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Journal of High Energy Physics, Gravitation and Cosmology, 2021, 7, 1190-1201
https://www.scirp.org/journal/jhepgc
ISSN Online: 2380-4335
ISSN Print: 2380-4327
DOI:
10.4236/jhepgc.2021.73070 Jul. 30, 2021 1190 Journal of High Energy Physics, G
ravitation and Cosmology
A New Theory for the Essence and Nature of
Electron Charge
Nader Butto
Dgania, Petah Tikva, Israel
Abstract
Charge is a fundamental physical property of matter that is responsible for its
interactions with electromagnetic fields. The real nature and the essence of
charge are unknown. In this paper, a new theory is
presented to describe the
nature and the essence of electric charge is formulated based on the vortex
model of the electron which has a finite size and has an irrotational
vortex
structure. This theory and the vortex model of the electron enables us, for the
first time, to describe the origin of bivalency, stability, quantization, equality
of the absolute values of the bivalent charges, to derive a
simple formulation
to cal
culate the electric charge based on hydrodynamics without the use any
constant. The difference between negative and positive charge,
is revealed and
the charged particles interactions are described. The electric charge is an ex-
pression of accelerated spherical mass per area reduced by the stiffness of the
vacuum which has the units
ε
0 ML3/T2
. The calculated results based on these
equations comply accurately with the experimental results.
Keywords
Electric Charge, Irrotational Vortex, Coulomb’s Law, Volume Flow Rate,
Charge Density
1. Introduction
A few hundred years have passed since the discovery of electricity and electro-
magnetic fields, a tremendous progress has been achieved in details and applica-
tions of the electron theories [1].
However, the nature of the electron has been a mystery confronting physicists
of past generations as well as contemporaries [2] [3].
While electrons are useful in the understanding of diverse phenomena, the
nature of the electron have never been really understood and the nature of the
How to cite this paper:
Butto, N. (2021)
A
New Theory for the Essence and Nature
of
Elec
tron Charge.
Journal of High Energy Phy
-
sic
s
,
Gravitation and Cosmology
,
7
, 1190-1201.
https://doi.org/10.4236/jhepgc.2021.73070
Received:
June 19, 2021
Accepted:
July 27, 2021
Published:
July 30, 2021
Copyright © 20
21 by author(s) and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creative
commons.org/licenses/by/4.0/
Open Access
N. Butto
DOI:
10.4236/jhepgc.2021.73070 1191 Journal of High Energy Physics, G
ravitation and Cosmology
electron has been an enigma confronting physicists of past generations as well as
contemporaries [2] [3].
In fact, many questions related to the nature of the electron still without an-
swers such as: what is the structure of the electron, what is the origin of the mass
of the electron, what is the spin, why must be a positron, why and how does the
electron manifest wave properties and how does the electron manifest wave
properties? What guides the interaction between two electrons to cause attrac-
tion or repel, why do particles with the same charge repel and opposing charges
attract, how electron interact with positron at short distances? And finally what
is electric charge?
In 1746, the American physicist named Franklin first propounded the idea of
positive charges and negative charges.
After finding the quantized character of charge, in 1891 George Stoney pro-
posed the unit “electron” for this fundamental unit of electrical charge. The dis-
covery of the electron in the 1890’s, based on several independent experiments a
negative charge
e
, and mass
m
were assigned to the electron. A few hundred
years have passed since the discovery of electricity and electromagnetic fields,
and Maxwell’s equations have been subjected to countless experimentation
based on the current definition of electric charge and are definitely correct;
however, the nature of an electric charge remains unknown.
Attempts have been made to clarify the nature of the electric charge [4]-[8].
None of these works provides an explicit formula for the exact value and the
nature of electric charge based on proven facts.
The main obstacle remains related to the failure to attribute structure to the
electron.
Therefore, the unit is today treated as nameless, referred to as elementary
charge, fundamental unit of charge, or simply as
e
. However, almost all physical
parameters (constants and variables) have a combination of the dimensions of
mass, length, and time.
