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 r of their rotation [1].
  r.
(1)
The mathematical model of the specified law is represented by Planck's constant h in the
developed record
h  mr 2  const  kg  m 2  rad / s
(2)
which follows from formulas for calculation energy of photons
E f  mC 2  m2 2  hv .
(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 radian / s . It write
down so s 1 . We agree with such simplification and we notice, that in the classical mechanics
this dimension corresponds kg  m 2  s 1 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 h 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 h of a ring
2
It is known, that photons, electrons, protons and neutrons have a uniform constant of localisation k 0 [1].
k0 
h mr 2

 m  r  2.210  10 42 kg  m  const .
C
r
(4)
Dimension of this constant contains accurate physical sense: with increase of mass m of a
ring its radius r 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 me  9.109  10 31 kg and an electric charge e  1.602  10 19 C . 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 re of a ring of
electron is defined by division of a constant k 0 (4) its localisations into mass me [1].
re (theor ) 
k 0 2.210  10 42

 2.426  10 12 m .
31
me 9.109  10
(5)
As, re  e there is a possibility to compare theoretical size of radius re (theor ) (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
  e (1  cos  ).
(6)
In this formula the size  е carries out a role of experimental factor which he named
length of a wave of electron. It has appeared equal
e (exp er )  2.426  10 12 m.
(7)
Coincidence of theoretical size radiuses re (theor ) (5) of electron and experimental size
of length e (exp еr ) of its wave (7) serves as the weighty proof of justice of equality е  rе .
Angular speed  e of rotation of a ring of electron we will define, using Planck's constant
which for the electron registers so
h  me re2 e  const.
(8)
e 
h
6.626  10 34

 1.236  10 20 s 1  const .
2
31
12 2
me re
9.109  10  (2.426  10 )
(9)
Speed Ve of points of a rotating base ring of electron is equal to a velocity of light С .
Ñ   e  re  1.236  10 20  2.426  10 12  2.998  10 8 m / s.
(10)
3
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)?
Ñ
1
1

 2.997925  108 m / s.
12
6
 0  0
8.854187  10  1.256637  10
(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
E e  me C 2 . 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 E e  me C 2 . 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 E e 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 Ek and potential E0 energy which sum is equal to its photon energy E e .
Ee  Ek  E0  meC 2  me re e  h  e .
2
2
(12)
Calculation under this formula gives such value of photon’s energy of electron
Ee  me C 2 
9.109  10 31  (2.998  10 8 ) 2
 5.110  10 5 eV .
19
1.602  10
(13)
If free electron rotates only concerning the axis angular frequency of rotation  e of ring
model of free electron defined of the formula (12), appears equal [1].
Ee 8.187  10 14

 1.236  10 20 s 1 ,
h
6.626  10 34
(14)
h
6.626  10 34

 2.426  10 12 m.
31
20
me   e
9.109  10  1.236  10
(15)
e 
and radius of ring
re 
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
e  re  2.426  10 12 m (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
4
mathematical models describing behavior of ring model of electron which would contain its
charge e the magnetic moment M e and intensity of a magnetic field H e 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].
me  Ve2
 e  H e  Ve .
R
(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 l of a ring will have mass m and a charge e (fig. 2, b).
On each element of a ring some forces will operate: force of inertia Fi  m  Ve 2 / re coulomb forces of pushing away, force of magnetic interaction and any others, while forces un-
5
known 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 Fe  e  Н e  Ve (fig. 2, b) [2]. The further analysis as it will be shown, will confirm fruitfulness of this assumption.
2
m  Ve
 e  Н e  Ve .
(17)
re
Let's check up dimensions of the right and left parts of the formula (17) [3].
M  L2 T  I  M  L

Н H.
T2 L
T 2  I T
(18)
They are identical, the formula (17) means is reliable. Designating mass density  m of a
ring, and charging e - we have [1]:
m  m  l  m  re  ,
(19)
e  e l  e  re  .
(20)
As
me
,
2re
e
e 
2re
m 
(21)
(22)
and Ve  C the equation (17) becomes
2
2
eH e
me C
0 2  d  0 2  re  d
.
Integrating, we will find
eН e 
me C mee re

 me  e .
re
re
(23)
(24)
So, we have received a mathematical parity into which enter: mass me of free electron, its
charge e intensity of a magnetic field Н e in a ring which is generated by a charge of a rotating
ring, angular frequency  e ring and radius re of electron. Lacks in this parity Bohr’s magneton
В .
eh
Â 
 9.274  10  24 J / T .
(25)
4  me
Let's pay attention to that fact, that in the resulted formula (25) - h size vector, it gives vector properties to bohr’s magneton  В .
Let's transform a parity (24) as follows [1]
He 
From this it is had
mee 4me he
he
Ee



