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Journal of High Energy Physics, Gravitation and Cosmology, 2021, 7, 14591471
https://www.scirp.org/journal/jhepgc
ISSN Online: 23804335
ISSN Print: 23804327
DOI:
10.4236/jhepgc.2021.74088 Oct. 20, 2021 1459 Journal of High Energy Physics, G
ravitation and Cosmology
A New Theory for the Essence and Origin of
Electron Spin
Nader Butto
Petah Tikva, Israel
Abstract
Spin is an intrinsic form of angular momentum carried by elementary par
ticles, composite particles, and atomic nuclei. It is wildly believed that spin is
a purely quantum mechanical concept and has
no classical analogue. In fact,
elementary particles are conceived as point objects which have no axis to
“spin” around. Therefore, there is no explaining how spin arises at the fun
damental level, why particles have the values they do, and what underpins
the
Pauli Exclusion principle and BoseEinstein behavior. However, spin is like a
vector quantity; it has a definite magnitude, and it has a “direction”, in order
to spin should be composite. In this paper we propose a physical explanation
for spin of the electron at the sub
particle level, relying on the vortex model
of the electron.
The electron is described as a superfluid frictionless vortex
which has a mass, angular momentum and spin to provide a complete expla
nation of all properties of the electron:
it composite, spinning around its own
axis, produces a tiny magnetic fields independent of those from its orbital
motions. The classical hydrodynamic laws are used to describe the quantum
properties of the electron, such as spin, angular momentum, magnetic mo
mentum and a magnetic dipole. The circulation in the vortex is constant, and
the angular momentum of the vortex is conserved and has the same value of
Planck constant. The direction of the angular momentum of a spinning elec
tron vortex is along the axis
of rotation and determined by the direction of
spin. The spin quantum number 1/2 has a fixed value which represents the
gap between the circulation rate of the core of the vortex and the boundaries
of the vortex. The changeable values +1/2 “spinup” or −1/2 “spindown” in
dicate the direction of the magnetic dipole of the vortex. The relation between
spin and Planck constant is discussed and the origin h/4pi angular momen
tum units are revealed.
Keywords
Higgs Field, Irrotational Vortex, Angular Momentum, Magnetic Momentum,
How to cite this paper:
Butto, N. (2021)
A
New Theory for the Essence and Origin of
Electron Spin
.
Journal of High Energy Physics
,
G
ravitation and Cosmology
,
7
, 14591471.
https:
//doi.org/10.4236/jhepgc.2021.74088
Received:
August 12, 2021
Accepted:
October 17, 2021
Published:
October 20, 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).
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Open Access
N. Butto
DOI:
10.4236/jhepgc.2021.74088 1460 Journal of High Energy Physics, G
ravitation and Cosmology
Quantum Spin Number, GFactor
1. Introduction
Spin is an essential property influencing the ordering of electrons and nuclei in
atoms and molecules, giving it great physical significance in chemistry and sol
idstate physics. Spin is likewise an essential consideration in all interactions among
subatomic particles, whether in highenergy particle beams, lowtemperature fluids
or the tenuous flow of particles from the sun known as the solar wind.
Indeed, many if not most physical processes, ranging from the smallest nuc
lear scales to the largest astrophysical distances, depend greatly on interactions
of subatomic particles and the spins of those particles. It is physically manifest in
multiple phenomena such as Pauli pairs, photon polarisation, selective spin of
neutrino species, superconductivity, entanglement and electron spin, gfactor
[1].
Spin magnetic moments create a basis for one of the most important prin
ciples in chemistry. The theory plays further roles than just the explanations of
doublets within electromagnetic spectrum. This additional quantum number, spin,
became the basis for the modern standard model used today, which includes the
use of Hund’s rules, and an explanation of beta decay.
Spin was originally conceived as the rotation of a particle around some axis.
However, at the current level of understanding, the electron like other elemen
tary particles such as quarks, and bosons (such as the photon) are all imagined as
pointlike, and are not solid “objects” that can “rotate” in space, therefore, it is
generally accepted that there is no explanation, that the properties are merely
intrinsic, that QM is complete as a theory as it is, e.g. [2].
