Without a conflict model of electron
The model of electron is offered with quark distribution of charge density and ”white hole” (on similarity of ”black hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal formula and on the impulse of the electromagnetic field. A model...
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irk-123456789-1951372023-12-03T16:03:40Z Without a conflict model of electron Tchaban, Vasil Nuclear physics and elementary particles The model of electron is offered with quark distribution of charge density and ”white hole” (on similarity of ”black hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal formula and on the impulse of the electromagnetic field. A model in order to please a classic electrodynamics keeps monolithic nature of elementary particle, and in order to please a quantum allows the separate charged zones to interpret as separate quarks. Coming from harmony of spheres of the separate charged zones, a white hole can be interpreted as white (neutral) quark conditionally in addition to three coloured. As after the electric radius re = 1.185246·10⁻¹⁵ m of white hole the laws of electricity do not operate, then the crisis of point charge is removed at the same time too, because of must be: r ≥ re. Запропоновано модель електрона з кварковим розподілом густини заряду й "білою дірою" (на подобу "чорної діри" в ґравітації) у центрі. Така структура скасовує кризу електромаґнітної маси, обчисленої за універсальною формулою енергії і за імпульсом електромаґнітного поля. Модель на догоду класичній електродинаміці зберігає монолітність елементарної частинки, а на догоду квантовій -- дозволяє окремі заряджені зони трактувати як окремі кварки. Виходячи з гармонії сфер окремих заряджених зон, "білу діру" можна умовно трактувати як білий (нейтральний) кварк на додаток до трьох кольорових (?). Оскільки за електричним радіусом "білої діри" re = 1.185246·10⁻¹⁵ m закони електрики не діють, то водночас знімається криза точкового заряду, як нереального, бо мусить бути r ≥ re . Предложена модель электрона с кварковым распределением плотности заряда и "белой дырой" (на подобие "черной дыры" в гравитации) в центре. Такая структура устраняет кризис электромагнитной массы, вычисленной по универсальной формуле энергии и через импульс электромагнитного поля. Модель на удовлетворение классической электродинамике сохраняет монолитность элементарной частицы, а на удовлетворение квантовой -- разрешает отдельные заряженные зоны рассматривать как отдельные кварки. Исходя из гармонии сфер отдельных заряженных зон, "белую дыру" можно условно рассматривать как белый (нейтральный) кварк в дополнение до трех цветных (?). Поскольку за электрическим радиусом "белой дыры" re = 1.185246·10⁻¹⁵ m законы електричества не действуют, то одновременно устраняется кризис точковости заряда, как недействительного, ибо должно быть r ≥ re . 2019 Article Without a conflict model of electron / Vasil Tchaban // Problems of atomic science and technology. — 2019. — № 3. — С. 16-20. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 11.25.-w, 12.60.Jv, 02.10.Ws http://dspace.nbuv.gov.ua/handle/123456789/195137 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear physics and elementary particles Nuclear physics and elementary particles Tchaban, Vasil Without a conflict model of electron Вопросы атомной науки и техники |
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The model of electron is offered with quark distribution of charge density and ”white hole” (on similarity of ”black hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal formula and on the impulse of the electromagnetic field. A model in order to please a classic electrodynamics keeps monolithic nature of elementary particle, and in order to please a quantum allows the separate charged zones to interpret as separate quarks. Coming from harmony of spheres of the separate charged zones, a white hole can be interpreted as white (neutral) quark conditionally in addition to three coloured. As after the electric radius re = 1.185246·10⁻¹⁵ m of white hole the laws of electricity do not operate, then the crisis of point charge is removed at the same time too, because of must be: r ≥ re. |
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Tchaban, Vasil |
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Tchaban, Vasil |
| title |
Without a conflict model of electron |
| title_short |
Without a conflict model of electron |
| title_full |
Without a conflict model of electron |
| title_fullStr |
Without a conflict model of electron |
| title_full_unstemmed |
Without a conflict model of electron |
| title_sort |
without a conflict model of electron |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Nuclear physics and elementary particles |
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http://dspace.nbuv.gov.ua/handle/123456789/195137 |
| citation_txt |
Without a conflict model of electron / Vasil Tchaban // Problems of atomic science and technology. — 2019. — № 3. — С. 16-20. — Бібліогр.: 6 назв. — англ. |
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Вопросы атомной науки и техники |
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AT tchabanvasil withoutaconflictmodelofelectron |
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2025-07-16T22:57:20Z |
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1837846125892075520 |
| fulltext |
WITHOUT A CONFLICT MODEL OF ELECTRON
Vasil Tchaban∗
Lviv Polytechnic National University, Lviv, Ukraine
(Received December 22, 2017)
The model of electron is offered with quark distribution of charge density and ”white hole” (on similarity of ”black
hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal
formula and on the impulse of the electromagnetic field. A model in order to please a classic electrodynamics keeps
monolithic nature of elementary particle, and in order to please a quantum allows the separate charged zones to
interpret as separate quarks. Coming from harmony of spheres of the separate charged zones, a white hole can
be interpreted as white (neutral) quark conditionally in addition to three coloured. As after the electric radius
re = 1.185246 · 10−15 m of white hole the laws of electricity do not operate, then the crisis of point charge is removed
at the same time too, because of must be: r ≥ re.
