- Retired aerospace engineer. Resides Los Angeles, CA.
Author: Quantum Wave Mechanics
ISBN 978-1-63492-964-6
.edit
Einstein's General Theory of Relativity is described in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to apparent space contraction... more
Einstein's General Theory of Relativity is described in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to apparent space contraction as a result of an energy density gradient. Gravitational attraction in an optical theory of gravity arises as a result of a polarizable vacuum (PV) with a variable refractive index. The gravitational potential well and EM energy density hill for a central mass object is depicted in tangent space. The acceleration of gravity is a measure of the spectral energy density gradient. Mass in motion generates a mass current with an associated gravitomagnetic and cogravitation field.
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A photon is a self-sustaining electromagnetic traveling spin wave disturbance in a polarizble vacuum. A photon is described as a spin 1 boson with helical geometry. A graviton represents a momentary resonance superposition of a photon... more
A photon is a self-sustaining electromagnetic traveling spin wave disturbance in a polarizble vacuum. A photon is described as a spin 1 boson with helical geometry. A graviton represents a momentary resonance superposition of a photon and a counter-propagating phase conjugate photon with additive spins. A graviton is described as a spin 2 boson with helicoid geometry with net zero linear momentum. Phase conjugate reflection occurs at EM wavefront interference anti-nodes at Fresnel zone boundaries.
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Inertial mass may be understood as the interaction of electromagnetic quantum fields. The confinement of EM radiation, consisting of massless photons, in a fixed reference frame of a standing wave resonance, acquires rest mass and... more
Inertial mass may be understood as the interaction of electromagnetic quantum fields. The confinement of EM radiation, consisting of massless photons, in a fixed reference frame of a standing wave resonance, acquires rest mass and inertia. Traveling EM waves such as photons represent freely propagating energy. Standing waves such as electron represent stored energy. Matter in motion with respect to an inertial observer exhibits Lorentz contracted moving standing waves, i.e. de Broglie matter waves. Rest mass and inertia of fermions result from confinement of electromagnetic radiation.
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Traveling EM waves represent freely propagating energy. Standing waves represent stored energy. Light is a traveling spin wave disturbance in a polarizable vacuum. Matter consists of standing wave resonances. Matter in motion with... more
Traveling EM waves represent freely propagating energy. Standing waves represent stored energy. Light is a traveling spin wave disturbance in a polarizable vacuum. Matter consists of standing wave resonances. Matter in motion with represent to an inertial observer exhibits internal Lorentz contracted moving standing waves (de Broglie matter waves). Rest mass and inertia result from confinement of electromagnetic radiation.
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An electron is shown modeled as a closed-loop standing spin wave of toroidal geometry. The charge path is in the form of a rotating Hopf link (simplest form of knot) generating a toroidal swept surface with circumference equal to the... more
An electron is shown modeled as a closed-loop standing spin wave of toroidal geometry. The charge path is in the form of a rotating Hopf link (simplest form of knot) generating a toroidal swept surface with circumference equal to the Compton wavelength. The electron is depicted as a precessing epitrochoid charge path composed of two orthogonal spinors with toroidal and poliodal current loop component of 2:1 rotary octave. The spin ratio of the Compton angular frequency and the zitterbewegung angular frequency corresponds to the observed 1.2 spin. Electric charge arises as a result of a slight precession due to an imbalance of electrostatic and magnetostatic energy equal to the inverse fine structure constant
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An electron is shown modeled as a closed-loop, standing spin wave of toroidal geometry. The charge path is in the form of a rotating Hopf link (simplest form of knot) generating a toroidal swept surface with circumference equal to the... more
An electron is shown modeled as a closed-loop, standing spin wave of toroidal geometry. The charge path is in the form of a rotating Hopf link (simplest form of knot) generating a toroidal swept surface with circumference equal to the Compton wavelength. The electron is depicted as a precessing epitrochoid charge path composed of two orthogonal spinors with toroidal and poloidal current loop components of 2:1 rotary octave. The spin ratio of the Compton angular frequency and the zitterbewegung angular frequency corresponds to the observed 1/2 spin. Electric charge arises a a result of a slight spin precession due to an imbalance of electrostatic and magnetostatic energy equal to the inverse fine structure constant.
