Electron and Its Accelerated Movement

14

ELECTRON AND ITS ACCELERATED MOVEMENT

Kanarev F.M.

The announcement. Increase of mass of elementary particles, moving accelerated, - the experimental fact protecting relativists, as they consider, from criticism. We will look possibilities of classical theoretical mechanics in the decision of this problem.

1. The prologue

The new theory of a microcosm convincingly shows, that formation of structures of elementary particles the law of preservation of the kinetic moment operates. It is easy to be convinced at the consecutive analysis of process of formation of structure of electron and its behavior in electric field.

As the law of preservation of the kinetic moment operates formation of elementary particles from it follows, that lengths of waves of the elementary particles, established experimentally, should be equaled to radiuses of their rotation [1].

. (1)

The mathematical model of the specified law is represented by Planck's constant in the developed record

(2)

which follows from formulas for calculation energy of photons

. (3)

Let's pay attention once again to dimension of a constant of Planck (2). Occurrence in this dimension of concept a radian automatically follows from equality (1) as it specifies that electron rotates. For a long time the agreement on record simplification is accepted. It write down so. We agree with such simplification and we notice, that in the classical mechanics this dimension corresponds to vector size and has names: the moment of quantity of movement or the kinetic moment. In the classical physics this dimension names the moment of an impulse or the angular moment [1].

Thus, it is possible to represent the basic elementary particles as a first approximation in the form of rotating rings (fig. 1). The vector is directed along an axis of rotation of a ring so, that if to look from its edge rotation will be directed against an hour hand course. Planck's constant (2) in this case name spin [1].

Fig. 1. Schemes to concept definition: the kinetic moment of a ring

It is known, that photons, electrons, protons and neutrons have a uniform constant of localisation [1].

(4)

Dimension of this constant contains accurate physical sense: with increase of mass of a ring its radius decreases. It is peculiar, as we have already shown, to photons [1]. If the mass is constant, as at free electron so its radius is constant too [1].

2. Radius of electron

The theoretical and experimental information about electron is extensive. From it follows, that electron has mass and an electric charge . Have agreed to consider a charge of electron negative.

The resulted information gives us the bases to present electron as a first approximation in the form of a ring. It is quite natural, that at once there is a necessity of definition of radius of a ring of electron theoretically and experimentally. The theoretical size of radius of a ring of electron is defined by division of a constant (4) its localisations into mass [1].

. (5)

As, there is a possibility to compare theoretical size of radius (5) with experimental length of a wave of electron, defined by Compton. He has found the empirical formula for calculation of change of length of a wave of the x-ray photon reflected from electron

(6)

In this formula the size carries out a role of experimental factor which he named length of a wave of electron. It has appeared equal

(7)

Coincidence of theoretical size radiuses (5) of electron and experimental size of length of its wave (7) serves as the weighty proof of justice of equality.

Angular speed of rotation of a ring of electron we will define, using Planck's constant which for the electron registers so

(8)

(9)

Speed of points of a rotating base ring of electron is equal to a velocity of light.

(10)

It is difficult to present such big speed of rotation of a point at such small ring. And at once there is a question: instead of whether is better in such cases to use a numerical equivalent of a velocity of light with other physical sense (11)?

(11)

We leave search of the answer to this question to other researchers. To receive the mathematical models containing other characteristics of electron, it is necessary to analyze in details the forces operating on rotating ring.

3. Ring model of electron

It is known, that electron has own energy which usually define under the formula . However the sense of such assumption is not always deciphered. And it consists that if all mass of electron to translate in mass of a photon energy of electron will be equal. This fact has experimental acknowledgement. It is known, that mass of electron and a positron are equal. Cooperating with each other, they form two photons. That is why we can attribute to electron the energy equal to energy of a photon, having the corresponding mass. Energy of electron equal to energy of a photon, we name photon’s energy of electron. And now we investigate possibilities of ring model of free electron [1].

For this purpose we assume, that electron has equal among themselves kinetic and potential energy which sum is equal to its photon energy.

(12)

Calculation under this formula gives such value of photon’s energy of electron

. (13)

If free electron rotates only concerning the axis angular frequency of rotation of ring model of free electron defined of the formula (12), appears equal [1].

(14)

and radius of ring

(15)

Apparently, theoretical sizes of angular speed of electron, defined under different formulas (9) and (14) are equal. Theoretical sizes of radius of a ring of electron, defined under formulas (5) and (15) are equal to experimental value compton’s lengths of its wave (7).

Thus, not having revealed while structure of electron, we have received its simplified model – a ring. This model helps us to analyze mechanical behavior of electron, but almost does not contain the information on its electromagnetic properties. Therefore we will look for such mathematical models describing behavior of ring model of electron which would contain its charge the magnetic moment and intensity of a magnetic field of electron [1], [2].

By search of these models not to do without new hypotheses. The bases for their formulation we take from the theoretical and experimental information describing behavior of charged elementary particles in magnetic fields. Experiments show, that electron moves in a magnetic field on a spiral (fig. 2,).