PACS: 11.25.-w, 12.60.Jv, 02.10.Ws
1. INTRODUCTION
Unfortunately until now the theory of the electro-
magnetic field does not have a trouble-free model
of the own simplest charged elementary particle - of
electron. Self-contradictions of the known construc-
tions are taken two problems.
The first from them is related to the paradox of
self-acting of electron on itself. Its essence consists
in that the electromagnetic mass of movable electron
me, got through the impulse of the electromagnetic
field, appears less than the mass of rest. Up the deci-
sion of this problem the lightest minds of creators of
theoretical physics took at one. But all their results
in any case, but required of intervention in fundamen-
tal equations of electromagnetism and even complete
abandonment from electromagnetic mass [1]. Only
Poincare as a temporal exit from a situation offered
self-acting of electron on itself which are the so-called
”Poincare’s springs”. Exactly energy of these magic
springs targeted at com-pensation of necessary deficit
of mass. But years passed, and nobody so found
out these springs. The second problem is related to
boundless energy and in concert by mass of point
charge at aspiration of radius of particle to the zero.
Speech will go in this article about both prob-
lems and about consequences that arise up as a result
of overcoming of them. Both they are a substantial
obstacle to understanding of fundamental essence of
electricity. From the point of view to meaningfulness
them for a theory we consider necessary to say and
own opinion that does not apply on final truth, but
has a right on existence, as well as known. Begin-
ning to bustle in advance, we will say, that it no way
enters into a dispute neither with the modern theory
of electricity nor with an experiment, and contrary,
appears on their background.
Historically all was begun with the paradox of
electromagnetic mass of electron. About itself will
say in beginning: we belong to those, who divides
the idea of Lorenz that mass of electron can be fully
electro-magnetic (all its 0.511MeV ), and a charge
is not a point, and ”sloping”, as accepted to talk in
physics.
2. IMPULSE OF MOVABLE ELECTRON
Electron is a stable, negatively charged ele-
mentary particle that enters in the structure
of all atoms (−e = −1.6021892(46) · 10−19 C,
me = 9.109554(906) · 10−31 kg). Time of life of it
is 1026 over. By stability, thanks you to the law of
conservation of electric charge. An anti-particle is a
positron. Mass of electron can be easily calculated
by his impulse for velocities v ≪ c [1]. The density
of impulse g⃗ of the electromagnetic field we will find
dividing the vector of Pointing Π⃗ = ε0c
2E⃗ × B⃗ by c2
g⃗ = ε0E⃗ × B⃗ , (1)
where E⃗, B⃗ are basic vectors of the electromagnetic
field, ε0 is an electric constant, c is speed of light.
An electron will examine as the charged sphere
with a radius a but also charge q that moves with
permanent velocity v⃗. In some point that is in the
distance r from the center of charge and under a cor-
ner Θ to the line of his motion, electric field is radial,
and the lines of force of magnetic field appear as cir-
cles round the line of motion [1]
B⃗ =
v⃗ × E⃗
c2
. (2)
Putting (2) in (1), we receive a value (1)
g =
ε0v
c2
E2 sinΘ . (3)
∗Corresponding author E-mail address: vtchaban@polynet.lviv.ua
16 ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2019, N3(121).
Series: Nuclear Physics Investigations (71), p.16-20.
The field is symmetric to the line of motion of charge
that is why transversal components give a zero in a
sum. As a result an impulse will be parallel to the
rate of movement (v⃗). The component of vector g
in this direction g sinΘ can integrate about all space.