The dimension of electric charge is 4π
ε
0 ML3/T2. One can easily decompose
ML/T into, e.g., mass (M) and velocity of a particle (L/T), and find a formula for
the linear momentum of a particle. This has not been accomplished for electric
charge.
Prediction of the anti-electron (positron) by P. Dirac in 1931, which was dis-
covered by C. Anderson in 1932. However, there is no scientific explanation for
the origin of difference between properties of electron and positron or really ex-
plained the internal mechanism of positive and negative charges.
Although the electric charge seems to be a primary abstract intrinsic property
of a particle, nonetheless, the electric charge and electromagnetic field are the
physical property of matter, can be directly measured and formulated. Therefore,
the relation between electric charge and known physical parameters should be
addressed and clarified. This cannot be done until the very nature of the electron
mainly its structure is identified, to provide explicit general formulas for the re-
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ravitation and Cosmology
lation between electron attributes and known physical parameters into which all
attributes of the electron could be incorporated in a self-consistent way.
The aim of this study is to present a new physical concept to fill this gap and
to constitute a physical explanation of the nature and the origin of charge.
This paper provides a new approach to this problem, considering the vacuum
as superfluid and the electron as an irrotational vortex of the vacuum. Compre-
hensible interpretation of electric charge is developed, based on the hydrody-
namics a meaningful and explicit description of the nature of the obscure physi-
cal parameter of electric charge is found, and an explicit formula that addresses
the relation between electric charge and known physical parameters is presented.
This approach allows to express the complicated dimension of the electric
charge in M, L and T units
(
4π
ε
0 ML3/T2) and converts it in an observable, mea-
surable, and explicable physical parameter.
2. The Vortex Structure of the Electron
Vacuum density is generally viewed as a fundamental property of the cosmos.
Therefore, the physical vacuum is assumed to be a non-trivial medium filled
with quantum mechanical zero-point energy to which one can associate certain
energy and density.
In superfluid vacuum theory, the physical vacuum is described as a quantum
superfluid and is characterized to behave like a frictionless fluid with density and
proposes a mass generation mechanism that may replace or supplement the
electroweak Higgs theory. It has been shown that the masses of elementary par-
ticles could be a result of interactions with a superfluid vacuum, similar to the
gap generation mechanism in superconductors [9] [10].
Although according to quantum mechanics the electron is cloud of probabili-
ties, therefore has no physical structure, many efforts are made to study the
shape of the electron. The current model predicts that electrons are slightly as-
pheric, with a distortion characterized by the electric dipole moment. However,
no experiment so far has detected this deviation [11].
Jehle spent a large part of his life developing a theory of the electron and ele-
mentary particles based on quantized magnetic flux loops, spinning at the Zit-
terbewegung frequency [12] [13] [14] [15] [16].
Also, Dirac suggested the existence of the magnetic monopole to describe the
charge of the electron [17].
Both these theories rely on a physical relationship between flux and charge.
The question of the relation between the electric and magnetic properties is
fundamental to electrodynamics. One expects a relationship as moving charge
produces magnetic flux.
In previuos articles [18], the electron is proposed to be a frictionless vortex
with conserved momentum made out of virtual photons that acquire mass when
moving in the vortex at the speed of light. The vortex shape electron allowed to
resolve the enigmatic wave-particle duality [19].
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The vortex shape of the electron and the Hydrogen atom give a full explana-
tion for the origin of fine structure constant [20]. The same model was presented
to explain the origin of gravitation force [21] and gravitation constant G [22] in-
dicating the universality of the phenomena.
Thus the proposed idea in this paper is that the electron is an irrotational vor-
tex of frictionless superfluid space with concentric streamlines that was created
from the primordial vacuum that converted to Higgs particles during the Big
Bang.
The vortex of the electron is made up by massless Higgs particles which ac-
quire mass when they travel around the vortex center. The rate of rotation of the
fluid in the irrotational vortex is greatest at the center and decreases progres-
sively with distance from the center until there is no gradient pressure on the
boundaries of the vortex where the flow is laminar and the friction is null.
