Fine structure constant

Fine structure constant
a Electron

a ≃ 1/137 ≃ 0.007
Why is nature characterized by this strange number?
Fine structure constant a

Contents
• Introduction
• Definition
• Interpretations
• Background
• Topologicalcharge
• Origin ofelectric charge
• Electron/Positronpairproduction
• Electronmodel
• Fine structureconstantderivation
• Inverse fine structureconstant
• Origin ofelectron rest mass
• Relativisticeffects
• Colorchargesymmetry
• Compositeparticlesmodels
• Electricandmagneticfield line structure
• Summaryremarks

• What is the mysterious fine structure constant, a, that describes the
strength of electromagnetic interactions?
• Why does a have the curious fixed value of ~1/137?
• The fine structure constant is a function of electric charge, a = e2/ħc
• What exactly is electric charge? Why is it quantized? Why is it dipolar?
• Electric charge is taken as a fundamental dimension on par with other
dimensions such as length, mass, time and temperature. We have at
least some intuitive sense of the physical nature of these other
dimensions, but the origin of electric charge has remained without
explanation. However, a significant clue is that electrical charge bears
mathematical similarity to topological charge & vortical charge.
• Rest mass and electric charge are intimately related. How is mass
generated? How can we calculate observed mass of fundamental
particles? The Standard Model of physics provides no answers.
• How can we derive a, electric charge, and mass from first principles?

Symbol: a A dimensionless quantity described as a fundamental
physical constant characterizing the strength of the electromagnetic interaction.
Introduced by Sommerfeld in 1916 to describe the spacing of splitting of
spectral lines in multi-electron atoms, it is formed from the four basic physical
constants, electric charge e, speed of light in vacuum c, the Planck constant h,
and the electric permittivity of free space e0:
a = e2/2hce0 = 0.0072973531… ≃ 1/137
For comparison, the strength of the strong interaction is 1, the weak interaction
has a strength of 10-13 and gravitation interaction of 10-38.
In order to understand why this mysterious dimensionless constant a has the
peculiar value of ~ 0.007293…, we must first comprehend the mechanism for
generation of electric charge e. We have some intuitive sense at least of other
fundamental dimensions such as mass, length, time and temperature, but what
exactly is this seemingly magical dimension of electric charge? The existence of
all matter in the universe and life itself depends on electric charge. However,
an explanation of electric charge is not found in extant literature.

The fine structure constant represents a relativistic correction to the Bohr
theory of the energy level of an electron and may be expressed as
a = ¼pe0(e2/ħc) = kCe2/ħc = (q/qP)2 [S.I. MKS units]
where
e = electric charge (= q = F/E = ħk/A = E/V = V·C) [C = kg·rad/sec]
qP = Planck charge (= √(4pe0ħc) = mPwP [kg·rad/sec]
e0 = permittivity of free space (= 8.854187817E-12 Farads/m) [F/m]
ħ = reduced Planck constant (= h/2p = p/k = (q0/A)/k = (S/c2)k = mc2/w) [J·s]
c = speed of light (= 1/√(m0e0) = E/B = w/k = lP/tP = mP
2(G/ ħ) [m/s]
kC = Coulomb constant (= 1/4pe0) [N·m2·C-2 = m3/kg·rad2]
F = Coulomb force (= q+E = kCq/r2) [N]
E = electric field intensity (= F/q = V/d = B·c) [volts/m = N/Coul]
E = energy (= T + V = √((pc)2 + (mc2)2) [Joules = N·m]
k = wave vector (= mv/ħ; wave no. k = |k| = 2p/l = nw/c) [1/m]
p = momentum (= mv) [kg·m/s]
A = magnetic vector potential (= (m0i/4p) ∮dl/r = ħk/e = vf/c2) [volt·sec/m = m/rad]
w = angular momentum (= r x mv) [rad·kg·m2/sec]
V = voltage (= W/q = J/Coul) [J/Coul = m2/(sec·rad)]
C = capacitance [= q/DV = W/(½ V2) [F = C/V = kg-1·m-2·s4·A2 = rad2·kg/m2]

