ArticlePDF Available

A New Theory on the Origin and Nature of the Fine Structure Constant

Journal of High Energy Physics, Gravitation and Cosmology, 2020, 6, 579-589
ISSN Online: 2380-4335
ISSN Print: 2380-4327
10.4236/jhepgc.2020.64039 Aug. 13, 2020 579 Journal of High Energy Physics, G
ravitation and Cosmology
A New Theory on the Origin and Nature of the
Fine Structure Constant
Nader Butto
Dgania, Petah Tikva, Israel
The nature and the origin of the fine structure are described. Based on the
vortex model and hydrodynamics, a comprehensible interpretation of the fine
structure constant is developed. The vacuum considered to have superfluid
characteristics and elementary
particles such as the electron and Hydrogen
molecule are irrotational vortices of this superfluid. In such a vortex, the an-
gular rotation ω is maintained, and the larger the radius, the slower the rota-
tional speed. The fine structure value is derived from the ratio of the rota-
tional speed of the boundaries of the vortex to the speed of the vortex eye in
its center. Since the angular rotation is constant, the same value was derived
from the ratio between the radius of the constant vortex core and the radius
of the hall vortex. Therefore, the constancy of alpha is an expression of
constancy relation in the vortex structure.
Fine Structure Constant, Angular Rotation, Irrotational Vortex,
Vortex Electron Structure, Hydrogen Atom Structure
1. Introduction
The fine structure constant (
), also known as Sommerfeld’s constant, was dis-
covered to be a ubiquitous constant and is one of the fundamental constants in
nature [1], characterizing the whole range of physics from elementary particles
to atomic, mesoscopic, and macroscopic systems (similar to the speed of light,
Planck’s constant, and Newton’s gravitational constant “G”). The values of these
constants of nature determine the nature of our universe. A small difference (as
little as 4%) in the value of the fine structure constant would have prevented
stars from sustaining the nuclear reactions in their cores that produced carbon
and allowed carbon-based lifeforms in our universe; for example, if
How to cite this paper:
Butto, N. (2020)
New Theory on the Origin and Nature of
the Fine Structure Constant
Journal of High
Energy Physics
Gravitation and Cosmol
, 579-589.
July 3, 2020
August 10, 2020
August 13, 2020
Copyright © 20
20 by author(s) and
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
Open Access
N. Butto
10.4236/jhepgc.2020.64039 580 Journal of High Energy Physics, G
ravitation and Cosmology
greater than 0.1, stellar fusion would be impossible, and no place in the universe
would have been warm enough for survival [2].
The fine structure describes the splitting of the spectral lines of atoms caused
by the interaction between the spin and orbital angular momenta of the outer-
most electron. It was first measured for the Hydrogen atom by Albert A. Mi-
chelson and Edward W. Morley in 1887 [3]. To explain the observed splitting or
fine structure of the energy levels of the Hydrogen atom, Sommerfeld extended
the Bohr theory to include elliptical orbits and the relativistic dependence of
mass on velocity, deriving the Bohr-Sommerfeld model [4] [5]. Introduced into
physics in 1916, the fine structure constant [6], has been discussed for decades. It
is commonly denoted by
and is a unitless and dimensionless physical constant
[7]. It is widely accepted that the value of
is related to the electromagnetic force
between subatomic charged particles and determines how an atom holds its elec-
trons. Thus, it is related to the elementary charge
, which characterizes the
strength of the coupling of an elementary charged particle with the electromag-
netic field:
is the unit electromagnetic charge,
0 is the permittivity constant,
Planck’s constant divided by 2π, and
is the velocity of light.
Alpha constant has stimulated laboratory tests to improve the precision of
measurements of the constancy of the fine structure constant [8] [9] [10]. The
value of
is approximately equal to 1/137, and its exact value according to
CODATA 2014 [11] is 0.0072973525664. It can be determined with a precision
better than a few parts in 10−7 using four independent ways: the AC Josephson
effect, the quantized Hall effect, the muonium hyperfine structure, and the elec-
tron anomalous magnetic moment. A determination of alpha based on an im-
proved theoretical calculation and the Penning traps measurement of the elec-
tron anomalous magnetic moments reached a precision exceeding 10−8 [12].
Currently, the value of
with the smallest uncertainty was obtained from the
comparison of the theoretical expression and experimental value of the anomal-
ous magnetic moment of the electron. Starting in the 1980s, a new and wholly
different measurement approach using the quantum Hall effect (QHE) has caused
excitement because the value of α obtained from it independently corroborates
the value of
from the electron magnetic moment anomaly. The QHE value of
does not have as small uncertainty as the electron magnetic moment value but
provides significant independent confirmation of that value.