Electromagnetic resonant wave interactions in a phased-locked resonator at rest and in motion are compared. The origin of mass and inertia as a standing wave interaction in a phased-locked cavity as demonstrated in work by Jennison is... more
Electromagnetic resonant wave interactions in a phased-locked resonator at rest and in motion are compared. The origin of mass and inertia as a standing wave interaction in a phased-locked cavity as demonstrated in work by Jennison is reviewed and phase relationships illustrated. For matter (composed of resonant EM standing waves) in motion, the Lorentz contraction is interpreted as a physical wavelength compression due to variation in EM field energy density as measured by vacuum refractive index KPV. Dipole radiation emitted from a phase-locked resonator in motion is described. A graphical representation of Ivanov-LaFreniere standing wave transformations is shown. Experimental possibilities for potential phase conjugate wave phase-locked resonator development are discussed.
Keywords: electromagnetic (EM), standing wave, photon, phase-locked resonator, confined light, Lorentz, mass, frequency, oscillator , inertia, phase conjugate waves
Keywords: electromagnetic (EM), standing wave, photon, phase-locked resonator, confined light, Lorentz, mass, frequency, oscillator , inertia, phase conjugate waves
Research Interests:
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... more
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 modelled 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. 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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In 1856, Maxwell showed that the induced electric field E and can be expressed in terms of the magnetic vector potential A and deduced that the vector potential A represents a potential electromagnetic momentum per unit charge. As defined... more
In 1856, Maxwell showed that the induced electric field E and can be expressed in terms of the magnetic vector potential A and deduced that the vector potential A represents a potential electromagnetic momentum per unit charge. As defined by Jefimenko an electric field Ek generated by motion of time-variable currents results in an induced electrokinetic force Fk on nearby electrical charges. The induced electrokinetic force Fk is proportional to the induced electric field (= qEk ). The induced current caused by the electrokinetic field is opposite to the inducing current when the current is increasing (positive time derivative) and in the same direction when the current is decreasing (negative time derivative). Jefimenko notes that Faraday induction is not an electromagnetic phenomena – induced currents are not caused by changing magnetic fields, but by an electrokinetic field created by changing electric currents. The induced electrokinetic field Ek provides an explanation for Lenz’s law of electromagnetic induction and Maxwell’s displacement current within capacitors.
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A freely-propagating photon corresponds to balanced curvature and torsion reflective of a balance of electrostatic and magnetic energy resulting in straight line motion. When a photon is slowed during passage in an optically dense... more
A freely-propagating photon corresponds to balanced curvature and torsion reflective of a balance of electrostatic and magnetic energy resulting in straight line motion. When a photon is slowed during passage in an optically dense medium, the photon acquires an effective mass which corresponds to decreased torsion. The decreased turn height H corresponds to a flatter helix angle. With smaller H, the longitudinal magnetic field decreases. The curvature increases as the radius is reduced as a result of conservation of energy and angular momentum. If H is much smaller than radius R, the curvature k increases and approaches 1/R. Increased curvature is equivalent to increased mass.
In the conversion of an energetic photon into an electron and positron in pair production, the helix is postulated to be transformed into two tori with each torus of revolution generated by rotation of a Hopf knot (the simplest knot possible), in effect closing the helix end-to-end. The confined electron topology reflects an imbalance of electrostatic and magnetic energy due to the combination of the toroidal and poloidal magnetic fields.
In the conversion of an energetic photon into an electron and positron in pair production, the helix is postulated to be transformed into two tori with each torus of revolution generated by rotation of a Hopf knot (the simplest knot possible), in effect closing the helix end-to-end. The confined electron topology reflects an imbalance of electrostatic and magnetic energy due to the combination of the toroidal and poloidal magnetic fields.
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Light slows down in a medium due to photon’s EM field interaction with the EM energy density of the medium. Wavefront curvature is associated with light deflection and gravitational lensing. Curvature is induced by variation in the vacuum... more
Light slows down in a medium due to photon’s EM field interaction with the EM energy density of the medium. Wavefront curvature is associated with light deflection and gravitational lensing. Curvature is induced by variation in the vacuum refractive index KPV locally altering the velocity of light resulting in wavefront retardation in regions of increased energy intensity. A general illustration of curved manifolds of a gravitational potential well and vacuum refractive index hill are depicted. In gravity-free region, Minkowski space is isomorphic to Euclidean tangent space. In a gravitational field, the energy density varies resulting in curved manifold parameter spaces while the tangent space of spacetime remains flat. Unlike embedding diagrams associated with illustration of spacetime curvature in GR, spacetime remains Euclidean while variables such as EM nodal distances and frequencies represented in tangent space exhibit dilation, contraction and curvature with an established physical causal means and demonstrable effect.