It means, that electron has a magnetic field similar to a magnetic field of a rod magnet and its magnetic poles, co-operating with in an external magnetic field, focus it definitely. If electron that rotates concerning the axis, moving in a magnetic field, it should describe a spiral in process of reduction of its speed which is formed by resistance of an environment (fig. 2)

Experiments on accelerators have shown, that the curvilinear trajectory of electron in a magnetic field is well described by the mathematical model reflecting equality between centrifugal force of inertia, operating on electron, and force of a magnetic field [2].

. (16)

а)

b)

Fig. 2. The scheme of ring model of electron

Here involuntarily there is an assumption, that process of formation of ring structure of electron the same law also operates. We will consider fruitfulness of this hypothesis. As electron as we assume, has the ring form for the description of process of formation of a ring it is necessary to translate a parity (16) in the differential form.

As the charge of electron is in regular intervals distributed on length of its ring model each element of a ring will have mass and a charge (fig. 2, b).

On each element of a ring some forces will operate: force of inertia coulomb forces of pushing away, force of magnetic interaction and any others, while forces unknown to us. We will assume, that centripetal force, i.e. a resultant the force bending a trajectory of separate elements of a ring and forcing a ring to make rotary movement round an axis, will be equal (fig. 2, b) [2]. The further analysis as it will be shown, will confirm fruitfulness of this assumption.

(17)

Let's check up dimensions of the right and left parts of the formula (17) [3].

. (18)

They are identical, the formula (17) means is reliable. Designating mass density of a ring, and charging - we have [1]:

(19)

(20)

As

(21)

(22)

and the equation (17) becomes

. (23)

Integrating, we will find

(24)

So, we have received a mathematical parity into which enter: mass of free electron, its charge intensity of a magnetic field in a ring which is generated by a charge of a rotating ring, angular frequency ring and radius of electron. Lacks in this parity Bohr’s magneton .

(25)

Let's pay attention to that fact, that in the resulted formula (25) - size vector, it gives vector properties to bohr’s magneton.

Let's transform a parity (24) as follows [1]

(26)

From this it is had

. (27)

Now we can define from a parity (26) intensity of a magnetic field in ring model of electron, angular speed of rotation of a ring and its radius.

(28)

Let's pay attention to very big intensity (28) magnetic fields in the centre of its symmetry. From (26) it is had [1]

, (29)

That completely coincides with the values of this size defined under formulas (9) and (14).

From the formula (26) one more mathematical model for radius calculation of electron follows

. (30)

From here

(31)

where - bohr’s magneton; - intensity of a magnetic field in the symmetry centre of electron.

So, the main parametre of ring model of free electron - the radius of a ring defined under formulas (5), (15) and (31), has appeared identical and equal to experimental size of length of a wave of electron (7) [1]. The ring model of electron forms intensity of electric field . It is defined under the formula

(32)

It is possible to tell, enormous intensity. It surpasses intensity of the electric fields created by the person, almost on seven orders.

Lack of ring model of electron that it does not open the reason of a birth of a positron, therefore the ring should have any internal structure. Search of this structure - the following problem.

Before to start its decision, we will pay attention to the scheme of ring model of electron, following from our calculations (fig. 2). The Most important feature of the theory and model of electron is coincidence of directions of vectors and . To simplify representation bohr’s magneton in drawings, we will designate it and we name the magnetic moment of electron.

4. Toroidal model of electron

So, electron as a first approximation has the ring form. As the second approach to electromagnetic model of electron we will consider torus. We will consider to begin with its hollow. Radius of a circle of section of torus (fig. 3) we will designate through. Then the area of its surface will be defined under the formula [1]

(33)

Let's designate superficial density of an electromagnetic substance of electron. Then

(34)

Fig. 3. The scheme of toroidal model of electron

Let's define the moment of inertia hollow torus. It is had from fig. 3

(35)

(36)

As electron shows simultaneously electric and magnetic properties and has the kinetic moment we have bases to assume, that it has two rotations. Usual rotation concerning an axis of symmetry with angular frequency we name the kinetic rotation forming its kinetic moment and kinetic energy. And the second - vortical rotation concerning a ring axis with angular frequency (fig. 3). We name its potential rotation forming its potential energy and the magnetic moment. Vortical rotation concerning a ring axis torus forms a magnetic field of electron, therefore potential energy of electron characterises its potential electric and magnetic properties [1].

At the energy analysis of electron as rotating ring, we have shown, that its full photon energy consists of kinetic and potential componentsequal among themselves. We will look at possibility of realisation of this postulate in toroidal model of electron. Kinetic energy of rotation hollow torus will be defined under the formula (fig. 3) [1].

(37)

Considering frequency ( 28), we have

(38)

Apparently (38), kinetic energy of electron is equal to half of its full, photon energy (13), confirming working capacity of our postulate [1]. The size of radius of a circle of section torus (fig. 3) is defined from potential rotation of electron with frequency. For this purpose we assume, that

(39)

As the velocity of light concerning space is constant, that is the bases to believe, that speed of points of an axial ring of torus in kinetic rotation is equal to speed of points of a surface of torus in potential rotation [1].

(40)

From these parities we will find