The fine structure constant measures the coupling strength between two electrons
and has several related ratio interpretations:
a = kCe2/ħc = e2/2e0ch = e2Z0/2h = (1/4pe0)e2/ħc = vt/c = R0/RC = RC/Rem =
(qe/qP)2
= wp/wC = Fe/Fm = Z0/Ze = p·(Es0 - Emo)/(Es0 + Em0) = 0.0072973525693… ≃ 1/20F4
where
Fine structure constant interpretations
kC = Coulomb’s constant (= 1/4pe0 = 8.98755E9 kg·m3·s-2·C-2)
e = qe = electron charge (= F/E = 1.6021764E-19 C = mw = 7.0719 kg·rad/s)
e0 = vacuum permittivity = 1/m0c2 = 8.854187E-12 F/m)
c = velocity of light (= E/B = w/k = c0/n = 2.99E8 m/s)
h = Planck’s constant (= E/n = Rk/c2 = 6.62607E-34 J·s)
Z0 = impedance of free space (= E/H = m0c = 376.7 W)
vt = tangential velocity @ RC (= c(1 + a/2p)
R0 = Classical electron radius (= e2/4pe0mec2 = 2.879E-15 m)
RC = Compton radius (ħ/mc = c/wC = ħc/E = 3.8616E-13 m)
Rem = Electromagnetic radius (= ħ/mc2 = 5.2917E-11 m)
qP = Planck charge (= √(e2/a) = 1.876E-8 C = 11.6 e)
wp = precession frequency (= awC = 1.7588E11 rad/s)
wC = Compton frequency (= e/m = 7.763E26 rad/s)
Fe = Coulomb force (= qE = 1.547E03 N)
Fm = max. force @ RC (= m2c3/ħ = 0.212 N)
F = Fibonacci no. (= 1.61803…)

Background Quotes:
Everything will be beautiful when 1/137 is fixed. – Wolfgang Pauli
It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists
put this number on their wall and worry abut it. Immediately you would like to know where this number comes
from….Nobody knows. It’s one of the greatest mysteries of physics. – Richard Feynman
Many of today’s physicists might be less optimistic than their predecessors about finding a direct ‘formula’ for
a, or other constants of nature. – Roger Penrose
Alpha sets the scale of nature…it controls everything we see. – Frank Close
The bridge between the electron and other elementary particles is provided by the fine structure constant, a
~1/137, as manifested in the factor-of-137 spacings between the classical electron radius, electron Compton
radius, and the Bohr radius… – Malcolm H. MacGregor
The theoretical determination of the fine structure constant is certainly one of the most important of the
unsolved problems in modern physics. – Wolfgang Pauli
Only three constants are significant for star formation: the gravitational constant, the fine structure constant,
and a constant that governs nuclear reaction rates. – Ian Stewart
There are no arbitrary constants…Nature is so constructed that it is possible logically to lay down such strongly
determined laws which only contains logically deduced constants. – Albert Einstein

Quotes (cont):
It is one of the greatest damn mysteries of physics; a magic number that comes to us with no understanding
by man. – Richard P. Feynman
The fine structure constant is undoubtedly the most fundamental pure dimensionless number in all of physics.
It relates the basic constants of electromagnetism (the charge of the electron), relativity (the speed of light),
and quantum mechanics (Planck’s constant). – David J. Griffiths
Jung and Pauli’s mutual effort to discover the cosmic number or fine structure constant, which is a
fundamental physical constant dealing with electromagnetism, or, from a different perspective, could be
considered the philosopher’s stone of the mathematical universe. – Todd Hayen
There are considerable mysteries surrounding the strange values that Nature’s actual particles have for their
mass and charge. For example, there is the unexplained ‘fine structure constant’…governing the strength of
electromagnetic interactions. – Roger Penrose
…it should be remembered that the atomicity of electron charge has already found its expression in the
specific numerical value of the fine structure constant, a theoretical understanding of which is still missing
today. – Wolfgang Pauli
If alpha [the fine structure constant] were bigger than it actually is, we should not be able to distinguish
matter from ether [the vacuum, nothingness]. – Max Born
The day when we shall know exactly what electricity is will chronicle an event probably greater, more
important, than any other recorded in history the human race. – Nikola Tesla