Recently, evidence indicating cosmological variations and the fine structure
constant may be drifting [13] [14] and has triggered much interest in theories
that account for the drift in fundamental constants [14]-[20].
The quantity
, which is equal to the ratio
, where
is the velocity of the
electron in the first circular Bohr orbit, and
is the speed of light in vacuum,
appeared naturally in Sommerfeld’s analysis and determined the size of the split-
ting or fine structure of the hydrogenic spectral lines. However, it has remained
N. Butto
10.4236/jhepgc.2020.64039 581 Journal of High Energy Physics, G
ravitation and Cosmology
enigmatic for over 100 years and is considered to be fundamental and not de-
rived. no compelling theory on its origin or a mechanism that explains its nu-
merical value or the range of its domain exists, and it was a key unsolved physi-
cal problem for many physicists, such as Max Born, Richard Feynman [21], and
Wolfgang Pauli [22], who wrote in 1948: “The theoretical interpretation of [the
fine structure constant’s] numerical value is one of the most important unsolved
problems of atomic physics.” Richard Feynmann called it a “magic number” and
its value “one of the greatest damn mysteries of physics.” [23] Some modern theo-
ries, such as String theory or anti-de Sitter/conformal field theory (AdS/CFT),
propose mechanisms on how this constant emerges from more fundamental ob-
jects but fail to predict its value.
Therefore, despite attempts that have continued to date to find a mathematical
basis for this dimensionless constant, no numerological explanation has yet been
accepted by the community. In this work, a natural and compelling answer to
the longstanding mystery of the meaning of α is proposed. The arguments pre-
sented below are based on the vortex model for the electron and the Hydrogen
atom. A brief description of the electron structure is presented, and the essence
and origin of the fine structure constant are derived. The proposed idea in this
paper is that the electron is an irrotational vortex of frictionless superfluid space
with concentric streamlines made up by massless Higgs particles, which acquire
mass when they travel around the vortex center. According to this model, every
elementary particle is made up of flux massless photons, which flow in a helix at
the speed of light
. The fine structure constant is the ratio between the rotation-
al velocity of the boundaries and the center of the electron and Hydrogen vortex.
Therefore, α is dimensionless, and it has the same value on each discrete cosmo-
logical scale of nature.
2. The Structure of the Electron
Despite the impressive successes and impeccable mathematical tools in the ap-
plication of quantum mechanics to many modern fields (such as semiconductors
and superconductivity), the physicists cannot still advance a physical theory to
answer the simple question “What is an electron?” The structure of the electron
is not known, and the questions about the nature, shape, and size of the electron
rarely have any place in modern physics. According to the quantum mechanics,
the electron has no known substructure [24] [24], and the current understanding
is that the electron is a point particle with a point charge and no spatial extent
[26]. Attempts to model the electron as a non-point particle have been described
as ill-conceived and counter-pedagogic. Therefore, the radius of the electron is a
challenging problem of modern theoretical physics, and the admission of the
hypothesis of a finite radius of the electron is incompatible to the premises of the
theory of relativity.
On the other hand, a point-like electron (zero radius) generates serious ma-
thematical difficulties due to the self-energy of the electron approaching infinity
N. Butto
10.4236/jhepgc.2020.64039 582 Journal of High Energy Physics, G
ravitation and Cosmology
If the electron has a mass and no size is to say that it has infinite density.
However, infinities of any quality rarely have a place in the real world. Never-
theless, it is useful to define a length that characterizes electron interactions in
atomic-scale problems. Thus, it is fair to suggest that an electron does have a
non-zero size, even though it is exceedingly small and irrelevant in most consid-
The classical understanding of an electron accepts that the electron has an ex-
tension, and the vortex shape can explain the angular momentum (spin), mag-
netic moment, and the internal oscillation. In 1861, James Clerk Maxwell, de-
scribed the electron as a vortex. He attempted to explain the magnetic field in
terms of a sea of such excessively small whirlpools. In his paper “On Physical
Lines of Force” [28]. He uses such a concept to explain magnetism on the basis
that these vortices are aligned solenoidally with their rotation axes tracing out
magnetic lines of force. He described the vortex lines as “lines of force” that are
sometimes called “flux,” meaning “flow lines.” This vortex model helped him
derive his famous Maxwell equations by which he unified magnetism and static
electricity into a single theory of forces.
In 1928, when Paul Dirac presented the wave function of the electron (the
“Dirac equation”), it became obvious that there must be not only an internal os-
cillation but also some internal motion at the speed of light.