The discovery of electron spin goes back to 1920s, by Otto Stern and Walther
Gerlach of the University of Hamburg in Germany during a series of important
atomic beam experiments. Knowing that all moving charges produce magnetic
fields, they proposed to measure the magnetic fields produced by the electrons
orbiting nuclei in atoms. They designed an experiment, which was done with
silver that was put in an oven and vaporized. The basic observation is that a
stream of quantum particles can be sent across a magnetic field that is directed
perpendicular to the stream.
To their surprise, the result was that silver atoms formed a beam that passed
through a magnetic field was observed to possess two possible discrete angular
momenta despite having no orbital angular momentum [3].
The screen reveals discrete points of accumulation, rather than a continuous
distribution [4], owing to their quantized spin.
The results show that particles possess an intrinsic angular momentum that is
closely analogous to the angular momentum of a classically spinning object, but
that takes only certain quantized values. If the particles deflect, then you can say
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ravitation and Cosmology
they have spin. If they don’t, you say they have spin zero.
Wolfgang Pauli in 1924 was the first to propose a doubling of electron states
due to a twovalued nonclassical “hidden rotation” [5].
And in 1927 he worked out the mathematical theory in depth. When Paul Di
rac derived his relativistic quantum mechanics in 1928, electron spin was an es
sential part of it and it predicted the discovery of the positron [6] and correctly
gave the value of the spin, h/4pi angular momentum units.
In quantum mechanics and particle physics, a spin is an intrinsic form of an
gular momentum carried by elementary particles, composite particles (hadrons),
and atomic nuclei [7] [8].
Spin is one of two types of angular momentum in quantum mechanics, the
other being orbital angular momentum.
In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University sug
gested the simple physical interpretation of a particle spinning around its own
axis and the term “spin”, however, still remains.
The spinning electrons produce tiny magnetic fields independent of those from
their orbital motions. Spin is like a vector quantity; it has a definite magnitude,
and it has a “direction”. All electrons have the same magnitude of spin angular
momentum, which is indicated by assigning the particle a spin quantum num
ber.
In addition, spin is quantized, meaning that only certain discrete spins are al
lowed it never changes, and has only two possible orientations: in electron for
example could be +1/2 and −1/2. Since the sign indicates the direction, we tend
to call these “spinup” and “spindown.”
Massless particles are a bit different, they don’t have a rest frame, instead they
have a different quantity that which is helicity. This too is quantized in half in
teger units of hbar. Helicity behaves similarly to spin and it is for this reason
that the photon is said to have spin 1, but there are real differences that shouldn’t
be overlooked.
The direction of the angular momentum of a spinning object is along the axis
of rotation and determined by the direction of spin. However, electrons are not
literally spinning balls of charge, but they do have intrinsic angular momentum.
Despite the fact that there is a mathematical description of how it behaves, in
particular, of how the total spin of a system of particles depends on the spins of
the constituents, the origin and the essence of the spin are not known and till
today there is no real deep understanding of what spin is, much beyond the fact
that it is an attribute of an elementary particle.
If the electron considering as a spinning ball with the known sizes, the surfac
es of the charged electron would have to be moving faster than the speed of light
in order to produce the measured magnetic moments. In addition, rotating the
spin of a spin1/2 particle by 360 degrees doesn’t get you exactly the state you
started with.
Furthermore, there is no explaining how spin arises at the fundamental level,
why particles have the values they do, and what underpins the Pauli Exclusion
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principle and BoseEinstein behavior.
Therefore, quantum mechanics, does not offer any deeper explanation of why
spin numbers prevent fermions from colocating. Why should spin be exclu
sively 1/2 for elementary fermions, yet merely predominately 1 for bosons? What
is the basis of this differentiation?
These situations create all sorts of complications that make spin one of the
more challenging aspects of quantum mechanics.
In this paper, based on vortex structure of the electron, the nature and origin
of the its spin is discussed, the origin of 1/2 of elementary fermion is explained,
in addition, the relation between spin and Planck constant is discussed.
