Pair production and annihilation • Collision of an electron e- and a • positron e+ results in production • of two oppositely directed photons • (gamma rays). • A high energy photon in the vicinity • of an atomic nucleus can decay into • an electron e- and a positron e+.
Electron model cross-section Chracteristic dimensions • Toroidal circumference equals Compton wavelength lC. • Electron Compton radius equals lC/2p
Electron ring 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.
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.
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 primative 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)
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 – b2) = 1/g
Electron Compton radius RC vs. Lorentz factor g Variation in electron radius as a function of Lorentz factor g (= 1/√(1 – b2) • Absorption of energy causes electrons to contract in size increasing the • wave function curvature, kinetic energy and volumetric energy density.
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 = Df/p = r/g)
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/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/positron production from an energetic photon
Electron Coulombic repulsion • Maximum Coulomb repulsive • force between electrons occurs • at closest proximity equal to a • separation distance ar Compton’s • radius RC. • The radiated EM wavefronts are in • the form of 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.
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 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.
Quark color charge Twist ribbon represention of quark color charge interactions and equivalent 3-phase circuit
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 p01.
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 • p01.
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 p01.
Gluon field Fresnel zone pattern • In-phase and out-phase gluon • field Fresnel zone patterns • with Airy diffraction cross- • section. • Quark separation in a proton • with Compton radius RCp of • 2.1031E-16 m suggest a gluon • field with a minimum distance • of ~0.33E-15 m or ~1.56 RCp.
Quantum Chromodynamic models Quantum chromodynamics (QCD) representations of protons and neutrons shown as quark composites
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 In free fall, the acceleration of gravity and associated frequency difference is equal to zero
Quantum Wave Mechanics 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 occuring 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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