In such a case, the absence of friction would make it impossible to create or
destroy the vortex motion.
There are two types of vortices, the first one like the whirlpool, in which the
flow goes from the periphery to the center, in such vortex the centripetal forces
prevail. This kind of vortex related to the electron. The second kind of vortex is
like the tornado where the flow goes from the apex to the periphery, related to
the positron in which the centrifugal forces prevails Figure 1.
The electric charge density in the core of the electron is less than the vaccum
density, while the core density of the positron is major than the vacuum density.
Furthermore, the charge density is inversely related to the radius of the vortex.
Therefore, if the vacuum density is
ρ
and the vortex core density is
ρ
0 then the
electric charge density would be:
00
2qr
ρρ ρ
π= −
(1)
The charge density is positive if
ρ
0 >
ρ
. The charge density is negative if
ρ
0 <
ρ
.
Necessarily, only two types of electric charge exist, positive and negative. Let n
be the number of boson Higgs particle in a given volume
V
. Since
n
=
ρ
0
V
' and
also
n
=
ρV
we get:
V
=
n
/
ρ
,
V
' =
n
/
ρ
0, Hence:
( )
( )
00
VV V
ρ ρρ
′′
− =−−
If
V
' >
V
is dilation,
V
' <
V
is contraction
The centripetal force of the electron pulls the surrounding Higgs field into the
centre of the electron vortex, hence causing a tension in the surrounding field
causing pull force to act on other particles.
Figure 1. The vortex is curling in the plane, expansive (red) or contractive (blue)
except in the core center where it is pointing out-of-plane, either up (polarity p = +)
red or down (p = −) blue.
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The centripetal forces of the electron and the lines of force made of Higgs par-
ticles are shown entering, allows due to attractive force to interact with protons
to form different chemical elements and the attraction between two electrons
with opposite spins. The positron instead in which the centrifugal forces and the
lines of force exerted are always shown leaving the center push the other par-
ticles thus cannot interact with matter in a stable manner.
3. The Nature of Electric Charge
One of the fundamental laws of electricity is expressed by coulomb’s law which
states that the electrical force between two charged objects is directly propor-
tional to the product of the quantity of charge on the objects and inversely pro-
portional to the square of the separation distance between the two objects.
In equation form, Coulomb’s law can be stated as
2
12
F kQ Q r=
, (2)
where
Q
1 represents the quantity of charge on object 1 (in Coulombs),
Q
2
represents the quantity of charge on object 2 (in Coulombs), and
r
represents the
distance of separation between the two objects (in meters). The symbol
k
is a
proportionality constant known as the Coulomb’s law constant = 1/4π
ε
0. The
value of this constant is dependent upon the medium that the charged objects
are immersed in.
However, the electric charge nature still mysterious and the reason of such
behavior still enigmatic. Furthermore, it is not clear why electrons with different
spin they attract despite they have the same charge. The vortex structure model
of the electron resolves completely all aspects related to the attributes and the
behaviour of the electron including the electric charge.
The field about a charged body is generally represented by lines which are re-
ferred to as electrostatic lines of force. The electron as a vortex made up of spiral
arms from which stems the fields of force which spread out in the space around
the center of the vortex and diminishes in proportion to the square of the dis-
tance from the center of the vortex [18].
These lines are real and represent the direction and strength of the field.
Both electron and positron vortices have electromagnetic field, magnetic mo-
ment and magnetic dipole.
In the electron vortex, the flow of Higgs particles that moves in spirals down-
ward in the funnel creates a pressure gradient normal to the vortex center and
acts along the central axis of vortex spin. It follows moving up around the spiral
and returns from the upper side of the central axis generating the magnetic mo-
mentum and magnetic dipole. The vertical magnetic pressure gradient is normal
to the horizontal electrostatic pressure gradient creating by the vortex and acts
along the central axis of spin Figure 2.