2. The Origin of the Spin Angular Momentum
Although the question of whether elementary particles actually rotate is ambi
guous, the rotating particle picture is correct insofar as spin obeys the same ma
thematical laws as quantized angular momentum do, in particular, spin implies
that the particle’s phase changes with angle.
The angular momentum of the electron indicates that there is an internal ro
tation (spin) that confers upon it its rest mass. According to Higgs theory, the
interaction between particles and the Higgs field is continuously maintained and
renewed, converting the amorphous potential energy of the field into individual
structures. The seemingly empty space that surrounds the electron is teeming
with pairs of particles and antiparticles that fleet in and out of existence to create
“virtual particles” cloud.
Although precisely measuring this cloud is beyond the capabilities of modern
methods, the current model predicts that electrons are slightly aspheric, with a
distortion characterized by the electric dipole moment. However, no experiment
so far has detected this deviation [9].
In previous article, the electron was presented as a classical vortex therefore
the spin could be explained in classical terms [10].
The proposed idea is that the electrons are irrotational vortices of frictionless
superfluid space with concentric streamlines that were created from the primor
dial vacuum during the Big Bang.
The superfluid accommodates the rotation by forming a lattice of quantized
vortices in which the vortex core, typically singular, breaks the topological con
straint against rotational motion.
The superfluid vortices are frictionless, have a mass, angular momentum and
spin that can be studied applying hydrodynamic laws. This allows us to compare
spin’s behavior to the behavior of other liquid or gas vortices that we feel we
understand better.
Maxwell worked out a theory of electromagnetism assuming that every mag
netic tube of force was a vortex with an axis of rotation coinciding with the di
rection of the force. Several properties have been mathematically proved for a
perfect frictionless fluid.
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Therefore, in order to understand the law that governs the electron structure
and behavior we should take into consideration the fluid dynamics of the vortic
es. To do so we can apply Helmholtz’s three theorems which are as follows [11].
The strength of a vortex filament is constant along its length
.
1) A vortex filament cannot end in a fluid; it must extend to the boundaries of
the fluid or form a closed path.
2) In the absence of rotational external forces, a fluid that is initially irrota
tional remains irrotational.
The hydrodynamic laws are applied to describe the particle properties in the
quantum scale domain.
Vortex is a mass of fluid in whirling or rotary motion in the absence of fric
tion would make it impossible to destroy vortex motion. This solution relies on
the current standard theory assumption that particle’s spin is the result of an ini
tial impulse generated in the Big Bang conserved over billions of years of evolu
tion in a frictionless environment.
Motion in such a fluid would be a permanent flow pattern; the velocity of the
fluid element instantaneously passing through a given point in space would be
constant in time, this is an irrotational vortex.
Therefore, there are two kinds of angular momentum of the electron: The spin
angular momentum and orbital angular momentum. The spin angular momen
tum is the angular momentum about the object’s centre of mass, while the orbital
angular momentum is the angular momentum about a chosen center of rotation.
Angular momentum is a form of inertia, reflecting the object’s size, shape,
mass, and rotational velocity. It is typically represented as a vector (L) pointing
along the axis of rotation.
3. The Origin of Spin 1/2 Particle
All particles can spin, like the planet on its axis, however, it would be possible in
theory to change the speed or direction of the planet spin. With particles, spin
has a fixed value that depends only on the type of particle. Once it was formed it
will remain very stable and their decay very slow due to the very low viscous
forces of the adjacent vacuum. Thus spin is quantized, meaning that only certain
discrete spins in which the vortex is stable are allowed.
The angular momentum around an axis is the generator of rotations about
that axis, and its value tells us the rate at which the wave function changes as it’s
rotated about that axis, and only a discrete set of rates are possible since we have
to get the original wave function back after the boundary rotation of the vortex
by 2π radians or 360 degrees.
In order to maintain stable rotation the vortex should complete 2π
r
, 360 de
grees, which allows the minimal time needed to exist t
= 2π
r
/
c
.