.
e
4  eh
4В 4В
(26)
6
4  H e   B  E e  h e .
(27)
Now we can define from a parity (26) intensity of a magnetic field Н e in ring model of electron, angular speed of rotation  e of a ring and its radius re .
Í
e

Ee
5.110  10 5  1.602  10 19

 7.017  10 8 T .
 24
4   Â
4  3.142  9.274  10
(28)
Let's pay attention to very big intensity (28) magnetic fields in the centre of its symmetry.
From (26) it is had [1]
e 
4   Â  Í
h
e

4  3.142  9.274  10 24  7.025  10 8
 1.236  10 20 s 1
34
6.626  10
,
(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
m r 2 2  r
hC
4В Н e  Ee  me C 2  e e e e 
.
(30)
re
re
From here
Ñ h
2.998  10 8  6.626  10 34
(31)
re (theor) 

 2.426  10 12 m,
 24
8
4   Â  Í e 4  3.142  9.274  10  7.025  10
where -  Â  9.274  10 24 J / T bohr’s magneton; - Í e  7.025  10 8 T intensity of a magnetic
field in the symmetry centre of electron.
So, the main parametre of ring model of free electron - the radius re 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 U E . It is
defined under the formula
UE 
e
40 re2

1.602  10 19 C
 2.448  1014 V / m  const. (32)
4  3.142  8.854  10 12 F / m  (2.426  10 12 ) 2 m 2
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 h and  В . To simplify representation bohr’s
magneton  В in drawings, we will designate it  В  M e and we name the magnetic moment of
electron.
7
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  e . Then the area of its
surface will be defined under the formula [1]
Se  2e  2re  4 2 e re .
(33)
Let's designate superficial density  m of an electromagnetic substance of electron. Then
m
me
m  e 
.
S e 4 2 e re
(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
I Z   m  re .
2
(35)
m  2e  l1  m  2e  m  re  .
2
me re 2
IZ  
 d  me  re 2 .
2

0
(36)
As electron shows simultaneously electric and magnetic properties and has the kinetic moment h we have bases to assume, that it has two rotations. Usual rotation concerning an axis of
symmetry with angular frequency  e we name the kinetic rotation forming its kinetic moment h
and kinetic energy E K . And the second - vortical rotation concerning a ring axis with angular
frequency   (fig. 3). We name its potential rotation forming its potential energy E0 and the
magnetic moment М е . 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 E e consists of kinetic E K and potential components E0 equal 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].
8
EK 
Ee 1
1
1
  I Z   e 2   me  re 2   e 2  h e .
2
2
2
2
(37)
Considering frequency  e  1.236  10 20 s 1 ( 28), we have
EK 
h e 6.626  10 34  1.236  10 20

 2.556  10 5 eV .
19
2
2  1.602  10
(38)
Apparently (38), kinetic energy E K of electron is equal to half of its full, photon energy
(13), confirming working capacity of our postulate [1]. The size of radius  e of a circle of section
torus (fig. 3) is defined from potential rotation of electron with frequency   . For this purpose
we assume, that
   2e .
(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].
C   e  re      e .
(40)
From these parities we will find
  2e  6.283  1.236  10 20  7.763  10 20 s 1
(41)
and
e 
C


2.998  10 8
 3.862  10 13 m.
20
7.763  10
(42)
Believing, that vortical rotation of electron generates its potential energy, we have
E0 
1
9.109  10 31  (3.862  10 13 ) 2  (7.763  10 20 ) 2
me   e2   2 
 2.555  10 5 eV .
2
2  1.602  10 19
(43)
Apparently, potential energy E0 of electron is equal to its kinetic energy E K (38). Putting
results (38 and 43), we will receive full photon energy of free electron (23).
So, equality kinetic and potential energies of electron gives the basis to consider proved
postulates (37), (38). We will define intensity U E of electric field on a surface of torus. Considering the area of its surface (33) and a parity between radiuses re  2e , we have [1]
UE 
e
4 2  0  e2