The acting forces electrostatic and magnetic are now interlinked in
self-balancing feedback loops that give great stability to the vortex structure
shape of the particle as a whole. These are the two forces that generate move-
ment and create currents. The currents are the avenues of movement made up of
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Figure 2. Artistic presentation of the
magnetic field around the electron.
Higgs particles, surrounding which are spaces or crevices through which flow
currents of lesser density comprising Higgs particles.
The interaction between vortices takes place in three different ways:
1) The electrostatic force which is attractive (gravitational) in the electron and
repulsive (anti-gravitational) in the positron;
2) Magnetic force which is attractive in the opposite polarity, expressed by
spin value −1/2 or +1/2;
3) Electrostatic centripetal force which depends on the rotation direction, is
attractive if one vortex rotates clockwise rotation and the other counter clock-
wise rotation.
The electron can have a magnetic dipole is oriented in a way that the negative
pole is up and the positive pole down. In this case, the projection value said to be
−1/2, while in the opposite direction said to be +1/2. The projection can be
changed, but the total spin of 1/2 related to the spiral arm curl is fixed for all
time.
Electron annihilation [23] [24] [25] is the phenomenon that consists in the
collision of electrons with positrons. This phenomena, can take place in Thibaud’
s experiment where free positrons were launched against a metal lamina
(tungsten) which is rich in conductive electrons or collision between free elec-
trons and free positrons with low speed.
The two particles disappear and generally energy quanta appear in their place.
As per the conservation law of momentum the two quanta have by practise op-
posite directions with an angle 90 degrees.
Each quantum has the energy of about 0.51 MeV, with frequency and wave-
length placed in the spectrum of gamma radiation (gamma rays):
f
= 1.2 × 1020
Hz; lambda = 2.5 × 10−2 Angstroms. As per the conservation law of energy, be-
cause the intrinsic total energy of both, electron and positron, is 1.02 MeV, the
produced quanta has about 1.02 MeV. This process is presented schematically by
Feynman diagram Figure 3.
Feynman diagram does not explain the interaction mechanism. However,
whirlpool structure of both electron and positron and rotation direction give us
good mechanical explanation
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Figure 3. Feynman diagram of the elec-
tron-positron collision at low energy.
The interaction between electron and positron takes place in the mouth of the
electron and in the apex of the positron which have attractive the force, therefore
the positron will be swallowed by the mouth of the electron, however, the colli-
sion at low energies causes overlapping opposite rotation direction, destructive
wave interference and annulation the rotation of both vortices, the annihilation
of the electron and positron, and materialisation of gamma photons Figure 4.
Electrons mostly repel each other due to having the same charge. However,
electrons with opposite spins not only lack of repulsion but they partially at-
tracted. The vortex model of the electron explains completely this behaviour.
The interaction between two opposite electrons, combines two different forces:
the first the opposite attractive electrostatic force of the spiral arm of the vortices
Figure 5.
Therefore, opposite spin electrons have this attraction, without any Coulomb’s
repulsion.
The second is the dipole opposite spin and magnetic force, the stream flows
mesh, the particles will attract one another Figure 6.
When two electrons are in the same rotation direction, the stream flows clash
and repel the two electron vortices Figure 7.
Furthermore, there is magnetic repulsion between similar magnetic dipole
moments. Each is like a tiny metal bar magnet that are directed in the same di-
rection. This is the origin of Pauli exclusion principle.
The description of magnetic pole attraction and repulsion will be discussed
separately in other articles that describe the internal structure of the monopole.
4. The Essence of Electron Charge
In hydrodynamics, the rotation of a vortex creates a drag force that attracts the
medium to the center of the vortex. This force is directly related to the density of
the vacuum, the speed of rotation, and the area according to the equation
2
12F cA
ρ
=
, (3)
where,
ρ
is the density of the vortex,
c
is the speed of light and
A
is the area of
the vortex.
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Figure 4. Electron–positron annihilation process caused by
the collision between the apex of the positron (upper vortex)
which has clockwise rotation and the mouth of the electron
(down vortex) which has counter clockwise rotation.