When Erwin Schrödinger found it as a result of the Dirac equation, he gave
the phenomenon the German name “Zitterbewegung,” meaning a type of poorly
defined oscillation. Jehle spent a large part of his life developing an electron
theory and elementary particles based on quantized magnetic flux loops, spin-
ning at the Zitterbewegung frequency [29] [30] [31] [32].
Both Dirac and Jehle theories rely on a physical relationship between flux and
charge. The question of the relation between electric and magnetic properties is
fundamental to electrodynamics. One expects a relationship because a moving
charge produces magnetic flux.
A spinning system along an axis with an angular momentum has a torque
when the force is directed toward the center of gravity known as Coriolis effect.
The flow to the center of the vortex due to Coriolis effect becomes vortex tube,
which is always composed of the same virtual particles that rotate at the speed of
light. Because it remains
, it has a ring-like structure.
Maxwell assumed that every magnetic tube of force was a vortex with an axis
of rotation coinciding with the direction of the force. Several properties have
been mathematically proved for a perfect frictionless fluid [33].
In previous paper, a new theory was proposed in which the electron has a
structure and a shape [34].
The vortex shape of the electron provides the correct relationship between the
parameters of the electron, such as its mass, density volume, time, constant an-
gular momentum (spin), electric charge, and magnetic moment. The electron as
an irrotational circular vortex of frictionless superfluid space with concentric
streamlines that was created from the primordial vacuum during the Big Bang.
N. Butto
10.4236/jhepgc.2020.64039 583 Journal of High Energy Physics, G
ravitation and Cosmology
The superfluid accommodates rotation by forming a lattice of quantized vortices
in which the vortex core (typically singular) breaks the topological constraint
against rotational motion.
In such a vortex, the magnitude of the vorticity in a vortex tube proportionally
increases as the vortex line stretched. Consider a very thin vortex tube round the
vortex line, so thin that the vorticity is practically constant over its width. As the
vortex tube stretches, the cross-sectional area decreases by the same factor, so
the vorticity must increase proportionally for the flux across the cross section to
remain constant.
Therefore, the rate of rotation of the fluid is the greatest at the center and
progressively decreases with distance from the center until there is no gradient
pressure in the boundaries of the vortex where the flow will be laminar and the
friction is null. If the speed of the space circulation reaches the limiting speed of
in the absolute vacuum, and the velocity-field gradient around the center
of the vortex becomes the postulated limiting angular rotation
, space breaks
down, creating a spherical void, which is defined as a field-less, energy-less and
space-less volume of nothingness at the vortex center.
These maxima occur at the point where the centrifugal force and radial force
are equalized, the inflowing medium and the free surface dip sharply, the in-
flowing medium turns at 90 degrees near the axis line with depth and velocity
inversely proportional to
2 to form a concave paraboloid.
3. Relation between Electron Vortex and the Fine Structure
The fine structure constant
was first interpreted as the ratio of the velocity of
the electron in the first circular orbit of the relativistic Bohr atom to the speed of
light in the vacuum [35]. The fine structure constant was proposed by Sommer-
feld as the ratio of the speed of the electron
in the ground state of Bohr’s Hy-
drogen atom model to the speed of light
2vc e c
= =
is the charge of the electron. However, why this ratio is constant is not
known. The value of constant
is a dimensionless quantity, which indicates that
this value is an expression of the ratio between two quantities that have the same
The irrotational vortex structure is universal, which can found in the micro
realm, such as the electron structure and Hydrogen atom structure, as well as in
the macro, such as in the spiral galaxies. In fluid dynamics, the irrotational vor-
tex dynamics has two different rotational speeds at two different radii; in the
electron and the Hydrogen atom, the internal one, where the rotation velocity is
at the speed of light and the second radius from the center to the boundaries.
The rotational speed in the boundaries is calculated and the ratio between the
external rotational speed and the center speed is derived. The constant alpha re-
lated to different constant ratios present in the irrotational vortex is the ratio
N. Butto
10.4236/jhepgc.2020.64039 584 Journal of High Energy Physics, G
ravitation and Cosmology
between the rotational speed on the boundaries of the vortex and speed of light
in the center. Since the angular velocity ω in the vortex is constant according to
the equation
Thus, the ratio of the radius of the core of the vortex to the radius from the
boundaries to the center is constant.
In hydrodynamics, the velocity of the fluid element instantaneously passing
through a given point in space in the vortex with radius
is constant in time;
therefore, the circulation or the vorticity Γ of the vortex is
rcΓ= π
where 2π
e is the circumference of the electron vortex.
Since Γm is the conserved momentum, 2π
is constant, which corresponds
to the Planck constant. Therefore, the Planck constant can be expressed as
2h rcm= π
Knowing the mass of the electron, then the radius of the eye of the vortex,
which rotates at speed of light is calculated as
2 3.86 10 m
r h mc
= = ×
is the rest mass of an electron = 9.10938356 × 1031 kg, and
6.61997943364 × 1034 kg∙m2∙s−1, and
is the speed of light,
= 3 × 108 m∙s−1.
