_{1}

This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.

Present article is the continuation of article [

The analogy with linear theory of elasticity, supporting propagation of both longitudional and transcendental waves, will give a strictly indication of how the basic equations of generalized electrodynamics should look like. Thus due to this the equation for the Maxwell electromagnetic field was derived from the transcendental component of the displacement vector, and an equation for the electroscalar field from the longitudinal component of the displacement vector. The continuity equation of the electromagnetic field contains displacement of current, and the electroscalar field contains displacement of charge. In the continuous medium the system takes the form for the Maxwell equation:

and another for the electroscalar fields

Such a system describes propagation of longitudinal waves in a continuous medium. Because the transverse and longitudinal waves propagate in the elastic continuum with different velocities,

where

The electroscalar radiation is produced by the structures of solar plasma providing a spectrum with a sign-alternating amplitude of order of 20 millivolt and a frequency (by Fourier) up to 500 Hertz. The averaged value of the spectrum is negative and equals minus 2 - 5 millivolt, with a positive-amplitude signal coming on every millisecond and a negative-amplitude signal following after an interval. The frequency analysis of the spectrum shows that this radiation has a long wavelength and a practically constant amplitude. A single radiation signal has an exceedingly small value of raising time of electrical signal of front and drop of the order of fractions of a picosecond.

The spectrum of the solar electroscalar radiation is given in

Positive signal is the electrical potential applying along line of spreading out and contributing to the repulsion of charges due to their polarization. Negative signal is the result of comression charges by rotation the electrical field on the contour of surface

surrounded the volume of charges. In solid states the electroscalar radiation losses their energy on the cavities and due to that reradiate corresponding plasmons electroscalar signal [

The spectrum of the Solar electroscalar radiation may be presented as a plane electroscalar wave. Particularly, the second equation of the electroscalar field is such that the electric field

Since

From this equation it follows that the potential of the electroscalar field may have maxima and minima as the field in vacuum differs from the Laplace equation for the electromagnetic field with a zero right side and second derivatives have equal signs.

In vacuum, with

In order to find a solution for this equation, we will present it in the form:

The equation for the plane wave has the following solution:

which describes two waves travelling in the direction +X:

as well as in the direction −X:

When

a particular value at some point, then in the time t it will take the same value at a point being at the distance ct from the previous place. This implies that for all the values of the electroscalar field it propagates in space with the velocity *c*. This will be in a similar way for the

i.e.

where n is a unit vector along the direction of the electroscalar wave propagation. Correspondingly, the energy of the wave will be as follows:

The flux of the field pulse is defined by the value of the field energy flux density. And the absolute value of the quantities

For the electromagnetic field the potentials can be chosen in such a way that

The properties of a charged particle relating to its interactions with the electroscalar field are defined by one parameter: that is the particle charge which can be both positive and negative. The properties of the electroscalar field are characterized by the four-dimensional scalar potential

where the integral is taken at the points a to b of the world line of a particle. The type of action can be established here on the grounds that the Lagrangian is a scalar, while the product of the charge and potential is the particle’s potential energy. Besides that, the relativistic invariance requirement allows for the scalar function the form:

Thus, the action for a charge in the electroscalar field appears as:

where the 1st term is the energy of a free particle, and the 2nd term is the potential energy of the particle. According to the principle of longitudinal superposition, the charge may be expressed in terms of the charge density:

In such a case, summation goes over all the linear charges.

The action can be represented as a time integral:

where L is the Lagrange function.

Since

So, the Lagrange function of the electroscalar field is:

In the non-relativistic case,

In order to determine the energy-momentum tensor of the electroscalar field and establish the equation of motion of a particle in the four-dimensional form, we apply the principle of least action in the relativistic case. The variables which vary in a principle of least action are field potentials and coordinates of the world line. The action of a charge in the electroscalar field in the three-dimensional form is as follows:

The principle of least action states:

and since:

the variation of action in the four-dimensional form is:

The action variation takes place along the world line from a to b.

Further:

In the first and third terms we integrate by parts; differentiation of

The expressions in the square brackets are equal to zero because in the limits

Since

The expression for variation takes the form:

Besides,

The expression takes thes form:

From the arbitrariness of

where

is the 4-dimential antisymmetric tensor of 2-nd order:

The tensor elements are:

Thus, we have obtained the equations for a particle moving in an electroscalar field.

By using the action variation expression in the case when at least one of the limits is not equal to zero, for instance,

Note that

Let us determine now the generalized momentum

From here we obtain the Hamilton-Jacobi equation:

By the way the equation of motion of a particle moving in an electromagnetic field thus has the form:

Here

So we obtain the tensor presenting the covariant law of motion of a charged particle in transverse electromagnetic and longitudinal electroscalar fields:

can be considered as a relativistic law of summation of electromagnetic and electro- scalar fields or as a generalized intensity. So the mechanical and electroscalar energis enter to the total energy of charged particle with a different sign. However the electro- magnetic energy do not change the mechanical one. This properties may signify that a charged particle could be ready to come into a compound system. The expression for action covers both the action of free charges and their action in the electroscalar field. The action that is depending on the properties of the field itself, without charges, is governed by the field structure and components. Such a term is represented by one of the invariants of the electroscalar field which is defined by the expression

From the system of Equations (1) and (5) it follows that longitudinal electroscalar waves are responsible for the transport of Coulomb field. In point of fact, the system of Equation (5) contains an equation for electrostatics

Latin indexes runs from 1 to 4;

where

Under Lorenz transformations, components of the four-vector

where

while

or in the three-dimensional notation

From the definition of the Maxwell electric field:

where

Note that the Maxwell field

We will calculate the generalized momentum for the relativistic Lagrangian (10) of the electroscalar field:

The equation of Euler for the in electroscalar field is:

The time derivative of the momentum vector is the force of the electroscalar field acting on a particle:

where the full derivative of the four-dimensional quantity

While the velocity varies in its magnitude, the force acting on a particle is directed along the velocity. Further, after simplifications we get:

The right side of the equation has the appearance:

It should be pointed out that the derivative of the Lagrangian with respect to the radius is taken at the constant velocity.