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Jennison and Drinkwater have shown that a standing EM wave trapped in a phase-locked cavity exhibits rest mass and intrinsic inertia and classically derived Newton’s Second Law (F = ma) and the Einstein relation (E = mc^2). For a... more
Jennison and Drinkwater have shown that a standing EM wave trapped in a phase-locked cavity exhibits rest mass and intrinsic inertia and classically derived Newton’s Second Law (F = ma) and the Einstein relation (E = mc^2). For a free-floating wave system consisting of two counter-propagating travelling waves in a phase-locked resonant cavity, application of an external force results in an imbalance of radiation pressure of Doppler-shifted waves causing the wave system to move as a whole in a stepwise series of velocity increments. Upon application of an external force to the motive boundary, the blue-shifted incident wave exerts an excess radiation pressure on the reflecting wall and the red-shifted reflected wave exerts a decreased radiation pressure on the motive wall provided the force was applied for an interval equal to or greater than the return of the reflected wave.
A freely-propagating photon represents a travelling wave. An electron represents a confined high energy photon trapped within a fixed reference frame. An electron at rest with respect to an observer is equivalent to a standing wave confined within a cavity resonator. An electron in motion is equivalent to a standing wave within a Lorentz contracted moving resonator. For a freely-propagating photon in vacuo, the photon travelling wave has no rest mass as there is no fixed reference frame and no defined position operator. In a standing wave resonator, the incident and reflected travelling waves combine to produce a standing wave with cancellation of momentum for a resonator at rest. Motion is the result of difference between the forward and backward matter wavelengths according to the Lorentz Doppler effect and a resulting wave energy imbalance. Once in motion, a phase-locked resonator acquires a relativistic increase in mass m and corresponding increase in energy E.
A freely-propagating photon represents a travelling wave. An electron represents a confined high energy photon trapped within a fixed reference frame. An electron at rest with respect to an observer is equivalent to a standing wave confined within a cavity resonator. An electron in motion is equivalent to a standing wave within a Lorentz contracted moving resonator. For a freely-propagating photon in vacuo, the photon travelling wave has no rest mass as there is no fixed reference frame and no defined position operator. In a standing wave resonator, the incident and reflected travelling waves combine to produce a standing wave with cancellation of momentum for a resonator at rest. Motion is the result of difference between the forward and backward matter wavelengths according to the Lorentz Doppler effect and a resulting wave energy imbalance. Once in motion, a phase-locked resonator acquires a relativistic increase in mass m and corresponding increase in energy E.
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The E and H wavefront vectors are in-phase far from the source dipole oscillator. Within the evanescent near field region, the E and H vectors are out-of-phase with a longitudinal polarization component. In the midrange or Fresnel... more
The E and H wavefront vectors are in-phase far from the source dipole oscillator. Within the evanescent near field region, the E and H vectors are out-of-phase with a longitudinal polarization component. In the midrange or Fresnel region, the E and H vectors are partially in-phase. In the near field region, dipole field effects are prominent and drop off as 1/r^2 whereas EM field drops off as 1/r. Induction term decays as 1/r2 and electrostatic field decays as 1/r^3 and rapidly decay beyond the evanescent region. The wave phase velocity is superluminal (vph > c) whereas the group velocity is subluminal (vg < c).
The radiation field emitted from a stationary dipole antenna and a rotating dipole antenna are shown illustrating the phase relationship of the electric field intensity E and magnetic field intensity H as a function of distance from the dipole antenna. An electron may be regarded as a rotating dipole antenna continuously emitting and absorbing pairs of entangled virtual photons. The emission and absorption of photons by separated electrons may be represented as points on a Bloch sphere. The degree of entanglement corresponds to the distance between points. Entangled quantum states represents points lying on the same wavefront, hence, their correlation is causally connected. Non-entangled states are isolated in time or space and are non-causally connected. As a result, instantaneous, non-local entanglement in which action on one particle instantly influences another particle by superluminal ‘spooky action at a distance’ or pilot wave interaction is a nonphysical illusion.
The radiation field emitted from a stationary dipole antenna and a rotating dipole antenna are shown illustrating the phase relationship of the electric field intensity E and magnetic field intensity H as a function of distance from the dipole antenna. An electron may be regarded as a rotating dipole antenna continuously emitting and absorbing pairs of entangled virtual photons. The emission and absorption of photons by separated electrons may be represented as points on a Bloch sphere. The degree of entanglement corresponds to the distance between points. Entangled quantum states represents points lying on the same wavefront, hence, their correlation is causally connected. Non-entangled states are isolated in time or space and are non-causally connected. As a result, instantaneous, non-local entanglement in which action on one particle instantly influences another particle by superluminal ‘spooky action at a distance’ or pilot wave interaction is a nonphysical illusion.