The radius on the boundaries of the electron vortex can be calculated if the
rotational speed is known.
In the electron vortex model, the electric charge is an expression of the vo-
lume flow rate of vacuum flux from the vacuum to the center of the electron
vortex. The electric force is the force needed to move the flow from the peri-
phery to the center. The force acting on the two charges is expressed by Cou-
lomb’s law expressed as
Fe r
In the vortex, this force is equivalent to the centripetal force
, where m
is the rest mass of the electron,
is the rotational speed at distance
from the
center, and
is the radius of the electron. Therefore,
2 22
F mv r e r
π= =
Based on this equation, the rotational speed of the vortex is
v e rm v
Since 2π
is the conserved momentum and constant, the rotational speed
of the vortex is equal to Planck constant
2 2.1876913 10 m sve h
= = ×
0 is the electric permittivity (8.854187817... × 1012 F∙m−1),
is the electric
charge (1.602176634 × 1019 C), and
is the Planck constant (6.62607004 × 1034
N. Butto
10.4236/jhepgc.2020.64039 585 Journal of High Energy Physics, G
ravitation and Cosmology
The ratio between the rotational speed on the boundaries and in the center of
the vortex is equivalent to
, which can be calculated as
2.1892212626 10 3 10 0.007292304333 1 137.13× ×= =
and is the same value of
From the rotational velocity, the radius of the electron
vortex in the boun-
daries can be calculated as
2 5.2895948 10 m
r h vm
= = ×π
The ratio between the radius at the boundaries of the electron
and the ra-
dius of the vortex the at the center
13 11
3.86 10 5.2895948 10 0.007297345347 1 137.036
=× ×= =
which is also has the same value of
, eliminating the uncertainty of the elliptic
4. Relation between Hydrogen Model and the Fine Structure
The fine structure constant in the formula for the energy levels of the Hydrogen
atom was first given by Sommerfeld. Bohr’s model of the atom postulated that
the electrons of an atom moved about its nucleus in circular orbits, or as later
suggested by Arnold Summerfeld (1868-1951), in elliptical orbits, each with a
certain “allowed” energy and relativistic dependence of mass on velocity.
According to quantum mechanics, an electron orbital is the position of the
electrons around the nucleus and is determined as the volume of space in which
the electron can be found with a 95% probability. Each orbital has a specific
energy. The position (the probability amplitude) of the electron is defined by its
coordinates in space, which is indicated by
) in Cartesian coordinates.
cannot be measured directly but is a mathematical tool.
The clouds of probabilities are known as shells. Each shell has sublevels and
subshells. The numbers of electrons that can occupy each shell and each subshell
arise from the equations of quantum mechanics, in particular, the Pauli exclu-
sion principle, which states that no two electrons in the same atom can have the
same values of the four quantum numbers. However, no theory explains the na-
ture or essence of the shells, sublevels, and subshells. Thus, the vortex model was
applied to the shell structure, which was discussed in detail in other papers.
In this article, the Hydrogen shell structure is considered and treated as a vor-
tex, where the proton in the center of the vortex and the electron located on one
of the spiral lines of the vortex. Therefore, the electron orbital rotation is not free
but is guided by the vortex rotation that produces the magnetic field of the atom.
The rotational speed of the proton vortex center is the speed of light as it is in
the center of the electron vortex. The internal radius of the proton is calculated
2 2.103104894 10 m
r h cm
= = ×π
N. Butto
10.4236/jhepgc.2020.64039 586 Journal of High Energy Physics, G
ravitation and Cosmology
is the mass of the proton (1.672621898 × 1027 kg). The electron charge
force is the force of attraction found on the boundaries of the electron that inte-
ract with the attractive force of the Hydrogen vortex, which is equal to the at-
tractive gravitation force of the Hydrogen vortex. Therefore, the rotational ve-
locity of the electron around the proton is
2 2.1876913 10 m s
v Ze h
= = ×
is the Hydrogen atomic number, 1, and the ratio between the electron
orbital velocity around the proton and vortex velocity at the core of the proton is
= 2.1876913 × 106/2.9979245 × 108 = 0.00729736383 = 1/137.035 which is
equal to
constant. Since the vorticity of the vortex is constant, the angular ro-
is constant. The angular rotation in the center of the proton vortex
= 6.3082019259 × 10−8 has the same angular rotation of the electron
around the proton.
