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Journal of High Energy Physics, Gravitation and Cosmology, 2020, 6, 579-589

https://www.scirp.org/journal/jhepgc

ISSN Online: 2380-4335

ISSN Print: 2380-4327

DOI:

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

Abstract

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

the

constancy relation in the vortex structure.

Keywords

Fine Structure Constant, Angular Rotation, Irrotational Vortex,

Vortex Electron Structure, Hydrogen Atom Structure

1. Introduction

The fine structure constant (

α

), 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

α

were

How to cite this paper:

Butto, N. (2020)

A

New Theory on the Origin and Nature of

the Fine Structure Constant

.

Journal of High

Energy Physics

,

Gravitation and Cosmol

o-

gy

,

6

, 579-589.

https://doi.org/10.4236/jhepgc.2020.64039

Received:

July 3, 2020

Accepted:

August 10, 2020

Published:

August 13, 2020

Copyright © 20

20 by author(s) and

Scientific

Research Publishing Inc.

This work is licensed under the Creative

Commons Attribution International

License (CC BY

4.0).

http://creativecommons.org/licenses/by/4.0/

Open Access

N. Butto

DOI:

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

α

and is a unitless and dimensionless physical constant

[7]. It is widely accepted that the value of

α

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

e

, which characterizes the

strength of the coupling of an elementary charged particle with the electromag-

netic field:

20

4

ec

αε

π

=

where

e

is the unit electromagnetic charge,

ε

0 is the permittivity constant,

ħ

is

Planck’s constant divided by 2π, and

c

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

α

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

α

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

α

from the electron magnetic moment anomaly. The QHE value of

α

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

α

, which is equal to the ratio

v

/

c

, where

v

is the velocity of the

electron in the first circular Bohr orbit, and

c

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

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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

c

. 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

[27].

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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-

erations.

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

unbroken

, 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.

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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

light

c

in the absolute vacuum, and the velocity-field gradient around the center

of the vortex becomes the postulated limiting angular rotation

ω

, 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

r

2 to form a concave paraboloid.

3. Relation between Electron Vortex and the Fine Structure

Constant

The fine structure constant

α

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

v

in the ground state of Bohr’s Hy-

drogen atom model to the speed of light

c

[36]:

2

2vc e c

α

= =

,

where

e

is the charge of the electron. However, why this ratio is constant is not

known. The value of constant

α

is a dimensionless quantity, which indicates that

this value is an expression of the ratio between two quantities that have the same

units.

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

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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

c

cr

ω

=

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

r

is constant in time;

therefore, the circulation or the vorticity Γ of the vortex is

2

e

rcΓ= π

where 2π

r

e is the circumference of the electron vortex.

Since Γm is the conserved momentum, 2π

rcm

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

13

2 3.86 10 m

o

r h mc

−

= = ×

π

where

mo

is the rest mass of an electron = 9.10938356 × 10−31 kg, and

h

=

6.61997943364 × 10−34 kg∙m2∙s−1, and

c

is the speed of light,

c

= 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

22

0

4e

Fe r

ε

π=

In the vortex, this force is equivalent to the centripetal force

mov

2/

r

, where m

is the rest mass of the electron,

v

is the rotational speed at distance

r

from the

center, and

r

is the radius of the electron. Therefore,

2 22

0

4

o

F mv r e r

ε

π= =

.

Based on this equation, the rotational speed of the vortex is

20

4

o

v e rm v

ε

π=

Since 2π

rmov

is the conserved momentum and constant, the rotational speed

of the vortex is equal to Planck constant

h

.

Therefore,

26

0

2 2.1876913 10 m sve h

ε

= = ×

where

ε

0 is the electric permittivity (8.854187817... × 10−12 F∙m−1),

e

is the electric

charge (1.602176634 × 10−19 C), and

h

is the Planck constant (6.62607004 × 10−34

m2∙kg/s).

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ravitation and Cosmology

The ratio between the rotational speed on the boundaries and in the center of

the vortex is equivalent to

v

/

c

, which can be calculated as

68

2.1892212626 10 3 10 0.007292304333 1 137.13× ×= =

and is the same value of

α

.

From the rotational velocity, the radius of the electron

re

vortex in the boun-

daries can be calculated as

11

2 5.2895948 10 m

e

r h vm

−

= = ×π

.

The ratio between the radius at the boundaries of the electron

re

and the ra-

dius of the vortex the at the center

rc

is

13 11

3.86 10 5.2895948 10 0.007297345347 1 137.036

ec

rr

−−

=× ×= =

,

which is also has the same value of

α

, eliminating the uncertainty of the elliptic

radius.

4. Relation between Hydrogen Model and the Fine Structure

Constant

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

ψ

(

x

,

y

,

z

) in Cartesian coordinates.

ψ

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

as

16

2 2.103104894 10 m

cp

r h cm

−

= = ×π

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ravitation and Cosmology

where

mp

is the mass of the proton (1.672621898 × 10−27 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

26

0

2 2.1876913 10 m s

e

v Ze h

ε

= = ×

where

Z

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

ve

/

c

= 2.1876913 × 106/2.9979245 × 108 = 0.00729736383 = 1/137.035 which is

equal to

α

constant. Since the vorticity of the vortex is constant, the angular ro-

tation

ω

=

crc

is constant. The angular rotation in the center of the proton vortex

ω

=

crc

= 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

rp

is

8 6 14

6.3082019259 10 2.1876913 10 2.8834972859 10 m

p

rv

ω

−−

= = × ×= ×

.

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

cp

rr

−−

= × ×= =

,

which is equal to fine structure constant

α

.

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-

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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.

Acknowledgements

The author would like to thank Enago (http://www.enago.com) 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-

per.

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