Quotes (cont):
Let us begin with the fine-structure constant… The fine-structure constant is really the ratio of two natural
units or atoms of action….We obtain action when we multiply energy by time. …We are challenged to find a
unified theory of electric particles and radiation in which the electrostatic type of action and the quantum type
of action are traced to their source. – Arthur Stanley Eddington
The fact however that alpha has just its value 1/137 is certainly no chance but itself a law of nature. It is clear
that the explanation of this number must be the central problem of natural philosophy. – Max Born
QED [Quantum electrodynamics] reduces…”all of chemistry and most of physics,: to one basic interaction, the
fundamental coupling of the photon to electric charge. The strength of this coupling remains, however, as a
pure number, the so-called fine-structure constant, which is a parameter of QED that QED itself is powerless to
predict. – Frank Wilczek
A contradiction – free union of the condition of quantum theory with the corresponding prediction of field
theory is only possible in a [theory] that provides a particular value of Sommerfeld’s constant e2/ħc. –
Wolfgang Pauli
Can you explain the fine structure constant? No? So see you again when you have done it. – Paul A. Dirac
When I die, my first question to the devil will be “What is the meaning of the fine structure constant?” –
Wolfgang Pauli

Origin of electron charge
Electrons and positrons are fermions with quantum spin ½ and are created from
an energetic photon, a spin 1 boson, in a process known as pair production:
g → e- + e+ Pair production
The photon requires a mass energy of at least twice the rest mass energy of an
electron (0.511 MeV) equivalent to 2.5 x 1020 Hz for pair production to occur.
Collision of an electron and a positron result in production of a pair of photons
(gamma rays) of frequency 1.25 x 1020 Hz with oppositely directed momentum:
e- + e+ → g + g Annihilation
Electrons and positrons have opposite charge, but have the same rest mass.
Positrons are the antimatter counter part of electrons. Photons have zero
electric charge and zero rest mass. Quantum Electrodynamics (QED) is silent as
to explanation for creation of electric charge or origin of rest mass. However, we
do know something of the initial and final states, hence, we ought to be able to
deduce the likely conversion process. Rest mass and electric charge are
intimately related, i.e., electric charge does not arise independent of mass.

Origin of electron charge (cont)
Electric charge has mathematical similarities to topological charge and vortical
charge. Topological charge is expressed as a dimensionless quantum number
that takes on only one of a discrete set of values. Knots in a twisted rubber
band, for example, correspond to topological charge as a result of differential
rotation. The number of twists in a kink soliton is its topological charge. When
two kinks collide, the number twists remains unchanged. A kink and anti-link
annihilate on collision. Such properties are reminiscent of electrical charge.
Topological charge represents a twist angle q corresponding to the number of
turns N about a point (q = 2pN). The winding number n describes the
number
of loops around the origin and is defined as
n = ½p ∮ Gf∙dr
where f = phase of the complex field y = |y|eif.
closed loop open loop spin precession
qp
torsion defect - loop
closure failure
w wp
N turns

A vortex considered as a topological object may be represented as a wave
function
y(r) = eiq(r - r0) = r|y
Topological charges of vortices and skyrmions (mass currents) are similar to
electric charges and are conserved quantities. The creation of a vortex requires
the simultaneous creation of an anti-vortex. Pair annihilation results if the
vortices subsequently collide cancelling the charges. Collision of a kink and anti-
kink soliton wave likewise results in annihilation of topological charge.
twisted ribbon model
A
Single kink soliton
q
twist q = 2pN
where N = No. of turns
Origin of electron charge (cont)

e+
e-
g
Pair production g → e- + e+
Electron/Positron Pair Production
w
Photon
c
E
H
s S
Electron s
m
w
wp
E
H
S
Positron
s
m
E
H
w
wp
S
spin angular momentum quantum no.: 1 = + ½ + ½
electric charge: 0 = + 1 – 1 Coulombs
mass-energy: 1.02 MeV/c2 = + 0.511 MeV/c2 + 0.511 MeV/c2

Inverse fine structure constant a-1

Fine structure constant derivation
Charge results from loop closure failure due to precession

The inverse fine structure constant a-1 (= 137.035999…) represents the spin
precession whirl number q of the electron. The electron exhibits a slight
precession due to an imbalance of electrostatic Es0 (= e2/C) and magnetostatic
energy Em0 (= ½Li2). The ratio of electrostatic energy and magnetostatic energy
for an electron at rest equals
Es0/Em0 = 4.10312E-14 J/4.0951E-14 J = 1.023936
The Lagrangian (L = T – V) represents the difference between the kinetic energy
T and potential energy V. The Lagrangian interaction energy
L = Es0(1 + a/2p) – Em0(1 – a/2p) = ½m(E2 – c2B2) = 1.75414E-16 J
The kinetic energy portion of the energy difference per the Virial theorem
½ (Em0 – Es0)/(Emo + Es0) = ½ L/H = 0.001160342 ≃ a/2p
a/2p = 0.00116140973 is the Schwinger correction to the electron g-factor and
represents orbital precession.
Inverse fine structure constant a-1