If the velocity of the electron around the proton is 2.1876913 × 106 m/s, then
the distance of the electron from the proton
8 6 14
6.3082019259 10 2.1876913 10 2.8834972859 10 m
= = × ×= ×
The ratio between the radius of the proton vortex core and in the radius where
the electron is located can be calculated:
16 14
2.103104894 10 2.8834972859 10 0.007292304332 1 137.13
= × ×= =
which is equal to fine structure constant
Therefore, the Hydrogen has a vortex structure similar to the electron struc-
ture with a different radius. This does not necessarily indicate the radius of the
proton but the distance of the electron from the center of the proton in the Hy-
drogen atom.
5. Conclusions
A new theory that describes the origin of the fine structure constant is presented,
based on the structures of the electron and the Hydrogen atom. Both are consi-
dered as irrotational superfluid vortices with a permanent flow pattern and dif-
ferential rotational velocity at the core of the vortex relative to its boundaries.
Previous article [36] described the nature and the origin of Constant G based on
superfluid vortex theory.
The radius of the electron vortex core, which rotates at speed of light was cal-
culated to have the same Coulomb radius value. The tangential velocity was cal-
culated based on the centripetal force on the boundaries of the electron, which is
equal to electric force between two charges according to Coulomb flux of force.
Once the tangential velocity was determined, the radius of the electron from the
center to the boundaries was calculated.
The same vortex model was applied to the Hydrogen structure. The orbital
velocity of the electron around the proton and the radius between the electron
and proton was calculated. The fine structure constant is proportional to the ra-
N. Butto
10.4236/jhepgc.2020.64039 587 Journal of High Energy Physics, G
ravitation and Cosmology
tio between the tangential velocity of the electron around the proton and the
speed of light at the center of the proton.
Consequently, we showed that the fine structure constant considering the elec-
tron as a vortex in which the core is rotating at the speed of light, the ratio be-
tween the core radius of the electron vortex and the radius to the boundaries has
the value of the fine structure constant. Furthermore, considering the Hydrogen
structure as an irrotational vortex, and the electron rotates around the proton
with constant angular rotation, the ratio between the radius of the proton at its
core and the distance of the electron orbital gives the same value of the fine
structure constant. We conclude that the fine structure constant may not be a
fundamental constant but is an expression of the constancy of the ratio of the
tangential velocity of irrotational vortices to the core velocity and the ratio of the
core radius to the vortex radius.
The author would like to thank Enago ( for the English
language review.
This research did not receive any specific grant from funding agencies in the
public, commercial, or not-for-profit sectors.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-
[1] Uzan, J.-P. (2003) The Fundamental Constants and Their Variation: Observational
and Theoretical Status.
Reviews of Modern Physics
, 75, 403-455.
[2] Carroll, S.M. (2010) The Fine Structure Constant Is Probably Constant.
[3] Michelson, A.A. and Morley, E.W. (1887) Phil Mag. 24.
American Journal of Science
34, 427.
[4] Sommerfeld, A. (1923) Atomic Structure and Spectral Lines. Methuen, London,
[5] Kragh, H.N. (2012) Bohr and the Quantum Atom. Oxford University Press, Oxford.
[6] Sommerfeld, A. (1940) Zur Feinstruktur der Wasserstofflinien. Geschichte und ge-
genwärtiger Stand der Theorie.
, 28, 417-423. (In German)
[7] Bouchendira, R., Cladé, P., Guellati-Khélifa, S., Nez, F. and Biraben, F. (2011) New
Determination of the Fine-Structure Constant and Test of the Quantum Electrody-
Physical Review Letters
, 106, Article ID: 080801.
[8] Prestage, J.D., Tjoelker, R.L. and Maleki, L. (1995) Atomic Clocks and Variations of
the Fine Structure Constant.
Physical Review Letters
, 74, 3511-3514.
N. Butto
10.4236/jhepgc.2020.64039 588 Journal of High Energy Physics, G
ravitation and Cosmology
[9] Damour, T. and Dyson, F. (1996) The Oklo Bound on the Time Variation of the
Fine-Structure Constant Revisited.
Nuclear Physics B
, 480, 37-54.
[10] Salomon, C., Dimarcq, N., Abgrall, M.,
et al
. (2001) Cold Atoms in Space and
Atomic Clocks. Comptes rendus de l'Académie des Sciences, Paris, Vol. IV, 1-17.
[11] Mohr, P.J., Taylor, B.N. and Newell, D.B. (2015) The CODATA Recommended
Values of the Fundamental Physical Constants (Web Version 7.0).
[12] Gabrielse, G. (2009) Why Is Sideband Mass Spectrometry Possible with Ions in a
Penning TRAP?
Physical Review Letters
, 102, Article ID: 172501.