Figure 5. Partial attraction between two opposite spins the
one has projection value said to be up with spin −1/2 and
the other as +1/2.
Figure 6. Right −1/2 spin electron, left, +1/2. The stream
flows mesh, the particles will attract one another.
Figure 7. The two-opposite head to head flux leads
to electron repulsion.
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However, any motion in a curved path represents accelerated motion, and
requires a centripetal force directed toward the center of curvature of the path
which inversely related to the radius according to the equation
2
12F c Ar
ρ
=
.
(4)
Multiplying and dividing the right side of Equation (4) by time
t
, we obtain
12 12F ctAc rt Vc rt
ρρ
= =
, (5)
where
ctA
is
the volume
V
. However, this force is reduced owing to interactions
with the adjacent vacuum. If the density of the vortex is
ρ
and the rotation speed
of the vortex is
c,
dividing the momentum
ρc
by the length of the circumference
of the vortex
λ
= 2π
r
will give the momentum
Pd
for a unit of length, thus:
d
Pc
ρλ
=
. (6)
Therefore, the momentum of the vortex is multiplied for every unit of length
by
ρc/λ
according to the equation
2
12F V c rt
ρρ λ
=
.
.
(7)
If
λ
= 2π
r
, then
2 22
12 24F Vcrt r Vc tr
ρρ ρρ
ππ= =
. (8)
In hydrodynamics,
ρc2
is the elasticity of the vacuum. In fact, the speed of a
particle in an elastic medium can be expressed by the formula
( )
12
cE
ρ
=
, (9)
where
c
, the speed of light,
E
is the elasticity, and
ρ
the density of the medium.
Therefore, the elasticity of the vacuum,
E
, can be written as
2
Ec
ρ
=
, (10)
which is the inverse of the stiffness of the vacuum and has the same value as the
electric permittivity,
i.e.
,
21
0
c
ρε
−
=
.
This makes sense in terms of dimensions because the elasticity modulus is
Newton × m−2 whereas the permittivity is Newton−1 × m−2 (C2/N m2).
Then, the Equation (6) becomes
2
0
4F V tr
ρε
π=
. (11)
The force at a point in a fluid divided by the density is the acceleration of the
fluid at that point known in fluid mechanics, as the force density
f
[26].
Therefore Equation (11) become
( )
2
0
4F Vt r
ρε
=π= f
. (12)
Force density is the negative gradient of the pressure which has physical di-
mensions of force per unit volume. The force density is a vector field representing
the flux density of the hydrostatic force within the bulk of a fluid.
In fluid dynamics, the volume of a fluid that passes per unit of time,
V/t,
is the
volume flow rate, which is usually represented by the symbol
q
. Its SI unit is m3/s.
therefore force density is expressed as:
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2
0
4qr
ε
π=f
, (13)
this is the same formula of the force of electric charge. Therefore, the electric
charge is the volume flow rate of vacuum flux from the vacuum to the center of
the electron vortex that can be expressed as:
2
0
4qfr
ε
π=
, (14)
the
q
charge equals to Force x Area of the sphere (4π
r
2) which is the cross prod-
uct between the potential energy and the radial distance of the sphere charge,
diminished by the vacuum stiffness
ε
0.
The SI unit of quantity of electric charge is the coulomb, which is equivalent
to about 6.242 × 1018
e
(
e
is the charge of a proton). Hence, the charge of an
electron is approximately −1.602 × 10−19 C. The coulomb is defined as the quan-
tity of charge that has passed through the cross section of an electrical conductor
carrying one ampere within one second.
According to
Newton
Law
f
=
ma
, thus we substitute
f
in Equation (14) to obtain
2
0
4
q ma r
ε
π
=
, (15)
This is an explicit combination of mass, length and time. If the
a
is
c
/
t
(
a
) its
units are L/T2 and 4π
r
2 units are L2 the final charge units will be 4π
ε
0 ML3/T2.
That indicates that the charge is the mass quantity M that pass area L2 per time T
at speed of light L/T diminished by the vacuum stiffness
ε
0.