As an element of volume we will take a ring which the
plane is perpendicular to the vector v⃗. An elementary
volume of such ring will be as dV = 2πr2 sinΘdΘdr.
Then a complete impulse takes look
p⃗ =
∫ ∞
a
∫ π
0
ε0v⃗
c2
E2 sin3 Θ2πr2dΘdr . (4)
Coming from spherical symmetry, the size of electric
field we will find by the Maxwell’s postulate
E =
q
4πε0r2
. (5)
According to (4), (5) we get finally
p⃗ =
2
3
α2
ac2
v⃗, α2 =
q2
4πε0
. (6)
Coefficient of proportion between an impulse and a
speed in (6) is electromagnetic mass of electron
me =
2
3
α2
ac2
. (7)
3. ELECTROMAGNETIC MASS
In relation to truth of expression (6) of differences in
opinion for physicists it is not. But problem in other
– in deviation from (6) mass of immobile particle, re-
ceived from universal expression me = W/c2, where
W is energy. Specific electric energy w of immobile
electron it easily to calculate according to the known
expression
w =
ε0
2
E2 . (8)
If to consider that a charge of particle is on its spher-
ical surface, then we find complete energy according
to volume integral
W =
ε0
2
∫ ∞
a
4πE2r2dr . (9)
Putting (5), (8) in (9), we get
W =
1
2
α2
a
. (10)
Dividing (10) by c2, we get mass of rest
m′
e =
1
2
α2
ac2
. (11)
As we have an obvious deficit of mass as compared to
(7), then logically to accept, that charge of particle
evenly ”sloping” for it the body that will bring in in-
ternal energy of particle in consideration. Expression
for the vector of tension of electric field at that rate
find by the Maxwell’s postulate too
E − q
4πε0a3
r . (12)
It is experimentally confirmed within 15 millionth,
that coefficient that appears in (12), on distances
10−10 m remains to the same. In classic physics his
truth confesses and on distances 10−15 m. is in rela-
tion to the conclusion (5) of warning, because does
not cross the limit of distances 10−15 m. And in rela-
tion to (12) they are, because as a result of bombard-
ment of protons by rapid electrons according to their
dispersion is set, that on distances a 10−16 m the law
of Coulomb does not operate! On founding (9), (12)
on condition of change of borders of integration scope
from 0 to a we obsessed, that
m′′
e =
1
10
α2
ac2
. (13)
Adding (11) and (13), we obsessed finally
me =
3
5
α2
ac2
. (14)
As see, the deficit of mass is farther present. Deficit
of mass between (7) and (14), as it was already said
before, on the first pores Henry Poincare proposed to
recompense by self-acting of electron on itself. This
action conditionally until is named as ”intensities” or
”springs” of Poincare. Clear, that nature there is not
solved!
In relation to the presence of ”springs” of Poincare
of dispute conducted until now. A basic argument on
their benefit is that, what an accelerated electron ra-
diates energy. But in that there is chicanery a ground.
Electron can not be accelerated without assistance.
Here must be added external force. It undertakes all
”charges”. Interestingly, that in an own idea to de-
cide a problem Feynman ladles this additional force
in interplaying of oscillating electron with all by other
charges in the world by means of passing ahead and
delayed waves, and ”radiation resistance in no way
arises up as a result of self-acting”. Understanding a
situation well, he finally acknowledges: ”Here physi-
cists are tangled in what loop (!)”.
Our idea is very simple. Keeping within the law
of classic electrodynamics, to reconcile with both
masses (7) and (14) in behalf on first from them.
For that we renounce a concept a point charge, and
consider the real up-diffused on the volume of active
zone, but not evenly, as accepted in a classic electro-
dynamics, and unevenly!
4. MODEL OF ELECTRON
The experimental fact of collapse of law of Coulomb
on distances a 10−16 m talks about one - after the
sphere of radius in neighborhood of such sizes the
electric field is absent, and it will be only then, when
its charges will not be able to step over. Thus, there
is electric emptiness that conditionally will name a
”white hole”. Certainly, about the laws of electro-
magnetism in such emptiness, talking will not be.
Fully reasonably to search the radius of such white
hole exactly in the elementary charge of the least
sizes, that is an electron. In gravitation too similar
17
is a ”black hole”, or sphere of Schwarzshild. A phys-
ical body after this sphere too tests a gravitational
collapse. So as a radius of sphere of Schwarzshild rg
is named gravitational, then we the radius re of our
sphere will name like - electric. For a typical neutron
star a gravitational radius presents about 1/3 from
its own radius. It is therefore possible to expect that
an electric radius too will be multiple 1/3 from an
own radius.