[13] Webb, J.K., Flambaum, V.V., Churchill, C.W., Drinkwater, M.J. and Barrow, J.D.
(1999) Search for Time Variation of the Fine Structure Constant.
Physical Review
, 82, 884-887.
[14] Webb, J.K., Murphy, M.T., Flambaum, V.V., Dzuba, V.A., Barrow, J.D., Churchill,
et al
. (2001) Further Evidence for Cosmological Evolution of the Fine Struc-
ture Constant.
Physical Review Letters
, 87, Article ID: 091301.
[15] Bekenstein, J.D. (2002) Physical Review. Part D. 66.
[16] Damour, T., Piazza, F. and Veneziano, G. (2002) Runaway Dilaton and Equivalence
Principle Violations.
Physical Review Letters
, 89, Article ID: 081601.
[17] Davies, P.C., Davis, T.M. and Lineweaver, C.H. (2002) Black Holes Constrain Va-
rying Constants.
, 418, 602-603.
[18] Forgacs, P. and Horvath, Z. (1979) On a Static Solution of the Einstein-Yang-Mills
System in Six Dimensions.
General Relativity and Gravitation
, 10, 931-940.
[19] Forgacs, P. and Horvath, Z. (1979) On the Influence of Extra Dimensions on the
Homogeneous Isotropic Universe.
General Relativity and Gravitation
, 11, 205-216.
[20] Magueijo, J. to be published in Reports in Progress of Physics.
[21] Resonance (1999) 14(4).
[22] Resonance (2011) 16(9).
[23] Eichten, E.J., Lane, K.D. and Peskin, M.E. (1983) New Tests for Quark and Lepton
Physical Review Letters
, 50, 811-814.
[24] Gabrielse, G., Hanneke, D., Kinoshita, T., Nio, M. and Odom, B. (2006) New De-
termination of the Fine Structure Constant from the Electron Value and QED.
Physical Review Letters
, 97, Article ID: 030802.
[25] Curtis, L.J. (2003) Atomic Structure and Lifetimes: A Conceptual Approach. Cam-
bridge University Press, Cambridge, 74.
[26] Shpolsky, E. (1951) Atomic Physics. 2nd Edition.
[27] Clerk-Maxwell, J. (1861) On Physical Lines of Force.
Philosophical Magazine
, 21,
N. Butto
10.4236/jhepgc.2020.64039 589 Journal of High Energy Physics, G
ravitation and Cosmology
[28] Jehle, H. (1971) Relationship of Flux Quantization to Charge Quantization and the
Electromagnetic Coupling Constant.
Physical Review D
, 3, 306-345.
[29] Jehle, H. (1972) Flux Quantization and Particle Physics.
Physical Review D
, 6,
[30] Jehle, H. (1975) Flux Quantization and Fractional Charges of Quarks.
Physical Re-
view D
, 11, 2147-2177.
[31] Jehle, H. (1977) Electron-Muon Puzzle and the Electromagnetic Coupling Constant.
Physical Review D
, 15, 3727-3759.
[32] Maxwell, J.C. (2010) On Physical Lines of Force.
Philosophical Magazine
, 90, 11-23.
[33] Butto, N. (2020) Electron Shape and Structure: A New Vortex Theory.
Journal of
High Energy Physics
Gravitation and Cosmology
, 6, 340-352.
[34] Introduction to the Constants for NonexpertsCurrent Advances: The Fine-
Structure Constant and Quantum Hall Effect. NIST Reference on Constants, Units
and Uncertainty. NIST.
[35] Sommerfeld, A. (1916) On the Quantum Theory of Spectral Lines.
Annals of Phys-
, 51, 125-167.
[36] Butto, N. (2020) New Mechanism and Analytical Formula for Understanding the
Gravity Constant G.
Journal of High Energy Physics
Gravitation and Cosmology
, 6,
... The number 137 is the approximate denominator of the fine-structure constant known as α  1/137.036. What really makes the fine structure constant amazing, as Feynman and others realized, is if it was somehow even a tiny bit different, the universe wouldn't be the same; in particular, human life would not have evolved (Born, 1935;Bouchendira et al., 2011;Butto, 2020;Eichten et al., 1983;Feynman, 1965;Kragh, 2012;Pauli, 1940Pauli, , 1946Schiff, 1968;Uzan, 2003). The fine structure constant governs the interacting strength of the electromagnetic force between charged elementary particles and their surrounding electromagnetic fields. ...
... In the derivation of equation (10), the reduced mass of the twin particles was taken as the equivalent mass of the corresponding photon, which will be verified theoretically later on. Equation (10) is the widely accepted formula for the fine structure constant that was first introduced by Arnold Sommerfield in 1916 (Butto, 2020;Kragh, 2012;Schiff, 1968;Sommerfeld, 1916;Uzan, 2003). The theoretically derived result of equation (10) puts the relation out of the best guess in equation (8) on a solid ground. ...