4 2  e
1.602  10 19 C


4 2  0 re2  8.854  10 12 F / m  (2.426  10 12 ) 2 m 2 .
(44)
 3.074  1015 V / m 2  const .
It is very big intensity of electric field, but, according to law Coulomb, it decreases proportionally to a square of distance from a surface torus of electron. The size of specific superficial density of mass hollow torus of electron is interesting. It will be defined under the formula
9
 mT 
me
m
9.109  10 31
 e2 
 2.464  10 8 kg / m 2  const .
2re  2e 2re
2  3.141  (2.426  10 12 ) 2
(45)
If we on a correct way from toroidal model of electron the mathematical model for calculation bohr’s magneton, should follow  B . Considering section radius of torus  е (42) and
known dependences between a current I and wire section  е
I  eC / 2е ,
(46)
And also dependence of the magnetic moment М 0 formed by a current round a conductor
М 0  I     e2 ,
(47)
Let's find bohr’s magneton [1]
 Â  0,5  C  e   e  0,5  2,998  108  1,602  10 19  3,862  10 13 
 9,274  10 24 J / T  const .
(48)
Let's check up dimension of this formula [1], [3].
 Â  0,5  C  e   e  const .  Ñe e  J / T 

L  T  I  L L2  M  T 2  I

 L2  I  L2  I .
2
T
T M
(49)
Dimension is observed, therefore the formula (48) is reliable. Coincidence of results of
calculation of photon energy of electron, bohr’s magneton and radius of electron under different
formulas, gives the basis to assume, that electron represents the closed ring whirlwind forming
toroidal structure which rotates concerning the axis of symmetry and to a ring axis of torus, generating thus its kinetic E K and potential E0 energy and also the magnetic moment of electron
equal М е to magneton of Bohr М е   В (fig. 4, a).
а)
b)
с)
Fig. 4: a) - the scheme of theoretical model of electron
(The part of magnetic power lines) is shown only; b) the scheme electronic cluster;
c) scheme radiations by electron 6 magnetic ring fields of a photon
If to show all set of the lines characterising a magnetic field of electron its model will
take the form, close to the apple form (fig. 4, a).
10
The new information about electron gives the bases to consider, that, the size resulted in directories named ree  2.817  10 15 m in classical radius of electron, is radius of the cylinder limiting rapprochement of magnetic power lines of electron, going along an axis of its rotation in one
direction (fig. 4, a). Reliability of it is confirmed with dimensionless size of thin structure which
 is equal to the relation of length of a circle of the specified 2ree cylinder to radius re of
electron [3].
2ree 2  3.142  2.817  10 15