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Dielectrophoretic and magnetophoretic force effects result in object motion with respect to a surrounding medium due to a nonuniform field gradient. Likewise, nonuniform gravitational fields result in object motion in the direction of... more
Dielectrophoretic and magnetophoretic force effects result in object motion with respect to a surrounding medium due to a nonuniform field gradient. Likewise, nonuniform gravitational fields result in object motion in the direction of the field gradient. Phase-displacement and space-displacement gives rise to travelling waves. Electromagnetic levitation effects can be readily produced by nonuniform, travelling wave EM fields by multi-phase electromagnetic induction. Repulsive and attractive forces arise with changes in scale (symmetry breaking) due to phase and frequency shift. Nonuniform potential energy fields give rise to force fields acting on immersed objects in the direction of the maximum scalar field gradient denoted by the Poisson relation.
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Ivanov and LaFreniere have shown that standing waves undergo wavelength (nodal) contraction in the direction of motion of the resonator. An object in motion relative to an observer undergoes a Lorentz contraction (wavelength compression)... more
Ivanov and LaFreniere have shown that standing waves undergo wavelength (nodal) contraction in the direction of motion of the resonator. An object in motion relative to an observer undergoes a Lorentz contraction (wavelength compression) and a Lorentz-Doppler shift in frequency (reduction). A comparison of the Lorentz-Fitzgerald transformation (applied to spacetime) and the Ivanov-LaFreniere transformations (applied to wavelength) are summarized. A mass object is equivalent to a standing wave resonator as are fermions. A resonator, once set in motion undergoes a phase displacement such that the energy flow is out-of-phase. Hence, the resonator under uniform motion becomes a harmonic oscillator and will continue to oscillate alternately compressing and expanding unless acted upon by an external force in accordance with Newton's first law. Application of an external force on a resonator as shown by Jennison and Drinkwater results in a radiation back pressure in proportion to the applied force and, if the force is applied for twice the critical reaction, the resonator will accelerate in accordance with Newton's second law. Resonator motion proceeds in hopscotch fashion alternately switching between dissonance (acceleration jumps) and consonance (constant velocity). Self-induced motion of matter has been experimentally demonstrated by Ivanov using ultrasonic acoustic standing waves as propulsion means.
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The use of phase conjugate to modulate an electromagnetic standing wave within a phase-locked cavity resonator to induce motion is discussed. Phase -conjugate wave (PCW) generation may be accomplished via three or four-wave mixing (FWM)... more
The use of phase conjugate to modulate an electromagnetic standing wave within a phase-locked cavity resonator to induce motion is discussed. Phase -conjugate wave (PCW) generation may be accomplished via three or four-wave mixing (FWM) in photorefractive crystals, nonlinear Kerr media or metamaterials. Pump beams of disparate frequency simulating a Doppler effect modulate a standing EM signal beam reflecting off the phase conjugate mirror (PCM). Self-induced motion of the resonator arises by generation of a contracted moving standing wave creating an internal radiation pressure imbalance. Motion is in the direction of nodal displacement. No external radiation pressure or expulsion of reaction mass is required. Kinetic energy of motion is provided by direct conversion of electromagnetic energy in the amplified pump beams. Acceleration is proportional to the frequency difference between the pump beams. Velocity is proportional to the phase difference.
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A concept for self-induced motion of a phase-locked, phase conjugate resonator with synthesized Lorentz-Doppler pump beams of disparate frequency is discussed. Amplified pump beams of simulated Lorentz-Doppler red- and blue-shifted... more
A concept for self-induced motion of a phase-locked, phase conjugate resonator with synthesized Lorentz-Doppler pump beams of disparate frequency is discussed. Amplified pump beams of simulated Lorentz-Doppler red- and blue-shifted frequencies acting on a phase conjugate reflector in a nonlinear medium may be used to modulate a standing wave resulting in a contracted moving standing wave. This effect is essentially the inverse of motion of matter generating de Broglie matter waves. Synthesis of contracted moving standing waves is a straight forward application of phase conjugate 4-way mixing using amplified Lorentz-Doppler pump beams to induce resonator motion using Rhymodynamic principles. Internal radiation pressure imbalance provides a net ponderomotive force. No external radiation pressure or expulsion of reaction mass is required. Energy of motion is provided by direct energy conversion of EM pump waves.