Origin of electron mass
• Rest energy of an electron E = ħc/RC = m0c2 = mf where RC = Compton’s radius,
ħ = Planck’s constant h/2p. Rest mass m0 = kCe2/aRCc2 ≃ 9.10941E-31 kg.
Electromagnetic mass energy ≃ 0.51099906 MeV/c2. Rest mass results from a
slight spin precession of the electron due to an imbalance of electrostatic and
magnetostatic energy creating wave function interference obstructing energy
flow.
• Inertial mass m is a measure of resistance to acceleration. Force required to
induce motion is described by Newton’s 2nd law (F = ma). Mass represents
obstruction to energy flow and arises as a result of wave function interference.
EM wave nodes impede energy flow. Nodal points mark zones of constructive
interference occurring in Fibonacci intervals. Anti-nodal points represent non-
destructive interference occurring in Pythagorean harmonic intervals.
• Gravitational mass mg(= m0/G) is equivalent to inertial mass mi (= m0/g) as both
arise from motion into regions of increasing EM energy density. Relativistic mass
m = √((E/c2)2 – (p/c)2) = m0/g where p = momentum. Relativistic mass results
from a difference in EM wave energy of Lorentz-Doppler shifted forward and
backward propagating waves.

• Electron rest mass m = F/a = F/2c2·ldB·r̂ = ħc·RC = q·E/(2c·Dn·r)̂ = e/(wC + wp)
= eV/c2 = E/(E/B)2 = ħ/c·(lC(a-1)/q137 = 2(Es0 - Emo)/(E2 – c2B2) = ħk/v = E/c2
= kCe2/aRCc2 = 9.10941E-31 kg.
• Mass arises as a result of EM wave function interference (decoherence) due to a
difference in phase f and/or frequency n. Phase displacement Df = vg·p/c =
p·b
= c·p/vp where vg = group velocity and vp = phase velocity. Frequency
difference
Dn = a/2c where a = acceleration and c = velocity of light.
• de Broglie matter wave frequency ndB (= nR – nL = E/h = E/DE/Dn) is equal to
the
Lorentz-Doppler frequency shift Dn which is the frequency difference of incident
and reflected waves within a moving standing wave resonator. The de Broglie
wave length ldB = h/p = h/gm(b·c) = h/gm(Df·c/p) = c/ndB.
• Gravitational mass mg(= m0/G) is equivalent to inertial mass mi (= m0/g) as both
arise from fermionic resonator motion into regions of increasing EM energy
density. Relativistic mass m = √((E/c2)2 – (p/c)2) = m0/g where p = momentum.
Relativistic mass results from a difference in EM wave energy of Lorentz-
Origin of electron mass (cont)

Electron and positron creation

Pair production and annihilation
• Collision of an electron e- and a
positron e+ results in production
of two oppositely directed photons
(gamma rays).
• Minimum required photon energy
required for pair production:
E = 1.02 MeV = 2 mec2
• Annihilation of an electron and positron
each with rest mass energy of 0.511 MeV
produces two gamma ray photons with
opposite momentum.
• A high energy photon in the vicinity
of an intense electric field of atomic
nucleus can decay into an electron e-
and a positron e+.

Photon & Electron geometry
Photon -
Traveling wave of
helical geometry
Electron –
Closed-loop
standing wave
of toroidal
geometry
Spin 1 boson
Spin ½ fermion

Helical photon model
• The contravariant vector T is tangent to the parametized speed curve
described by the Frenet-Serret equations.

Freely-propagating photon
• Photons are transverse EM excitations of the Planck vacuum with quantized energy
E = hn= ħl. Energy flow is in the direction of the Poynting vector S (= E x H).

Toroidal electron model
• Toroidal electron formed by a
high energy photon topologically
confined inside the Compton
radius.
• Propagation of the rotating spin
wave describes a current loop
equal to ½ of Compton radius.
• Charge path rotation generates
toroidal swept volume.
• Electric charge results from a
slight spin precession as
measured by the fine structure
constant owing to an imbalance
of electro- and magnetostatic
energy. Rest mass arises a result
of wave interference due to this
internal precession.