 0.0073   .
re
2.426  10 12
(50)
And now we will present, that external forces start to rotate such torus in the opposite direction or to brake its rotation. At once on an equatorial surface of torus it is formed six vortical, radially directed ring fields (fig. 4, c). Leaving from electron, they form structure of six ring magnetic fields closed with each other (fig. 4, c). The slightest change of density of one of this field
or its slightest remoteness from the geometrical centre forms noncentral forces which start to rotate such structure. Arising asymmetry between its fields forms the unstable position of such
structure automatically attracting it in rectilinear movement with a velocity of light С [1].
The rest part of electron restores again the vortex movement, having changed accordingly
angular speeds e ,   and radiuses re , e so that difference between them in time 2 has remained. Energy of electron will decrease E e accordingly.
As energy of electron is equal to product of a constant of Planck on angular frequency
E e  h e  me re2 e2 after radiation of a photon energy of electron will decrease at the expense
of change of its mass. That Planck's constant has kept the constancy, radius re of electron should
increase, and frequencies -  e to decrease.
The changed parametres of electron break stability of its condition therefore it is compelled to restore initial mass. If close there is a photon with such mass of electron will immediately absorb it and will restore all constants. If close there is no the photon necessary for restoration of the lost mass of electron one possibility – to restore the mass by absorption of a substance
of environment which we name an aether. It will absorb such quantity of this substance which
will restore its constant mass me . All its other parameters and the constants operating its stability will automatically be restored also.
Thus, free electron has strictly constant mass me a charge ee and radiuses re ,  e . When
it establishes connection with another valency electron it radiates a photon, and its parameters
change, but stability remains thanks to energy of communication with another valency of electron. If this communication to break off mechanical by stay conditions of electron in a stable
condition disappear. To restore these conditions, electron should absorb the radiated photon or
quantity of an electromagnetic substance equivalent to it from environment which we name an
aether. Only after that it will keep the stability.
Let's pay attention to that radiuses of light and infra-red photons on many orders is more
than radius of electron. It means, that at the moment of radiation leaving ring magnetic fields
form photon structure on considerable distance from electron (fig. 4, c), defined by duration of
transient from V to С . As the radius of electron is equal to radius of a x-ray photon electron
cannot radiate a gamma photon. This function is carried out by a proton at synthesis of nucleus.
Thus, electron has the form rotating hollow torus (fig. 4, a). Its structure appears steady
thanks to presence of two rotations. The first - concerning an axis which are passing through the
geometrical centre of torus of perpendicularly plane of rotation, and the second - vortical rotation
concerning the ring axis which are passing through the centre of a circle of section torus.
11
Some methods of calculation of base radius of torus, including its various power and electromagnetic properties, yield the same result coinciding with experimental value Compton’s
length of a wave of electron, namely m e  re  2.426  10 12 .
So, at a model substantiation of electron we have involved in the analysis already existing
laws Columb both Newton and following constants: a localisation constant k 0 a velocity of light
C, Planck's constant h mass me of rest electron, its charge e energy of rest electron, an electric
constant  0 a magnetic constant  0 Bohr's magneton  В which we designate as  e  M e
Compton's length of a wave of electron which now it is necessary to name Compton's radius re
of electron.
Other important characteristic of electron is his spin. It is equal in accuracy Planck's constant h  6.626 10 34 . Its vector properties follow from its dimension - kg  m 2 / s the kinetic
moment.
The third important characteristic of electron - the magnetic moment М е which generates
intensity of a magnetic field Н е of electron (fig. 4, a). It is equal in its geometrical centre Í e  7.025  10 8 T . It is considerable size, but it intensively decreases in process of removal
from the geometrical centre of electron along an axis of its rotation.
Thus, electron represents hollow torus which has two rotations: concerning an axis of symmetry and to a ring axis of torus. Rotation of electron concerning the central axis the kinetic
moment - h vector size operates. Rotation concerning a ring axis of tirus forms a magnetic field
of electron, and directions of magnetic power lines of this field form two magnetic poles: northern N and southern S (fig. 4, a).
The model of electron (fig. 4, a) involuntarily forms representation about formation possibility clusters of electrons. Heteronymic magnetic poles can pull together them, and the electric
charges with the same name to limit this rapprochement. As a result electrons, incorporating with
each other, can form clusters (fig. 4, b). In the course of formation of cluster electrons radiate
light photons which form an electric spark and the crash is thus heard. The crash is a consequence of sharp increase of pressure in a spark zone the radiated light photons which sizes on 5
orders there are more than sizes of electrons which radiate them.
In the Nature electric sparks turn to lightnings, and a crash of an electric spark - in powerful peals of thunder. Thus it is necessary to mean, that natural lightnings form the photons radiated by electrons at formation clusters of ОН  . A Primary factor raising pressure in a zone of
a lightning, - the increased volume of the photons radiated by electrons. They have more volume
on 5-7 orders than electrons which radiate photons,.
Thus, pressure in cartridges, shells and rocket engines is formed by the photons radiated
by electrons of molecules, participating in chemical reactions during this moment. Quite naturally, the more the length waves (radius) of the photon radiated by electron, is the more pressure
and more speed of a rocket. The loop of a smoke leaving a nozzle of a rocket «Iskander» convincingly proves, that pressure in the chamber of combustion of the engine of this rocket is
formed by the infra-red (invisible) photons which sizes can be more sizes of light photons on 2
and even - 3 order. As a result speed of the specified rocket as it is declared on TV, reaches 2100
m/s. These are more speeds of a bullet. But it not the unique physical factor providing so big
speed of the given rocket. So old physical and chemical idea that the pressure pushing out bullets
and shells and forming speed of a rocket, is created by gases, deeply wrongly.
The analysis of the stated shows, that structure formation of electron (fig. 4, a) operate more
than 20 constants in which reliability of all hypotheses formulated by us was reflected and they