Full-text available
A dynamic elementary dipole model, with a spinning twin elementary unit charge particles having opposite signs of the charges, is proposed to explain the internal structure and the mutually induced oscillating electric and magnetic fields of a propagating photon. The twin elementary unit charge particles under electric attraction force form a dynamic elementary dipole and achieve a relatively stable orbital motion with a constant drifting speed of its mass centre. From a combined mechanical and electromagnetic analysing, the widely accepted formula for the fine structure constant is derived. It is revealed that the fine structure constant is the ratio of the radius of the dynamic elementary dipole to the corresponding radius of its photon. The fine structure constant is also derived as the ratio of the spinning angular frequency inside the dynamic elementary dipole to the corresponding angular frequency of its photon. In the effect of the spin, the drift movement of the mass centre of the dynamic elementary dipole, accomplished in the joined action of the electric and the magnetic fields, is derived as the light speed in the free space. Base on the derivation of the least action of the spinning elementary unit charge particle, a modified uncertainty principle is proposed. The modified uncertainty principle permits dramatically increased levels of precision for scientific measurements and engineering design in comparison with the Heisenberg Uncertainty Principle. The spin energy of the elementary unit charge particle inside the dynamic elementary dipole is derived as just half of the energy of its photon. The quantum number of half for the spinning elementary unit charge particle is deduced. The free space is revealed as a dielectric medium full of dynamic elementary dipoles, having electric and magnetic polarizability naturally. I am grateful that this paper has been accepted for publication in the Canadian Journal of Pure and Applied Science in 02.2022, Vol 16 No.1.
... In previous articles [1], the nature and the origin of the fine structure constant was described. Furthermore, new mechanism and analytical formula for understanding the gravity constant G was presented [2]. ...
... This study opens up a new approach to determine the nature and essence of the fundamental constants of nature, related to vacuum density and thus to reduce the number of fundamental constants to one. The origin and essence of gravitation constant G, fine structure constants was published in previous papers [1] [2], electric constant ε 0 , speed of light c constant and Planck constant will be presented in separate papers in the near future. ...
... Moreover, the fine structure constant was found to be directly related to the vortex shape of the electron and hydrogen nucleus [13]. ...
... The vortex shape of the electron and the Hydrogen atom give a full explanation 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] indicating the universality of the phenomena. ...
... In previous articles, the nature and the origin of the fine structure constant [7], the gravitational constant G [8], magnetic constant μ 0 [9] and electric permittivity [10] were described. ...
... In previous articles the nature and the origin of the fine structure constant, [2] the gravitational constant G, [3] and magnetic constant μ 0 [4] were described. ...
Full-text available
If quarks and leptons are composite at the energy scale $$\Lambda${}$, the strong forces binding their constituents induce flavor-diagonal contact interactions, which have significant effects at reaction energies well below $$\Lambda${}$. Consideration of their effect on Bhabha scattering produces a new, stronger bound on the scale of electron compositeness: $$\Lambda${}>750$ GeV. Collider experiments now being planned will be sensitive to $$\Lambda${}$\sim${}1$-${}5$ TeV for both electrons and light quarks.
The theory of atomic structure proposed by the young Danish physicist Niels Bohr in 1913 marked the true beginning of modern atomic and quantum physics. This is the first book that focuses in detail on the origin and development of this remarkable theory. It offers a comprehensive account of Bohr's ideas and the way they were modified by other physicists. By following the development and applications of the theory, it brings new insight into Bohr's peculiar way of thinking; what Einstein once called his 'musicality' and 'unique instinct and tact'. Contrary to most other accounts of the Bohr atom, the book presents it in a broader perspective, which includes the reception among other scientists, popular expositions of the theory, and the objections raised against it by scientists of a more conservative inclination. Moreover, it discusses the theory as Bohr originally conceived it, namely, as an ambitious attempt to understand the structure of atoms as well as molecules: the chemical aspects of the theory are given much attention. The book covers the successes as well as the failures of Bohr's theory, arguing that the latter were no less important in the process that led Bohr to abandon the original model and Heisenberg to propose a new 'quantum mechanics'. By discussing the theory in its entirety-following it from its birth in 1913, through its adolescence round 1918, to its decline in 1924-it becomes possible to understand its development and use it as an example of the dynamics of scientific theories.
Thesis (M.A.)--University of Texas at Austin. Vita. Includes bibliographical references.