Divergence of expressions (7) and (14) proves sim-
ply, that a density of electric charge must be up-
diffused on the volume of particle unevenly. We have
a few reasonable variants of this unevenness, but here
will show the simplest, and at the same time most re-
liable from them - quark distribution.
Quarks were thought in 1964 by Hell-Mann and
independently by Zweig for explanation of symme-
try in properties of strongly interactive particles -
hadrons. An electron after imagination of quantum
physics consists of three quarks that own an elec-
tric charge multiple e/3. This repetition factor meets
in physics often enough, for example, the relation
of magnetic moments of neutron and proton equals
−2/3, super proton and proton –−1/3 and others like
that. Indeed, as an electric radius of electron will be
shown farther presents about 2/3 from its own ac-
tual radius and. Why actual? – Because conditional
r0 = 2.82 · 10−15 m from the vagueness of digital co-
efficients in (7) and (14), gravitating to (7), for the
real the masses of me and charge of e overpriced in
3/2 times.
There are written about quarks differently. Ex-
perimenters consider them as structure less body,
point, that ”tested up to 5 · 10−18 m”. A quantum
chromo dynamics considers that a ”colorless” elec-
tron consists of three ”coloured” quarks (red, yellow,
blue), and each of two has them charges −e2/3 and
one quark of the third color – +e1/3. But is and
candid: ”In this time any experimental or theoretical
ideas are absent in relation to distribution of quarks
in the volume of electron... From this point of view
a hypothesis about an electron as a sphere is simpler
in all and most acceptable [1]”.
We do not examine an electron as quark struc-
ture. We only will accept quark distribution of den-
sities of charge in three active zones of identical vol-
ume along of radius r: −e2/3, −e2/3, +e1/3. Thus,
such their sequence is certain a condition (7)! It even
something simplifies an analysis, because two zones
give an opportunity of the first to unite in one. In
separate zones charge densities are considered per-
manent. Such model of electron is or not only, that
touch not of interests of neither classic nor quantum
electrodynamics. Because in order to please classic
keeps monolithic nature of elementary particle, and
in order to please a quantum interprets the separate
charged zones as separate discrete quarks.
At of such structure of active zones and presence
in the center of white hole with a radius re inter-
nal energy of the charged hollow bullet can be easily
found after according to the postulate of Maxwell, as
a sum of energies of its separate zones (it is specified
comparatively with [2]):
wei(ξ) =
α2
2a
(
m2
1
4b2
(
k5
r2 − ξ5
5
)
− ξ3(k2
r2 − ξ2)+
+ξ6
(
1
ξ
− 1
kr2
)
+
m2
2
b2
1− k5
r2
5
−
−
(
m1m2
b
+
m2
2
b2
k3
r2
)
(1− k2
r2) +
+
(
m2
2
b2
k6
r2 +
2m1m2
b
+m2
1
)(
1
kr2
− 1
))
,
(15)
where: m1 = −4/3; m2 = +1/3; re = ξa; r1 = k1a;
r2 = k2a are external radiuses of white hole first and sec-
ond active zones; find other coefficients, coming from the
condition of equality of volumes of separate active zones:
k1 = 3
√
(1 + 2ξ3)/3; k2 = 3
√
(2 + ξ3)/3; b = (1− ξ3)/3 .
Only single value that answers to condition (7) we
find as a solving of such nonlinear equation
wei(ξ) =
α2
6a
. (16)
As of result ξ = 0.62996 ≈ 0.63, what is, as well as it was
expectantly in neighbourhood 2/3 with divergence 5%.
Now attention! It is a rare case in science, when the
solution of difficult physical equation turns out without
the use of mathematical vehicle, and only coming from
striking harmony of external spheres of while hole and all
three active zones [2-4]:
0 0 = 3
√
0/4a
ξ = 0.6300 re = 3
√
1/4a
k1 = 0.7937 r1 = 3
√
2/4a
k2 = 0.9087 r1 = 3
√
3/4a
1 r1 = 3
√
4/4a
Will quote the same Poincare [5]: ”That we name ob-
jective reality, finally ... there can be only harmony that is
expressed by mathematical; laws. Thus, exactly this har-
mony and there is only objective reality, only truth that
we can attain; and if will add, that universal harmony
of the world is source of every beauty, then it will be un-
derstood, how we must value those slow and heavy steps
forward, that little by little discover its to us”.