This equation demonstrates that the electric charge is equivalent to mass change
in a particle. This is a momentum equation which is conserved, and the net charge
is always conserved, and this is the origin of law of conservation of charge.
In this article, the nature and the essence of a single charged was discussed,
the charge interaction and Coulomb Law will be discussed in detail in separate
article.
5. Conclusions
Herein, a new theory connects the structure of the electron and presents a new
and explicit description of the obscure physical parameter of electric charge. The
electron is presented as a frictionless vortex with conserved momentum made
out of condensed vacuum.
The electron as a vortex rotates around an axis in such a way, that it possesses
an angular momentum, spin and charge. This understanding enables us to apply
hydrodynamic laws to derive and calculate the electron attributes including spin
and charge.
This model shed light on the difference between electron and positron, com-
paring them to water whirlpool and tornado. The electron negative charge is re-
lated to the attractive force toward the center of the vortex, while the positron
has repulsive force from the center to the periphery. The attraction or repulsion
between charged particles depends on three different forces:
1) The kind of vortex (whirlpool or tornado type) that determines the charge
negative or positive respectively.
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2) Clockwise or counter clockwise rotation of the vortex that is related to the
spin.
3) The dipole orientation.
The attraction between two oppositely oriented electrons despite they have
the same charge is explained by dipole attraction and opposite spin rotation
direction.
The centripetal force of the electron vortex that attracts Higgs particles to the
center of the vortex which depends on the density of the vacuum, the area and
the radius of the vortex is formulated. Taking into consideration the reduced
momentum of the vortex, the density force in a giving point in the vortex and
the net final momentum in that point is formulated. This is actually the flux
density of the hydrostatic force within the bulk of a fluid. The force density equ-
ation is an expression of volume flow rate which is equivalent to the electric
charge q per unit of area of a sphere 4πr2 reduced by the stiffness of the vacuum
expressed as the constant of permittivity
ε
0. This comes to indicate that the
charge has a sphere shape. Accordingly, the electric charge is an expression of
Force x Area which is the cross product between the potential energy and the
radial distance, diminished by the vacuum stiffness
ε
0. In other words, it’s the
accelerated mass per area reduced by the stiffness of the vacuum which has the
units
ε
0 ML3/T2. It appears that dimensional analysis is not only a reliable me-
thod for assessing the validity of equations, but also it can help to find a mea-
ningful interpretation for a category of unknown physical parameters.
The vortex model of the electron may turn out to have far-reaching conse-
quences, for theoretical physics and to be indeed very useful and even almost es-
sential auxiliaries of reasoning. The essence and nature of the electric charge
could make a major breakthrough in the field of electromagnetics.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this pa-
per.
References
[1] Springford, M. (1997) Electron: A Centenary. Cambridge University, Cambridge.
[2] Hestenes, D. and Weingartshofer, A. (1991) The Electron New theory and Experi-
ment. Kluwer Academic, Dordrecht. https://doi.org/10.1007/978-94-011-3570-2
[3] Mac Gregor, M.H. (1992) The Enigmatic Electron. Kluwer Academic, Dordrecht.
https://doi.org/10.1007/978-94-015-8072-4
[4] Mahdi, J.F. (1999) The Nature of Electric Charge.
International Journal of Physical
Sciences
, 9, 54-60. https://doi.org/10.5897/IJPS2013.4091
[5] Krasnoholovets, V. (2003) On the Nature of the Electric Charge.
Hadronic Journal
Supplement
, 18, 425-456.
[6] Shpenkov, G.P. and Kreidik, L.G. (2004) Dynamic Model of Elementary Particles
and Fundamental Interactions.
GED Special Issues
,
GED-East
, 15, 23-29.
[7] Tiwari, S.C. (2006) The Nature of Electronic Charge.