Electron model cross-section
• Toroidal circumference equals Compton wavelength lC.
• Electron Compton radius RC = lC/2p =√(E/mw2) = aa0 = c/wC
• Electron rest mass m = ħ/RCc = kce2/aRCc2 = E/c2 = E/(E/B)2

Electron/positron configuration
• Electron depicted as a
precessing epitrochoid
charge path composed of
two orthogonal spinors of
2:1 rotary octave
• Spin ratio of Compton
angular frequency wC and
Zitterbewegung frequency
wzbw (= 2wC) corresponds
to observed spin ½.
• Electric charge arises as a
result of a slight precession
of angular frequency we/m.

Electron spin precession
• Electron spin precession we/m
is due primarily to imbalance
of electrostatic and magnetostatic
energy resulting in an eccentric
whirl orbit of the charge path
about the spin axis.
• Precession follows a zoom-orbit
whirl with a periapsis advance q137
that is a function of the fine
structure constant a and the
Compton radius RC.
• Synchronization occurs every a-1
revolutions. Electric charge is a
result of a slight spin precession.
• Electron mass me = e/(wC + wp)
= e/wC(1 + a/2p) ≃ e/wC.

Electron spin angular momentum
s = ½ ħ where ħ = 1.0545E-31 J·s
Electron charge e = m(wC + wp)
= 7.0719E-10 kg·rad/s = 1.6021E-19 Coul
q137 = 0.04458 rad
0 p 2p 3/2p 4p rad
q137
Compton frequency wC = c/RC = mc2/ħ = 7.7634E26 rad/s
torsion defect:
loop closure
failure
Precession frequency wp = we/m = e/m = 1.7588E11 rad/s
Electron spin precession
y
x
lC
wC
RC
c
1 cycle rotation = 720 o (spin quantum no. s = ½)
Compton radius RC = lC/2p = ħ/mc = 3.8616E-13 m
Precession angle q137 = (lC/a-1)/RC  0.04458 rad = 2.62o
Rest energy E = m0c2 = ħc/RC = Eso + Emo = 8.8187E14 J
Electrostatic energy Eso = e2/2C = 4.103212E-14 J
Magnetostatic energy Emo = LI2/2 = 4.08412E-14 J
Electron rest mass m = q+E/a = e/(wC + wp) = eV/c2
= ħ/(RC·c) = ħ/c·(lC(a-1)/q137 = E/f
= kCe2/aRCc2 = hn/c2 = 9.10941E-31 kg
Inverse fine structure constant
a-1 = 1/a = ħc/kCe2  137.0359
light speed
circle
y = y+
y-
y
Reduced fine structure const. a/2p = 0.0011641
Average energy imbalance
= ½(Em0 - Eso)/(Emo + Es0) = 0.001160342  a/2p
Electron spin precession wave interference
Rest mass results from internal wave interference due to precession

Electron toroidal electric field
• Electrostatic E-field of an
electron is shown time
averaged over one rotation
period.
• For a positron, the electric
flux is directed radially
inward.
• At distances greater than
the Compton radius RC,
the electric flux distribution
for an electron at rest is
spherically symmetric
equivalent to a point charge.

Electron as a rotating spin wave
• The electron continuously
generates an external dipolar
spin wave in the form of a
Archimedean spiral rotating
at the Compton frequency fC
(= 1.236E20 Hz).
• The electron acts as a spinning
dipole antenna with virtual
radiation of a pair of entangled
photon wavetrains emitted
along the spin axis.
• The electron consists of a closed
loop rotating internal standing
wave and an external open-ended
dipolar spin wave

Electric field of an oscillating electron
• Oscillation of the electron
at frequencies less than the
Compton frequency fC in
response to excitation by an
external EM field results in
generation of observed EM
waves in resonance with
the imposed frequency.
• Entangled states represent
different points on the same
wavefront.
• Acceleration over time Dt
creates a local flux field
distortion with the farfield
flux pointing in direction of
the retarded initial starting
position.

Electron toroidal magnetic field
• Magnetostatic B-field of an
electron is shown time
averaged over one rotation
period.
• External magnetic field is
toroidal while the internal
field is poloidal.
• Magnetic flux is concentrated
in the central region with
increased potential magnetic
energy.

Electron represented schematically
as a primitive electrical machine

Electron energy storage
• During acceleration of an electron, kinetic energy is stored in the magnetic field.
• The radiation field dissipates during and subsequent to electron deceleration as
the electromagnetic field regains symmetry.