Lorenzo Curtis offers a new conceptual approach to atomic structure that utilizes conceptual semiclassical models to introduce empirical systematizations of measured data. These models reveal the dynamical behavior of the various interactions that specify the energies and lifetimes of complex atoms. Curtis emphasizes the historical basis of the field as well as the relationship to modern fundamental theory. He also includes many solved problems that provide connections with astrophysics, chemistry, condensed matter, and other related fields.
On the basis of a heuristic model we argued in an earlier paper (paper C of this series) electric field (and of course the magnetic field, too) of a lepton or of a quark may be formulated in terms of a closed loop of quantized magnetic flux whose alternative forms ("loopforms") are superposed with probability amplitudes so as to represent the electromagnetic field of that lepton or quark. The Zitterbewegung of a single stationary ("elementary") particle suggests a kind of quasiextension, which is assumed, in the present theory, to permit concepts of structuralization of the electromagnetic field even for leptons. Mesons and baryons may be represented by linked quantized flux loops, i.e., quark loops (as in paper B). The central problem now (in this paper D) is to formulate those probability-amplitude distributions in terms of wave functions to characterize the internal structure of the lepton or quark in question. As probability-amplitude functions one may choose bases of irreducible representations of the group with respect to which the model is to be invariant. It is seen that this implies the SO(4) group. As both the electron-muon mass ratio and the electromagnetic coupling constant depend, in this flux-quantization model, on the correct formulation of the structuralization of probability-amplitude distributions, we should expect to get an insight into both these puzzles from finding the right probability-amplitude wave functions. Furthermore, it is seen that this same structuralization of probability-amplitude distributions also permits one to estimate the rate of weak interactions, thus relating them to electromagnetic interactions.
The concept of a closed quantized flux loop ("elementary loop") which avoids the implication of magnetic monopoles is investigated, leading to a theory of a charged lepton (muon or electron). In order to reconstruct a continuous magnetic dipole field of a source lepton, it is assumed that the flux loop adopts a statistical distribution of alternative forms characterized by a complex probability amplitude superposition, in a manner somewhat analogous to the superposition of path histories in Feynman's space-time approach to quantum mechanics. Flux quantization results from the equivalence of a line discontinuity of the phase factor of a ψ function of a field lepton (due to its phase multivaluedness by ±2π) to the presence of a line of quantized flux. On the same basis as quantized flux arises from such a singularity of that phase factor, so also an electric field arises when this singularity line is moving. In particular, the source's Coulomb field results from a spinning of the quantized flux loop (about the center of the source) with an angular velocity equal to the Zitterbewegung frequency 2mc2/ℏ, if the statistical distribution of flux loopforms properly represents the magnetic dipole field of a muon or of an electron. The reconstruction of the magnetic and electric fields of a charged lepton and the comparison of them with the quantized flux hc/e gives a numerical estimate of the electromagnetic interaction constant e2/ℏc, i.e., an understanding of the relationship between e and ℏ. The energy mc2 and angular momentum ℏ/2 may be interpreted as electromagnetic. The theory should work for both muon and electron and is expected to give some insight into the ratio of the masses of these two leptons. A representation of quarks in terms of linked quantized flux loops is suggested to describe a low-lying meson as a linkage of an elementary loop with an antiloop, and a low-lying baryon as three interlinked elementary loops. We are here developing a model approach to problems of structure and conservation laws in particle physics. A more abstract version of a quantized flux theory of particles should be preceded by such an heuristic model.
Quantized flux has provided an interesting model for muons and for electrons: One closed flux loop of the form of a magnetic dipole field line is assumed to adopt alternative forms which are superposed with complex probability amplitudes to define the magnetic field of a source lepton. The spinning of that loop with an angular velocity equal to the Zitterbewegung frequency 2mc2/ℏ implies an electric Coulomb field, (negative) positive, depending on (anti) parallelism of magnetic moment and spin. The model implies CP invariance. A quark may be represented by a quantized flux loop if interlinked with another loop in the case of a meson, with two other loops in the case of a baryon. Because of the link, their spinning is very different from that of a single loop (lepton). The concept of a single quark does not exist accordingly, and it is seen that a baryon with a symmetric spin-isospin function in the SU(2) × SU(3) quark representation might not violate the Pauli principle because the wave function representing the relative position of linked loops may be chosen antisymmetric. Weak interactions may be understood to occur when the flux loops involved in the interaction have to cross over themselves or over each other. Strangeness is readily interpreted in terms of the trefoil character of a λ quark: Strangeness-violating interactions imply crossing of flux lines and are thus weak and parity-nonconserving. ΔS=ΔQ is favored in such interactions. Intrinsic symmetries may be interpreted in terms of topology of linked loops. Sections I and II give a short résumé of the 1971 paper.