Putting a numerical value ξ in (15) and dividing the
got result by c2, we received the mass of electron, caused
by its internal electric energy
mei =
1
6
α2
ac2
. (17)
Mass m′
e that appears in (11) predefined by external
electric energy of electron. It follows out from the limits
of integration: a ≤ r ≤ ∞.
Adding the got masses of electron (11) and (17)
me =
1
2
α2
ac2
+
1
6
α2
ac2
=
2
3
α2
ac2
, (18)
we get a result that identically converges from (7). That
it this, what was necessary to prove.
18
As both masses are equal now, then for the veritable
radius of electron it is possible to take its natural value a.
We will consider that the laws of electricity are
deprived sense into a ”white hole” with the radius
re = 1.183487 · 10−15 m as electric charges can not pen-
etrate for its. It is a very important conclusion, because
it abolishes the duty problem of boundless energy (5) at
r = 0, and in concert the masses (7) point charge at
a = 0. Because according to (16) neither r nor a can not
step over the boundary of radius of ”white hole”. Har-
mony of external spheres of white hole and all three active
zones strikes [2-4]:
If to examine such structure of electron as quark, then
coming from this harmony, a white hole can be interpreted
as fourth white (neutral) quark. But at that rate for the
sake of presence of orbital moments we will not to forbid
for our quarks to be revolved one in relation to other.
The results of simulation are shown in Figure.
The offered model of electron abolishes two impor-
tant problems of electricity at least, not entering into con-
tradiction with its classic laws. About other elementary
charged particles and about quarks speech will go sepa-
rately.
Interestingly, that J. Zweig named quarks as aces, but
such name did not get accustomed, because aces were
four, but quarks there were three in a primary model.
Maybe our white and is that fourth ace (?).
Distribution of intensity of electric field into an electron
by the radius
Interestingly, that on this theme discussions are con-
ducted in the Internet [3], where the paradox of the
masses got even the proper name as ”Paradox 4/3” [6]. It
once again convinces about importance of these scientific
efforts. In this connection it is necessary to mark that
quark distribution of charge of electron is offered with
a white hole in a center does not exhaust possibilities
offered approach. Here a basic idea consists in uneven
distribution of charge for volume of elementary particle.
But offered as yet most aesthetic. And yet. We executed
calculations for v ≪ c. But a problem remains at rela-
tivistic speeds, as a formula (6) takes away with itself the
same problem fully [1]
p⃗ =
2
3
α2
ac2
v⃗√
1− v2/c2
. (19)
In other words, electromagnetic mass too grows with
speed inversely proportional to the multiplier of Lorenz.
5. CONCLUSIONS
1. In order to avoid the crisis of electromagnetic mass
of electron, we must give up the ”Poincare’s springs” and
even distribution of densities of charge in its body in be-
half on uneven, and also from existence of point charges
in behalf on hollow.
2. If to take such proposed structure as quark struc-
ture, then a white hole can be interpreted as white quark
(?) in addition to red, yellow and blue.
3. The solution of nonlinear power equation of elec-
tron of 6-th order on a miracle turns out in a round to
the mathematical actions, going only from harmony of
outerspheres of ”quark” zones.
4. Even if to fill the body of electron by three spheri-
cal quarks, then nevertheless a white hole in a center not
to avoid.
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ëåêöèè ïî ôèçèêå, ò.6. Moñêâà: ,,Mèð,,, 1977.
2. Â.×àáàí. Ãiïîòåçà ïðî åëåêòðè÷íi áiëi äiðè // Teõ-
íi÷íi âiñòi (Technical news). 2015, ò.1(41), ò.2(42),
ñ.9-10.
3. Â.×àáàí. Åëåêòðîìàãíiòíi ïðîöåñè. Ë.:
,,Ïðîñòið,,, 2017, 412ñ.
4. ß.Áóäæàê, Â.×àáàí. Åíåðãåòè÷íi òà êiíåòè÷-
íi âëàñòèâîñòi íàïiâïðîâiäíèêîâèõ êðèñòàëiâ. Ë.:
,,Ïðîñòið,,, 2017, 190ñ.
5. À.Ïóàíêàðå. Î íàóêå. Ì.: ,,Ìèð,,, 1983, 560ñ.