Foundations of Physics Let-
N. Butto
DOI:
10.4236/jhepgc.2021.73070 1201 Journal of High Energy Physics, G
ravitation and Cosmology
ters
, 19, 51-62. https://doi.org/10.1007/s10702-006-1848-x
[8] Nguyen, H.V. (2013) A Foundational Problem in Physics: Mass Versus Electric Charge.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.303.975&rep=rep1&type=pdf
[9] Zloshchastiev, K.G. (2011) Spontaneous Symmetry Breaking and Mass Generation
as Built-In Phenomena in Logarithmic Nonlinear Quantum Theory.
Acta Physica
Polonica B
, 42, 261-292. https://doi.org/10.5506/APhysPolB.42.261
[10] Avdeenkov, A.V. and Zloshchastiev, K.G. (2011) Quantum Bose Liquids with Loga-
rithmic Nonlinearity: Self-Sustainability and Emergence of Spatial Extent.
Journal
of Physics B
:
Atomic, Molecular and Optical Physics
, 44, Article No. 195303.
https://doi.org/10.1088/0953-4075/44/19/195303
[11] Hudson, J.J., Kara, D.F.M., Smallman, I.J., Sauer, B.E., Tarbutt, M.R. and Hinds, E.A.
(2011) Improved Measurement of the Shape of the Electron.
Nature
, 473, 493-496.
https://doi.org/10.1038/nature10104
[12] Jehle, H. (1971) Relationship of Flux Quantization to Charge Quantization and the
Electromagnetic Coupling Constant.
Physical Review D
, 3, 306-345.
https://doi.org/10.1103/PhysRevD.3.306
[13] Jehle, H. (1972) Flux Quantization and Particle Physics.
Physical Review D
, 6, 441-457.
https://doi.org/10.1103/PhysRevD.6.441
[14] Jehle, H. (1975) Flux Quantization and Fractional Charges of Quarks .
Physical Re-
view D
, 11, 2147-2177. https://doi.org/10.1103/PhysRevD.11.2147
[15] Jehle, H. (1977) Multiquark Hadrons. I. Phenomenology of Q2 Q-2 mesons.
Physical
Review D
, 15, 267 p. https://doi.org/10.1103/PhysRevD.15.267
[16] Force Density (2012) Eric Weisstein’s World of Physics.
[17] Dirac, P. A. M. (1948) The Theory of Magnetic Poles.
Physical Review
, 74, 817-830.
https://doi.org/10.1103/PhysRev.74.817
[18] Butto, N. (2020) Electron Shape and Structure: A New Vortex Theory.
Journal
of
High
Energy
Physics
,
Gravitation
and
Cosmology
, 6, 340-352.
https://doi.org/10.4236/jhepgc.2020.63027
[19] Butto, N. (2020) A New Theory on Electron Wave-Particle Duality.
Journal
of
High
Energy
Physics,
Gravitation
and
Cosmology
, 6, 567-578.
https://doi.org/10.4236/jhepgc.2020.64038
[20] Butto, N. (2020) A New Theory on the Origin and Nature of the Fine Structure
Constant.
Journal
of
High
Energy
Physics,
Gravitation
and
Cosmology
, 6, 579-589.
https://doi.org/10.4236/jhepgc.2020.64039
[21] Butto, N. (2020) New Theory to Understand the Mechanism of Gravitation.
Journal
of
High
Energy
Physics,
Gravitation
and
Cosmology
, 6, 462-472.
https://doi.org/10.4236/jhepgc.2020.63036
[22] Butto, N. (2020) New Mechanism and Analytical Formula for Understanding the
Gravity Constant G.
Journal
of
High
Energy
Physics
,
Gravitation
and
Cosmology
, 6,
357-367. https://doi.org/10.4236/jhepgc.2020.63029
[23] Persico, E. (1970) Gli atomi e la loro energia. Zanichelli Editor Bologna, Italy.
[24] Ford, K.W. (1965) The World of Elementary Particles/Arnoldo Mondadori Editore,
Milano.
[25] Matthews, P.T. (1972) The Nuclear Apple. Arnoldo Mondadori Editore, Milano.
[26] Griffiths, D.J. (1989) Introduction to Electrodynamics. 2nd Edition
,
Prentice Hall,
New Jersey, 64 p.