Electrostatic & Magnetostatic energy
vs. Velocity ratio b
Variation of electron energy as a function of velocity ratio b (= v/c).
The fine structure constant a arises as a result of imbalance of electrostatic
and magnetostatic energy of the electron inducing internal spin precession.

Electromagnetic energy E vs. Lorentz factor g
After Bergman
The Lorentz factor g is inversely proportional to the Lorentz contraction g.
g = 1/√(1 – v2/c2) = 1/√(1 – be) = 1/g
Electromagnetic energy of an electron as a function of Lorentz factor g.

Electron Compton radius RC vs. Lorentz factor g
• Absorption of energy causes electrons to contract in size increasing the
wave function curvature, kinetic energy and volumetric energy density.
Spin angular momentum is conserved - spin quantum no. remains constant.
Variation in electron radius as a function of Lorentz factor g (= 1/√(1 – be)

Electron Compton radius RC vs. Velocity ratio b
Variation in electron radius as a function of velocity ratio b (= v/c)
• The Compton radius reflects an equilibrium between torsion and the
gravitomagnetic field. Contraction in radius occurs as spin remains
constant and torsion decreases accordingly.

Electron mass energy MeV/c2 vs. Velocity ratio b
Relativistic increase in electron mass energy as a function of velocity ratio b (= v/c)

Electron Inductance L & Capacitance C
vs. Velocity ratio b
Relativistic variation in electron inductance L and capacitance C
as a function of velocity ratio b (= v/c = DOF/p = r/g)

Symmetry breaking
• Mass has been usually associated with curvature of a potential and attributed in the
Standard Model as due to U(1) spontaneous symmetry breaking due to interaction with a
hypothetical all-pervading spin-zero Higgs field f of unknown source with undefined
free prameters which is said to give fermions mass by an unknown mechanism.
• In the electron model shown, it is asserted that mass arises as a result of self-interaction
due to precession-induced wave function interference. Symmetry breaking results from
an imbalance of electrostatic Es0 and magnetostatic energy Em0 which is responsible for
generating electrical charge and is the origin of the fine structure constant a. Mass
represents impedance to energy, i.e., a resistance to change in frequency.
• Electron rest mass m = kCe2/aRCc2 where kC = Coulomb constant (= 1/4pe0), e = electric
charge, inverse fine structure constant = a-1, Compton radius = RC, c = velocity of light.
Mass m is thus proportional to curvature k = 1/RC, 1/c2 (= mass-to-energy conversion
constant), inverse fine structure constant 1/a (= whirl no. q) and square of the potential
energy U (= kCe2/c2).
• Minimization of imbalance of electrostatic energy Es0 (= e2/2C) and electromagnetic energy
Em0 (= LI2/2) appears to offer the technological possibility of reduction in inertial mass by
reduction of fermionic wave function interference, i.e., spin precession.

Electron wave-function eigenstates in a deep
harmonic oscillator 2D potential well
• Electron represented as a resonant
spin density wave confined in an
oscillating deep potential well in a
quantum vacuum.
• Zitterbewegung corresponds to the
motion of the center of charge
around the center of mass with a
frequency twice the Compton
frequency.
• Electron rest mass results from
self-interaction, i.e., wave inter-
ference due to internal precession,
not interaction with an ill-defined
all-pervading hypothetical Higgs
field.

Quantum electrodynamics (QED) diagrams

Electron/positron pair production
Electron Compton wavelength, zitterbewegung wavelength, and de Broglie
wavelength compared to the wavelength of an energetic photon required
for pair production of an electron e- and positron e+.

Energy diagram
electron/positron pair production

Electron Coulombic repulsion
• Maximum Coulomb repulsive
force between electrons occurs
at closest proximity equal to a
separation distance at Compton’s
radius RC.
• The radiated EM wavefronts are in
the form of Archimedean spiral
forms. Two electrons on approach
are repelled by constructive EM
wavefront interference.
• Positron spin waves rotate in a
direction opposite to electrons.
Electron and positron interaction
give rise to destructive interference.

Spin wave precession
• Electric charge is intrinsic to matter and exhibits similarities to topological
and vortical charge.
• Electric charge of the electron has dimensions of spin angular momentum
and appears to be the result of a slight precession equal to the inverse
fine structure constant a-1.