6. STO KED Paradox 4/3 forum. forum.
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ÁÅÑÊÎÍÔËÈÊÒÍÀß ÌÎÄÅËÜ ÝËÅÊÒÐÎÍÀ
Âàñèëèé×àáàí
Ïðåäëîæåíà ìîäåëü ýëåêòðîíà ñ êâàðêîâûì ðàñïðåäåëåíèåì ïëîòíîñòè çàðÿäà è "áåëîé äûðîé"(íà
ïîäîáèå "÷åðíîé äûðû"â ãðàâèòàöèè) â öåíòðå. Òàêàÿ ñòðóêòóðà óñòðàíÿåò êðèçèñ ýëåêòðîìàãíèòíîé
ìàññû, âû÷èñëåííîé ïî óíèâåðñàëüíîé ôîðìóëå ýíåðãèè è ÷åðåç èìïóëüñ ýëåêòðîìàãíèòíîãî ïîëÿ.
Ìîäåëü íà óäîâëåòâîðåíèå êëàññè÷åñêîé ýëåêòðîäèíàìèêå ñîõðàíÿåò ìîíîëèòíîñòü ýëåìåíòàðíîé ÷à-
ñòèöû, à íà óäîâëåòâîðåíèå êâàíòîâîé � ðàçðåøàåò îòäåëüíûå çàðÿæåííûå çîíû ðàññìàòðèâàòü êàê
îòäåëüíûå êâàðêè. Èñõîäÿ èç ãàðìîíèè ñôåð îòäåëüíûõ çàðÿæåííûõ çîí, "áåëóþ äûðó"ìîæíî óñëîâ-
íî ðàññìàòðèâàòü êàê áåëûé (íåéòðàëüíûé) êâàðê â äîïîëíåíèå äî òðåõ öâåòíûõ (?). Ïîñêîëüêó çà
ýëåêòðè÷åñêèì ðàäèóñîì "áåëîé äûðû"re = 1, 185246 · 10−15 m çàêîíû ýëåêòðè÷åñòâà íå äåéñòâóþò, òî
îäíîâðåìåííî óñòðàíÿåòñÿ êðèçèñ òî÷êîâîñòè çàðÿäà, êàê íåäåéñòâèòåëüíîãî, èáî äîëæíî áûòü r ≥ re.
ÁÅÇÊÎÍÔËIÊÒÍÀ ÌÎÄÅËÜ ÅËÅÊÒÐÎÍÀ
Âàñèëü×àáàí
Çàïðîïîíîâàíî ìîäåëü åëåêòðîíà ç êâàðêîâèì ðîçïîäiëîì ãóñòèíè çàðÿäó é "áiëîþ äiðîþ"(íà ïîäîáó
"÷îðíî¨ äiðè"â ðàâiòàöi¨) ó öåíòði. Òàêà ñòðóêòóðà ñêàñîâó¹ êðèçó åëåêòðîìà íiòíî¨ ìàñè, îá÷èñëåíî¨
çà óíiâåðñàëüíîþ ôîðìóëîþ åíåðãi¨ i çà iìïóëüñîì åëåêòðîìà íiòíîãî ïîëÿ. Ìîäåëü íà äîãîäó êëàñè÷-
íié åëåêòðîäèíàìiöi çáåðiã๠ìîíîëiòíiñòü åëåìåíòàðíî¨ ÷àñòèíêè, à íà äîãîäó êâàíòîâié � äîçâîëÿ¹
îêðåìi çàðÿäæåíi çîíè òðàêòóâàòè ÿê îêðåìi êâàðêè. Âèõîäÿ÷è ç ãàðìîíi¨ ñôåð îêðåìèõ çàðÿäæåíèõ
çîí, "áiëó äiðó"ìîæíà óìîâíî òðàêòóâàòè ÿê áiëèé (íåéòðàëüíèé) êâàðê íà äîäàòîê äî òðüîõ êîëüî-
ðîâèõ (?). Îñêiëüêè çà åëåêòðè÷íèì ðàäióñîì "áiëî¨ äiðè"re = 1, 185246 · 10−15 m çàêîíè åëåêòðèêè íå
äiþòü, òî âîäíî÷àñ çíiìà¹òüñÿ êðèçà òî÷êîâîãî çàðÿäó, ÿê íåðåàëüíîãî, áî ìóñèòü áóòè r ≥ re.
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