Next, we define the force acting on the particle motion in the electroscalar field:

Thus, the electroscalar force is longitudinal, and its value is

By transforming this expression, we derive:

The magnitude of the force

If

of a particle in the electromagnetic and electroscalar fields. According to the definition of energy:

and the particle energy depends on the velocity. The energy of a particle in the electroscalar field equals:

The electroscalar energy enters into the full energy with a negative value relative to the mechanical energy, while variation of the particle energy with the time is the work done on the particle. In the case of an electromagnetic field, this work is equal to the product of the particle velocity and the force exerted on the particle by the transverse electromagnetic field:

In an electroscalar field this work is the product of the particle velocity and the force acting in the velocity direction:

From this expression it is evident that in the cases when the field

Today, we do not yet comprehend the nature and origins of how various manifestations of the electromagnetic, electroscalar, electroweak types of interaction are combined in one charged particle, for instance, in an electron. The continuity equation of the electroscalar field comprises a displacement charge, which leads to the necessity of taking into account both the field produced by these charges and the field of the charges themselves. Thus, an electron contains a “basic” charge and a displacement charge, which provides enlargement of its size due to the Coulomb law. Now we will try to find the energy of an electron in the electroscalar field. The second equation of the electroscalar field may be written in another form if we employ here the Gauss theorem:

The flux of the longitudinal electric field through a spherical surface with the radius R equals:

We equate the sides and obtain the law of electric intensity (Coulomb law) of the electroscalar field:

Thus, the electric field is conditioned both by the charge e and charge displacement

Further, we define the energy of a system of charges proceeding from the expression for the electroscalar field energy density:

Since

Here, the first integral by the Gauss theorem equals the integral taken through the surface that limits the volume, and the field equals zero at infinity. The second equation of the electroscalar field is substituted into the second integral, and the energy expression for the electroscalar field of a system of charges assumes the form:

If this formula is used for one charge, we can obtain that for

Thus, an electron contains a “basic” charge and a displacement charge, which provides enlargement of its size due to the Coulomb law. During the electron’s motion, the work done by the electroscalar field on the electron discloses the physical meaning of its negative energy and losing its electric status. So, a change in the electric status of the electron depends on the electroscalar energy and provides conditions for its transition into a compound state. If there is no appropriate object to get into a compound state with, the electron can continue to lower its electric status and can be practically neutral with a small mass.

The following conclusions can be made from this study:

1) A remarkable characteristic of the electrodynamics of electroscalar and electro- magnetic fields is that one and the same charged particle may exhibit fairly different properties.

2) The continuity equation of the electroscalar field comprises a displacement charge (by analogy with the field created by Maxwell’s displacement current), which leads to the necessity of taking into account both the field produced by these charges and the field of the charges themselves.

3) The time-dependent density of the electric charges accumulated along a longitudinal line enhances the longitudinal superposition of the charges. With the growth of the number of charges along the longitudinal line, the electroscalar field strength increases as well. On the contrary, the electromagnetic field generated by the field of charges incurs energy losses in the course of propagation and has no sources of replenishment.

4) In solid states the electroscalar radiation loses its energy in the cavities and due to that produces a corresponding plasmon electroscalar signal. The ability to detect the amplitude and frequency of this radiation would allow to observe the internal structure of the object.

5) The work done by the electroscalar field on a charged particle discloses the physical meaning of the negative energy of charged particles, shows the meaning of motion velocity for any charged particle and its ultimate value, as well as how the particle is transferred into the compound state by way of changing its electrical status. It should be noted that in the absence of an appropriate object to get into a compound state with, the particle can continue to lower it electrical status.

6) Decreasing the electrical status of the particle causes the particle to couple with any other body and make a transition into a compound state during the contact with an object. This state is the state of PHYSICAL VACUUM.

Thus, there is a possibility that the changes entailed by this new electroscalar dynamics are of profound nature and do not come into contradiction with those properties of the electromagnetic dynamics which make it convincing and, as a result, these properties can be included into the electrodynamics as a second dynamics of charge motion. The observation of neutrinos from the pp-cycle sheds light [

The properties and potentialities of the electroscalar field find their ways of realization in nature and in the live bio-organism of this field which represents a new type of energy. Organisms and fishes with electrosensitivity and a capability to register the electroscalar radiation can be observed in nature [

I thank the Editor and the referee for their remarks and comments. Also, I would like to thank Dr. V.B. Priezzhev for his attention and discussions. I am deeply obliged to my wife Liudmila for assistance in printing and supporting me.

Zaimidoroga, O.A. (2016) The Natural Law of Transition of a Charged Particle into a Compound State under the Action of an Electroscalar Field. Journal of Modern Physics, 7, 2188-2204. http://dx.doi.org/10.4236/jmp.2016.715190