have got statuses of postulates.
12
5. Behavior of electron at increase in speed of its movement
Modern relativists, not in forces to keep a stream of criticism concerning their erroneous
views, expose as protective boards results of some experiments which as they consider, it is possible to understand only on the basis of relativistic ideas. The experimental fact of increase in
mass concerns their of electrons at increase in speed of its progress. They interpret result of this
experiment by means of a relativistic parity
m
me
1V 2 / C 2
.
(51)
Really, from this parity follows, that with increase in speed of progress V of electron its mass
m increases in comparison with mass of rest me . Ask them: why and at the expense of what it
occurs? You do not receive the answer, as their interpretation is based not on knowledge, and on
belief in infallibility einshtein’s ideas of a relativity. Thus they assert, that this parity can be received only from relativistic ideas and anywhere more.
To show, that variants of a conclusion of the formula (51) and variants of its interpretation
can be a little, we will try to find also a new conclusion of this formula and new interpretation of
the reason of increase in mass of rest of electron (fig. 4, a) at its accelerated movement [4].
On fig. 5 model movement of electron in electric field is shown. As the charge of electron is
formed on its toroidal surface a movement direction of electron in electric field will form, first of
all, equatorial points of this surface. And in a free condition, and in movement of electron possesses the kinetic moment h  me re2  e  meCre which vector h  me re2  e  meCre is directed
along a rotation axis of torus [4].
Considering, that the accelerated movement of electron occurs under the influence of external influence which changes a condition of environment (in which moves electron), forming
some resistance to its movement, we will designate mass of electron in its progress through m .
It will mean, that we have included factor of resistance of environment unknown to us in a symbol m . It also differs from a symbol in me expression of the kinetic moment. In this case the
impulse of electron will register so: mV (fig. 5).
Thus, at compulsory progress to electron two are enclosed perpendicular each other a
mechanical vector h and mV . The first of them characterises rotation of electron concerning
the axis of symmetry, and the second - compulsory progress. At once there is a question: what
total movement will have electron in that case? It after all too should be characterised by the vector size equal to the sum of first two vectors. But we cannot put these vectors as their numerical
values have different dimensions. To eliminate this lack, it is necessary to change mV numerical
value of the second vector mV so that it had the same dimension, as well as a vector h . For this
purpose we will increase it by size re . It is quite natural, that the sum of first two vectors will be
equal to the third vector which should characterise at once two mentioned movements of toroidal
model of electron (fig. 4, a). That the third vector, also as well as the second, considered resistance of environment, we will designate in its expression mass of electron a symbol m . Besides, the third vector should have the same dimension, as well as first two. For this purpose we
will increase also its numerical size on re (fig. 5, b).
13
Fig. 5. The movement scheme of electron in electric field
After such preparation we have the right to find the geometrical sum of first two vectors
h and mV . From fig. 5 we will receive
(mCre ) 2  (meCre ) 2  (mVre ) 2
(52)
or
m 2C 2  m 2V 2  me2C 2 .
Let's definitively find
m
me
1V 2 / C 2
.
(53)
It is the well-known relativistic parity showing increase of mass of electron at increase
of speed of its progress in electric field (51). At once we will note the most important thing. We
have received this parity not in psevdoevclidean geometry of Minkovsky, but in geometry of Euclid and within the limits of the Axiom of Unity of space – matters - time.
Now there is clear a kinematic sense of the relation V 2 / C 2 . When on electron no external forces and V  0 and m  me it rotates only concerning the axis operate V  0 , m  me . The
instant centre of rotation P in this case coincides with the geometrical centre of electron (fig. 5,
b, c).
As soon as electron receives also progress at once its instant centre of rotation starts P to
leave from the geometrical centre to periphery of its toroidal structure (fig. 5, d). During the
moment when forward speed will come from V to nearer speed C which the ring axis of torus
rotates, the instant centre of rotation will leave from the geometrical centre of electron on size
(fig. 5, d, in a point k). In this case V  C and m  . these changes occur in the system of
14
readout connected with the observer or an external source, compulsorily forming its accelerated
progress.
And now we will recollect, that in this case except forward and rotary movements of electron
is also potential (vortical) rotation. We already noticed, that sharp change of parities between kinetic and potential rotations of electron results either in absorption, or to radiation of a photon
depending on a direction of change of this parity. If this change slows down kinetic rotation there
is a process of radiation of photons and if accelerates - absorption. From the described the reason
of radiation of photons by electrons, moving in any environment, named effect Cherenkov follows.
It is easy to present, that both these of a case are possible at variable movement of electron in
electric field. In one of them radiation of photons should be observed and it name brake, and in
other - absorption, but not photons, and a substance of the environment formed by electric field
in which moves electron. Roughly speaking, the toroid of electron will wind on itself power lines
of a field and at the expense of it to increase the mass m at V  C (fig. 5,).
Thus, we have bases to assume, that energy so also mass of electron, increase at the expense
of absorption of a material basis of the environment accelerating its movement. We can name
this environment an aether or a dark matter. Even the superficial analysis of movement of toroidal model of electron in electric field gives answers to questions: why and at the expense of what
the mass of electron increases? And, these answers have all signs which allow to carry them at
the first stage to the category of the hypothetical.
It is quite natural, that Planck's constant should h  me re2 e  me re C  Const remain a
constant and at the accelerated movement. If the mass me of electron increases, at preservation
of a constancy of speed of equatorial C  Const points of torus its radius should re decrease. That
is why with increase in speed of electron in an electronic microscope as conformists speak, their
resolution increases.
Using a parity (53), we will find mass of electron at the speed of its movement close to a
velocity of light V  0.99C .
me
me
(54)
m
m
 7.089me .
1V 2 / C 2
1  (0.99C ) 2 / C 2
As the mass of electron has increased to m1  7.089me we and should use this
m1  7.089me size at radius calculation of electron
r1 
h
6.626  10 34

