Fine structure constant

1. Fine structure constant a Electron

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

3. Contents • Introduction • Definition • Interpretations • Background • Topological charge • Origin of electric charge • Electron/Positron pair production • Electron model • Fine structure constant derivation • Inverse fine structure constant • Origin of electron rest mass • Relativistic effects • Color charge symmetry • Composite particles models • Electric and magnetic field line structure • Summary remarks

4. Fine structure constant a • 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?

5. Fine structure constanta 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.

6. Fine structure constanta 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 = mP2(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]

7. Fine structure constant interpretations 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 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…)

8. Fine structure constanta • 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

9. Fine structure constanta 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

10. Fine structure constanta • 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

11. 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.

12. 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. qp torsion defect - loop closure failure N turns w wp closed loop spin precession open loop

13. Origin of electron charge (cont) 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 twist q = 2pN where N = No. of turns q A Single kink soliton

14. Electron/Positron Pair Production Pair production g→ e- + e+ s Electron wp w H e+ E S m g Photon w e- s S wp Positron S E H m 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 w s E H c

15. Inverse fine structure constant a-1

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

17. Inverse fine structure constant a-1 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.

18. 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.

19. Origin of electron mass (cont) • 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- • Doppler shifted forward and backward propagating waves.

20. Electron and positron creation

21. 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+.

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

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

24. 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).

25. 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.

26. 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

27. 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.

28. 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.

29. Electron spin precession wave interference Electron spin precession y+ y- Compton frequency wC = c/RC = mc2/ħ = 7.7634E26 rad/s y = Precession frequency wp = we/m = e/m = 1.7588E11 rad/s torsion defect: loop closure failure y c light speed circle RC y q137 lC x wC 1 cycle rotation = 720 o (spin quantum no. s = ½) Electron spin angular momentum s = ½ ħ where ħ = 1.0545E-31 J·s 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 q137= 0.04458 rad Electron charge e = m(wC + wp) = 7.0719E-10kg·rad/s = 1.6021E-19 Coul Inverse fine structure constant a-1 = 1/a =ħc/kCe2 137.0359 Reduced fine structure const. a/2p = 0.0011641 Average energy imbalance = ½(Em0- Eso)/(Emo + Es0) = 0.001160342  a/2p 0 p 2p 3/2p 4p rad Rest mass results from internal wave interference due to precession

30. 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.

31. 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

32. 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.

33. 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.

34. Electron represented schematically as a primitive electrical machine

35. 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.

36. 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.

37. Electromagnetic energy E vs. Lorentz factor g Electromagnetic energy of an electron as a function of 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

38. Electron Compton radius RC vs. Lorentz factor g Variation in electron radius as a function of Lorentz factor g (= 1/√(1 – be) • 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.

39. 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.

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

41. 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)

42. 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.

43. 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.

44. Quantum electrodynamics (QED) diagrams

45. 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+.

46. Energy diagram electron/positron pair production

47. 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.

48. 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.

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

50. 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.