At the moment of formation of the particle, a gap remains between the core
rotation and the boundaries speed rotation. The core could make a complete ro
tation then the streamlines follow this rotation with some retardation. This is
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actually the reason for the curvature of the streamlines.
Indeed, during the vortex formation, the different angular speed creates diffe
rential rotation so virtual photons closer to the center complete greater fraction
of orbit in a given time (Figure 1).
The spin is the rate of rotation between the boundaries and the center of the
vortex. When the center complete two orbital rotation in relation to the bounda
ries the spin is considered to be 1/2. Similar behavior is observed in different
spiral galaxies.
Hence the magnitude of the spin quantum number is an intrinsic attribute of
a particle related to the relation between the numbers of torque of the core of the
vortex to the numbers of torque in the external part. A spin 1/2 particle needs
two
full rotations (2 × 360˚ = 720˚) of the core until it is again in the same state
of complete rotation in the boundaries of the vortex.
4. Relation between Angular Momentum and the Reduced
Planck Constant
Niels Bohr (1913) found that the Plank constant could explain the energy struc
ture of electrons in the atom [12].
Electron spin is the particles’ intrinsic angular momentum (
S
) quantified by
the equation
1Ss= +
, (1)
where
s
=
n
/2 and
n
is any nonnegative integer and is described in units N∙m∙s,
or kg∙m2∙s−1.
In hydrodynamics, the velocity of the fluid element instantaneously passing
through a given point in space in the vortex with radius
r
is constant in time;
therefore, the circulation or the vorticity Γ = 2π
rc
is constant. Γ
m
is a conserved
momentum; therefore, 2π
rcm
is constant, which corresponds to the Planck con
stant.
Thus,
2,
e e ee
rc h mΓ=Γπ=
, (2)
and
constant
ee
hmΓ= =
(3)
Figure 1. The differential rotation is due to a greater fraction of their orbit in a given
time, when the boundaries complete one circle of 360 degrees the center complete two
circles of 720 degrees.
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Therefore, the Plank constant is the expression of
the angular momentum of
the electron vortex which describes the angular momentum of the internal ener
getic filaments which are rotating with angular velocity and angular frequency
typically measured in cycles or rotations per unit time measured with units of
radian per second. One radian is the angle subtended at the center of a circle by
an arc that is equal in length to the radius of the circle.
The length
S
of the enclosed arc is equal to the radius multiplied by the mag
nitude of the angle in radians is given by,
Sr
θ
=
(4)
where
S
is arc length,
r
is the radius of the circle,
θ
is the subtended angle en
closed by the arc in radians. The magnitude in radians of such a subtended angle
is equal to the ratio of the arc length to the radius of the circle; that is,
Sr
θ
=
(5)
It follows that the magnitude in radians of one complete revolution (360 de
grees) is the length of the entire circumference divided by the radius, or 2π
r
/
r
, or
2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to
180/π degrees. The angular momentum of one radian is a minimal discrete value
which is equal to the Planck constant divided by (or reduced by) 2π, and de
noted
ħ
(“hbar”). However, angular momentum is a description of particle spin.
Therefore, the final angular momentum is a multiple of the spin value which is
1/2 times the vortex angular momentum to restore the original state. The final
angular momentum will be expressed as Planck’s constant divided by 2π × 1/2 =
4π.
The SI unit of spin is (kg·m2·s−1), just as with classical angular momentum in
dicating that Planck constant is an expression of classical angular momentum.
5. The Formation of Magnetic Field
In the irrotational vortex, the rates of rotation of the fluid in the vortex is great
est at the center and decreases progressively 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 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. If the velocity of the space circulation
reaches the limiting speed,
c
, which is the speed of light in the absolute vacuum,
and the velocity field gradient around the core of the vortex becomes the post
ulated limiting angular rotation,
ω
, the space breaks down, creating a spherical
void, which is defined as a fieldless, energyless, and spaceless volume of va
cuum at the vortex center.
It follows moving down in the center and around the spiral and returns from
the upper side of the central axis generating the magnetic momentum and mag
netic dipole (Figure 2).