Elementary Particles of Matter
Mass, charge and spin characteristics of fundamental particles and anti-particles

Electric and color charge symmetry
• When there is symmetry,
there is conserved charge.
• Symmetry alone does not
provide a dynamical origin
of charge or define underlying
fundamental dimensionality
• Electric charge has pronounced
mathematical similarities to
topological charge and vortical
chrge providing a strong clue
as to origin.

Electric charge vs. topological charge
• Geometrical relation of electric charge (e-, e+) to topological charge F
is illustrated in the form of a Tusci couple (2-cusp hypocycloid) which
corresponds to Special Unitary Group SU(2)

Spinor representation of ½ spin characteristic
Spinor examples of 720 degree rotation to return to initial orientation
involving two rotational frequencies differing by a factor of 2.

Electron/Positron Pair Production
• Electron and positron formation from an energetic photon is attributed to
Faraday rotation and Levi-Civita effects in an intense EM field of an atomic
nucleus.
• Transformation of a photon into an electron and positron involves conversion
of linear momentum into rotary momentum to absorb energy of collision.

Neutral Pi-meson (Pion)
• Neutral Pion p0 consists of a
spin 0 neutral pi-meson
composed of positron-electron
pair (Sternglass model)
• The positron and electron pair
each have spin angular
momentum oriented either
parallel or anti-parallel to each
other.
• The orbital angular momentum
is equal to twice the spin
angular momentum (L = ħ). A
spin 0 neutral pion has a life-
time of ~0.83E-16 sec and can
decay into gamma rays.
• Binding energy is decreased
when magnetic moments are
parallel due to mutual repulsion.

Positively charged Mu-meson (Muon)
• Positive Muon m+ consists of a
positron-electron pair and orbital
positron (Sternglass model)
• Positron e+ is at rest relative to
the precessing frame KP of the
central pair system consisting
of a spin 1 neutral pi-meson p0
1.

Positively charged Pi-meson (Pion)
• Positive pion p+ consisting of
a positron-electron pair and
orbital positron (Sternglass
model)
• A positron e+ is in orbital
motion relative to the
precessing frame Kp of a
central pair system consisting
of a spin 1 neutral pi-meson
p0
1.

Negatively charged Tau-meson (Tauon)
• Negative Tauon t- consisting of
a positron-electron pair and
orbital electron (Sternglass
model).
• Electron e- is in orbital motion
relative to the precessing
frame Kp of the central pair
system consisting of a spin 1
neutral pi-meson p0
1.

Electron-positron coaxial wave interference
• Coaxial coupling of an e-e+ pair with
aligned spins as a hypothetical quark
model with a massless spin 1 field.
• A charge screen formed by depolar-
ized Planck mass dipoles prevents
Coulombic attraction.
• The electron and positron oscillate
along the spin axis alternating
between a state where charge
screening is effective at close
distance and further out where
charge screening is ineffective
thus exhibiting asymptotic freedom.

Quantum Chromodynamic models
Quantum chromodynamics (QCD) representations of protons and
neutrons shown as quark composites

Dimensionless coupling constants
Coupling
constant
Symbol Relative
Strength
n-gon
1/n
Precession
angle
(radians)
Strong as 1 1 2p
Electromagnetic a 1/137 137 0.01459
Weak aw 3 x 10-7 3.33 x 106 6 x 10-7
Gravity aG 5.9 x 10-39 1.69 x 1038 1.7518 x 10-45
• Fine structure constant a = e2/(4pe0)ħc = eP
2 = kce2/ħc = Z0/Ze ≃ 0.0072973525693…
• Inve rse fine structure constant a-1 = whirl no. q = lC/Se = 137.0359…
• Reduced fine structure constant a/2p = ½(Es0 – Em0)/(Es0 + Em0) = 0.0011614…
• Electric charge qe = E/V = 1.6021E-19 Coulomb = me/we = 7.0719E-10 kg·rad/s
• Planck charge qP = mP/wP = √(4pe0ħc = √(e2/a = 11.70943qe
• Gravitational coupling constant ag = Gme
2/ħc = (me/mP)2 = tP/wC)2. The spin 2 graviton gg*
consists of momentary superposition of a spin 1 photon g and counterpropagating spin 1
phase conjugate g* each with zero charge. Hence, gg* has no effect on the ag constant.