 3.423  10 13 m .
31
8
m1  C 7.089  9.109  10  2.998  10
(55)
Apparently (55), the radius of electron (5), (15), (31) is decreases at increase in speed of
its movement. As behavior of electron as well as behavior of a photon, the law of localisation of
particles product of the increased mass m1 of electron on its reduced radius r1 should be equaled
to a constant of localisation (4) operates in movement m1 r1 .
k e  r1  m1  3.423  10 13  7.089  9.109  10 31  2.210  10 42 kg  m .
(56)
And now we will present, that external forces not only have braked kinetic rotation of
electron, but also have changed its direction. What will occur to a direction of potential rotation?
It too will change and electron will turn to a positron. But this very unstable electromagnetic
formation, therefore time of a life of a positron is insignificant a little.
On fig. 4, a the part of magnetic power lines and the lines characterising electric field of
electron is shown only. If to show all set of these lines the model of electron will take the form,
15
close to the apple form. As power lines of electric field are perpendicular to power lines of a
magnetic field electric field in such model becomes almost spherical, and the magnetic field under the form will be close to a magnetic field of a rod magnet.
Let's pay attention to that magnetic power lines have the maximum rapprochement in the
symmetry centre of electron (fig. 4, a). It gives us the basis to believe, that the radius of a circle
limiting r ee magnetic power lines in the centre of symmetry of electron, is equal to size which
has been named by classical radius of electron (4).
The model of electron (fig. 4, a) involuntarily forms representation about possibility of
their formation clusters. Heteronymic magnetic poles can pull together them, and the electric
charges with the same name to limit this rapprochement. As a result electrons, incorporating,
with each other, can clusters. Already there is an experimental proof to this fact [5], [6], [7], [8].
THE CONCLUSION
The stated information proves an inconsistency of last support relativists – reception of
mathematical model for calculation and an explanation of increase of mass of elementary particles at increase in speeds of their movement only from relativistic ideas. The specified effect is
realised and within the limits of laws of classical mechanics.
Литература
1. Kanarev F.M.The Foundation of Physchemistry of Microvorld. The monography. Volume I.
15 edition. http://www.micro-world.su/
2. Sourtz. E.Neobyknovennaja of the physicist of the ordinary phenomena. Volume 2. М: "science"1987.
3. Burdun G. D. The directory on the international system of SI. Standards Publishing House. M.
1977.
4. Kanarev F.M. The Foundation of Physchemistry of Microworld. The monography. 5 edition.
Krasnodar 2004.396pages.
5. Kenneth R. Shoulders, "Method of and Apparatus for Production and Manipulations of High
Density Charge", U.S. Patent 5,054,046, issued Oct 1, 1991.
6. Ken Shoulders & Steve Shoulders, "Observations on the Role of Charge Clusters in Nuclear
Cluster Reactions", J. of New Energy, vol. 1, no 3, pp 111-121, Fall 1996, 7 refs, 22 figs.
7. Hal Fox, Robert W. Bass, & Shang-Xian Jin, "Plasma-Injected Transmutation", J. of New
Energy, vol. 1, no 3, Fall 1996, pp 222-230, 23 refs, 4 figs.
8. Shang-Xian Jin & Hal Fox, "High Density Charge Cluster Collective Ion Accelerator," J. of
New Energy, vol. 4, no 2, Fall 1999, pp 96-104, 47 refs, 4 figs., 3 tables.