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From classical electrodynamics, a rotating electrically charged body creates a
magnetic dipole with magnetic poles of equal magnitude but opposite polarity.
A spinning system along an axis with angular momentum has a torque when
the force is directed toward the center of gravity; known as the Coriolis effect,
and when the boundaries of the vortex complete on cycle the magnetic field rotates
making the whole structure rotate as a rigid sphere acting on the vortex to main
tain its rotation as one unit and the spiral arm curl is fixed for all time (Figure 3).
One consequence is that an external magnetic field exerts a torque on the
electron magnetic moment and the vortex creates the magnetic field and the
magnetic field maintain the rotation of the vortex.
For magnetic dipoles, the dipole moment points from the magnetic south to
the magnetic north pole. The electron exists in a magnetic field which exerts a
Figure 2. The charge flowing through a circular torque experienced by a vortex forms
magnetic energy who’s field lines are perpendicular to the direction of the charge rotation.
Figure 3. Artistic presentation of the rotating egg shape magnetic field around the electron
.
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torque opposing its alignment creating a potential energy that depends on its
orientation with respect to the field.
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 (Figure 4).
The magnetic field separates the vortex from the adjacent vacuum and con
verts it in independent entity with perpetual mobile. The projection can be
changed, but the total spin of 1/2 related to the spiral arm curl is fixed for all
time.
If the electron is visualized as a classical charged particle rotating about an
axis with angular momentum
L
, its magnetic dipole moment
μ
is given by:
2
e
qgL m
µ
= −
(6)
where
q
is the electron charge,
g
is the gfactor of the electron,
L
is the angular
momentum and
me
is the electron rest mass.
The magnetic energy of an electron is approximately twice what it should be
in classical mechanics. The factor of two multiplying the electron spin angular
momentum comes from the fact that it is twice as effective in producing mag
netic moment. This factor is called the electronic spin
g
factor.
The
g
factor is an essential value related to the magnetic moment of the sub
atomic particles and corrects for the precession of the angular momentum.
The intrinsic magnetic moment
μ
of a particle with charge
q
, mass
m
, and
spin
s
, is
( )
2gq ms
µ
=
(7)
where the dimensionless quantity
g
is called the
g
factor. The
g
factor is a part of
the calculation for the gyromagnetic ratio, which is the ratio of the magnetic
moment of a particle to the angular momentum of the same particle. The spin
g
factor is approximately two. The reason of this has been a source of mystery
ever since spin was discovered. The vortex structure of the electron help solve
this mystery.
6. The Spin Angular Momentum and Magnetic Momentum
Angular momentum can be considered a rotational analog of linear momentum.
Figure 4. Two opposite spins the one has projection value said to be up with spin up (left)
+1/2 and spin down (right) −1/2.
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Thus, where linear momentum
p
is proportional to mass
m
and linear speed
v
,
p mv
=
(8)
The magnitude of the angular momentum of the vortex
L
is proportional to
moment of inertia
I
and angular speed
ω
measured in radians per second.
LI
ω
=
(9)
L
should be referred to as the angular momentum
relative to that center
.
Because
2
I rm=
for a single particle and
cr
ω
=
for circular motion, an
gular momentum can be expanded,
2
L r mc r=
and reduced to,
e
L rm c=
(10)
where
r
is the radius of the vortex
me
is the electron rest mass and
c
is the speed
of light.
A spin magnetic moment is the magnetic moment caused by the spin of the
charged electron vortex. The magnitude of the magnetic dipole moment of the
vortex is:
IA
µ
=
, (11)
where is the current of the charge inside the vortex and
A
is the area of the
vortex of both sides which is 2π
r
2 where
r
is the radius of the vortex.
The current inside the vortex passes by a particular point on the vortex in a
certain time, so we can calculate a current
I qT=
. (12)
where
q
is the magnitude of the electron charge and is its cycle period of the
vortex [13].
The electron as a vortex has a minimum time less than which the electron
converts into a virtual particle. If we assume that the electron vortex has a circu
lar shape that needed to complete one rotation cycle 2π
re
, the orbital period will
be:
2T rv= π
, (13)
where
r
is the radius of the core of electron vortex and
v
is the rotation speed of
the electron vortex.
