nucleons in atomic nuclei. As a result, both photons and atomic nuclei
turn out to be very stable objects.
The physical mechanism of action of the fluxes of tiny charged particles
of vacuum in the matter is described in [6]. Charged particles have both charge
and mass, and therefore they interact with electric and magnetic fields, as
well as with strong gravitational fields and torsion fields (gravitomagnetic
fields) of the atomic nuclei and electrons of the matter. Such interaction is
described by the Lorentz force, which does not significantly change the amplitude
of the particles’ velocity, but changes the direction of motion of these
particles. As a result, the particles change the direction of their momenta,
which leads to the emergence of electromagnetic and gravitational forces in the
matter. Since the particles almost do not lose their energy when moving in the
matter, no noticeable heating of the bodies is observed.
An increase in thermal energy
in the matter is accompanied by an increase in the Lorentz factors of motion of
atoms, nucleons and electrons, while all the fields in the matter are
proportional to these Lorentz factors. This leads to an increase in the
interaction of the vacuum’s charged particles with the matter, to an increase
in the energy and inertial mass of the system. Based on the presented
mechanism, the Le Sage’s model explains contribution of any kind of energy to
gravitational and electromagnetic phenomena.
On the other hand, in the equilibrium relativistic uniform system the
temperature at the center always exceeds the temperature of the matter at other
points of the system. In equilibrium, at specified sizes of the system, taking
into account the thermal energy emission into the outer space, certain temperature
distribution is preserved inside the system. Since the motion of the system’s
matter and the forces acting in this matter are a consequence of action of the
fluxes of vacuum’s charged particles, it can be assumed that the kinetic energy
and some heating of the matter occur due to the loss of energy by the fluxes of
charged particles in the matter.
The denser is the matter, the more it heats up. Thus, an estimate of the
temperature at the center of a neutron star found using the field theory with
the help of the Lorentz factor 
gives the value
K [7].
Another way to estimate the average temperature 
of the stellar
matter is to use the virial theorem [28]. For more convenience, in [34] the
kinetic energy 
of motion of
the system’s typical particles was associated not only with the total potential
energy of the system, as in the ordinary virial theorem, but also with the
energy of the gravitational and electromagnetic fields outside the system,
which can be easily calculated:
.
Here 
and 
denote the total invariant mass and the
total charge of all the system’s typical particles, respectively; 
is the radius of the system. We can assume
that
, 
,
where 
is the
Boltzmann constant, 
is the number of typical particles, 
is the mass of a typical particle.
Hence, for the case 
we have:
.
In an uncharged neutron star ; is practically equal to the mass of a
typical star 
, where 
is the mass of the Sun; 
can be assumed equal to the proton
mass; is equal to the radius of the star 12
km; 
. As a result we obtain the volume-averaged
temperature 
K. Thus, if the star’s radius does not change, the virial theorem
guarantees a certain constant temperature of the star’s
matter. In our opinion, this is possible when a cooling star, after its
formation, loses by radiation part of its initial energy, obtained at the moment
of a supernova explosion. At some point, the loss of energy due to radiation
will become equal to the inflow of energy from the fluxes of vacuum’s charged particles
falling on the star, and an equilibrium state will be reached.
4. Conclusion
From the equations of vector fields acting in the considered physical
system, we conclude that the charge four-current 
is the source
of not only the electromagnetic field tensor 
, but also of the tensor 
. Also it
should be noted that the main contribution to 
is made by the
gravitational field tensor 
. The tensors and represent the tensor of the general field’s charge component and the
tensor of the general field’s mass component, respectively. In [25],
it was assumed that the general field’s charge component manifests itself in
connection with the vacuum field’s charge component, and the general field’s
mass component is associated with the vacuum field’s mass component. But the
dependence of and on 
indicates that
the vacuum field’s charge component in the form of fluxes of charged particles like
praons can play a central role in the emergence of electromagnetic and
gravitational effects, in the action of acceleration fields and pressure fields
in the matter, as well as in the manifestation of action of other vector
fields.
By definition in [20] the dissipation field is considered as a vector
field and it describes the additional forces that appear in the matter in the
process of friction. These forces also convert the energy from the kinetic
form into the potential form and vice versa. The weak and strong interaction
fields can also be considered as vector fields, so that they can be assigned
their own tensors and stress-energy tensors [21]. These fields are most
important for calculations in stellar interiors, where active reactions
involving weak and strong interactions take place. Since we reduce any motion
in the matter to the action of the fluxes of charged particles of multicomponent
electrogravitational vacuum, it is logical to assume that the dissipation field
and the macroscopic fields of weak and strong interaction also emerge due to
the charge component of the force vacuum field.
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