Proton model
• A proton composed of
electrons and positrons
equivalent to QCD quark
representation.
• Proton absorption of an
antineutrino results in
transformation into a
neutron with emission of
a positron and neutrino
in inverse beta decay.
• The bulk of the proton’s mass
is due to kinetic energy of
component quarks.

Gravitational force on electron
Increase of kinetic energy of a falling mass results froman influx of gravitational
energy via the gravitational Poynting vector Sg. In free fall, the acceleration of
gravity g and associated frequency difference Dn is equal to zero.

Electric flux lines
• Faraday electric flux lines fE are
postulated to be an effect of
synchronous alignment of positive
and negative Planck mass dipoles
of the quantum vacuum.
• Alignment results in tension along
the flux lines due to attraction of
positive and negative masses and
compression perpendicular to the
flux lines.
• Electric field intensity E is a function
of the product of the Planck electric
dipole moment m0P and the Planck
mass mP.

Magnetic flux lines
• Magnetic flux lines fB are interpreted
as vortex filaments of rotating Planck
mass dipoles. Magnetic field lines
are the result of spin axis alignment
of multiple dipoles.
• Magnetic field intensity H is a measure
of the vortex strength of entrained
dipoles
• Photons and electrons are spin waves
in the Planck quantum vacuum
composed of positive and negative
Planck masses. Photons are traveling
waves. Electrons are standing waves.

Electron vacuum resonance
Electron and Planck vacuum resonance characterized by lP /lC ratio. Electron charge e
results from a slight precession with whirl no. equal inverse fine structure constant a-1.
Electron rest mass m0 results from wavefunction interference due to this precession.

Summary Remarks
• Electric charge has mathematical similarities to topological charge and vortical
charge providing a significant clue as to the origin of electric charge. A viable electron
model must account for pair production, annihilation and creation of electric charge.
• The electron not only spins but has a slight precession as evidenced by the fine
structure constant and measured physical observables. The whirl no. q (= ħc/kCe2
= lC/Se) is equal to the inverse fine structure constant a-1 (≃137.03599967…).
• Imbalance of the electron’s electrostatic and magnetostatic energy results in spin
precession corresponding to a torsion defect (loop closure failure). Reduced fine
structure constant a/2p = ½ ((Es0 – Em0)/(Es0 + Em0)) ≃ 0.0011614 0…
• Electric charge Q (= 1.6021E-19 C = me(wC + wp) = 7.0719E-10 kg·rad/sec) arises as a
result of a slight spin precession of the electron where Compton angular frequency wC
(= 7.7634E20 kg·rad/sec) and spin precession wp (= e/m = 1.758882E11 kg·rad/sec) .
• Electron rest mass (me) is a result of internal quantum wave interference due to spin
precession (= kCe2/aRCc2 = 9.1094E-31 kg). Mass represents impedance of energy
flow.
• The fine structure constant, electron charge, and rest mass are intimately related and
may be understood as quantum wave interference effects due to internal electron spin
precession without recourse to putative Higgs field, fanciful string theory or the like.

Book Details:
Author: Larry J. Reed
Pages: 724
Publisher: BookLocker
Language: English
ISBN: 978-1-63492-964-6 paperback
Publication date: 2019-01-13
QuantumWaveMechanics

Abstract
A comprehensive description of the nature of light, electricity and gravity is provided in
terms of quantum wave mechanics. Detailed models include the photon as a travelling
electromagnetic wave and the electron as a closed loop standing wave formed by a
confined photon. An electron is modeled as a torus generated by a spinning Hopf link
as a result of an imbalance of electrostatic and magnetostatic energy. Electric charge is a
manifestation of a slight precession characterized by the fine structure constant. The
physical vacuum as a polarizable medium enables wave propagation and appears
ultimately to be quantized at the Planck scale. Standing wave transformations for objects
in motion are reviewed and Lorentz Doppler effects compared. The mechanism for
generation De Broglie matter waves for objects in motion is depicted including the inverse
effect of induced motion of an object by synthesis of contracted moving standing waves.
Gravity is viewed as a frequency synchronization interaction between coupled mass
oscillators. The acceleration of gravity is described by a spectral energy density gradient.
Antigravity corresponds an inversion of the naturally occurring energy density gradient.
Gravitons are shown to be phase conjugate photons. The metric of curved spacetime
corresponds to the electromagnetic wave front interference node metric. Hence, the
gravitational field becomes quantized.

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