The area of the vortex is approximately a circle, however, the surface depres
sion in the center double the surface area, therefore,
2
2Ar= π
(14)
then the magnitude of the magnetic dipole moment will be
( )
2
22
IA qv r r qcr
µ
π =π= =
. (15)
where
q
is the electron charge.
The ratio between magnetic momentum and angular momentum
ee
L qcr rm c q m
µ
= =
(16)
Therefore
( )
e
qm L
µ
=
. (17)
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Thus, the electron is visualized as a vortex charged particle rotating about an
axis with angular momentum
L
, its magnetic dipole moment
μ
in full vector
form, is written as
( )
e
qm= − L
µ
(18)
The negative sign appears because the electron has a negative charge.
Therefore there is no need to add the mysterious gfactor in order to obtain
the experimental results.
If the angular momentum of one radian is a minimal discrete value which is
equal to the Planck constant reduced by 2π. Bohr magneton
μB
express the
magnetic moment of one vortex radiant in terms of the reduced Planck constant
ħ
.
2
Be
em
µ
=
(19)
Since the magnetic moment is quantized in units of
μB
, correspondingly the
angular momentum is quantized in units of
ħ
.
7. Conclusions
The electron quantum properties can be accurately described using classical phys
ics and hydrodynamics laws.
Most individual particles and combinations of particles produce a magnetic
field very much like that of a spinning vortex of charge. Experiments and obser
vations showed that this spin is most easily described as an angular momentum.
In the vortex, spin acts like angular momentum because it is related to the spiral
arm rotation, so everything we know about angular momentum is also true of
spin.
Hydrodynamic laws are applied to study the behavior of the superfluid vortex
of the electron which has internal rotation, and angular momentum, and spin,
which confers upon it its rest mass.
The electron is a cloud, a composite web and energy motion processes which
has irrotational vortex, created during the big bang.
The angular momentum of a vortex filament of the particle is the sum of an
gular momenta of the individual Higgs particles which behave as a fluid. In this
way, angular momentum is sometimes described as the rotational analog of li
near momentum.
The 1/2 spin is an expression of the gap between the rotation rate of the vortex
core which is double rotation rate of the vortex boundaries. This unchangeable
gab is fixed at the moment of electron formation during the big bang. The −1/2
and +1/2 are indication of the orientation of the magnetic dipole like south and
north.
The conserved angular momentum of the electron is related to constancy of
circulation or vorticity in the irrotational vortex multiplied by its mass which has
the same value of Planck constant. Planck constant expresses the angular mo
mentum of 2π radians which is equal to 360 degrees. The minimal discrete value
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which is equal to the Planck constant reduced by 2π radians denoted as
ħ
(“hbar”).
The angular momentum of one radian is the minimal discrete Bohr magneton
μB
expresses the magnetic moment of one vortex radiant in terms of the reduced
Planck constant
ħ
.
Since the magnetic moment is quantized in units of
μB
, correspondingly the
angular momentum is quantized in units of
ħ
.
The final angular momentum of the electron is a multiple of the spin value
which is 1/2 times the vortex angular momentum, which might be expressed as
Planck’s constant divided by 4 pi.
The origin of spin completes the properties of the electron. All properties such
particle wave duality [14], electron charge, mass, spin angular momentum and
magnetic momentum, can now be derived from the vortex structure and match
all experimental observations of the electron. The hydrodynamic process of the
vortex may open new horizons to understand the properties and behavior of
fermions such as quarks and the internal structure of the proton and neutrons,
and to understand the hydrodynamic process of interaction with large scale spiral
shock fronts that might be responsible for the observed rotational properties of
giant molecular clouds in galactic disk, and better describe the formation and
structure of galaxies, supernovas, and other astrophysical systems such as black
holes, their plasma dynamics and electromagnetic fields giving a new model for
unification of the four forces and the basis for the theory of everything.
Acknowledgements
This research did not receive any specific grant from funding agencies in the
public, commercial, or notforprofit sectors.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa
per.
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