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In the Plank aether hypothesis advanced by Winterberg, the physical vacuum is composed of a 2-component superfluid of positive and negative Planck mass particles with net zero mass. Electric field lines are interpreted as a phase... more
In the Plank aether hypothesis advanced by Winterberg, the physical vacuum is composed of a 2-component superfluid of positive and negative Planck mass particles with net zero mass. Electric field lines are interpreted as a phase alignment of Planck mass dipoles. Magnetic field lines are represented as closed-loop vortical filaments formed by rotating, spin-aligned Planck mass dipoles. Spin wave disturbance of such dipoles enable propagation of electromagnetic waves and provide a physical mechanism for polarization of the vacuum. Planck dipoles are depicted as vortical structures of rotating yin/yang geometry. Spin precession provides the means for generation of Planck charge.
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A detailed geometric electron toroidal model is illustrated which accounts for the observed physical properties of the electron and positron including spin angular momentum, size, magnetic moment, electrostatic energy, magnetostatic... more
A detailed geometric electron toroidal model is illustrated which accounts for the observed physical properties of the electron and positron including spin angular momentum, size, magnetic moment, electrostatic energy, magnetostatic energy, rest-mass energy, fine structure constant, g-factor, Compton radius, Compton frequency, zitterbewegung frequency, mass radius, charge radius, energy radiation and absorption, energy storage, electric charge and mass. The origin of the fine structure constant, charge, rest mass and relativistic mass are elucidated.
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Quantum Electrodynamic (QED) theory, while providing a mathematical formalism to describe electromagnetic interactions, conveys little insight into the nature or structure of the electron. Feynman diagrams, a graphical representation of... more
Quantum Electrodynamic (QED) theory, while providing a mathematical formalism to describe electromagnetic interactions, conveys little insight into the nature or structure of the electron. Feynman diagrams, a graphical representation of probability amplitudes, yield scant information on the internal details of the interaction processes at the vertex points or geometrical description of the propagator. While various models of photons and electrons have been proposed which can account for some of the observed characteristics, an additional screening is necessary to discriiinate viable candidates. A process description must account for not only the initial and final configuration states but also the transition path between demonstrating convertibility and conservation of quantum mechanical properties. Pair production and annihilation processes provide a severe test of any proposed geometrical models of such particles.
A detailed geometrical model of electron/positron pair production and annihilation is illustrated describing transformation of a propagating photon helicoid traveling wave into and electron and positron topologically confined rotating standing waves. The electron and positron are each depicted as a torus of revolution (Hopf link embedded within an annular manifold) with opposite charge, spins and magnetic moments.
A detailed geometrical model of electron/positron pair production and annihilation is illustrated describing transformation of a propagating photon helicoid traveling wave into and electron and positron topologically confined rotating standing waves. The electron and positron are each depicted as a torus of revolution (Hopf link embedded within an annular manifold) with opposite charge, spins and magnetic moments.
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The electrostatic force of attraction between two stationary point electric charges in scalar form is defined by Coulomb's law published in 1785 by Charles Augustin de Coulomb F e = (1/4pe 0)q 1 q 2 /r ^2 = kq 1 q 2 /r^2 . Coulomb's law... more
The electrostatic force of attraction between two stationary point electric charges in scalar form is defined by Coulomb's law published in 1785 by Charles Augustin de Coulomb F e = (1/4pe 0)q 1 q 2 /r ^2 = kq 1 q 2 /r^2 . Coulomb's law is analogous to Newton's law of gravitation. The magnitude of the Coulomb proportionality constant is much greater than Newton's Gravitation constant resulting in much greater electrostatic force of attraction between unit charges than gravitation force between unit masses.
For the case of moving charges, Wilhelm Weber in 1846 derived a relation for two charges in relative motion now known as Weber's law which reduces to Coulomb's law in the limit where velocities and accelerations are zero. With relative motion, Weber's law of electrical action accounts for Ampere's law of electrodynamics. A variety of similar equations have subsequently been derived to describe other dynamic effects include those of Neumann, Grassman, Ampere, Whittaker, Assis, Lucas and Klyuschin.
For the case of moving charges, Wilhelm Weber in 1846 derived a relation for two charges in relative motion now known as Weber's law which reduces to Coulomb's law in the limit where velocities and accelerations are zero. With relative motion, Weber's law of electrical action accounts for Ampere's law of electrodynamics. A variety of similar equations have subsequently been derived to describe other dynamic effects include those of Neumann, Grassman, Ampere, Whittaker, Assis, Lucas and Klyuschin.
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The fine structure constant alpha (= 0.0072973552... ~ 1/137) is a dimensionless quantity described as a fundamental physical constant characterizing the strength of the electromagnetic interaction. Introduced by Sommerfeld in 1916 to... more
The fine structure constant alpha (= 0.0072973552... ~ 1/137) is 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 in terms of electric charge, speed of light and Planck;s constant, the alpha constant represents a relativistic correction to the Bohr theory of the energy level of an electron.
The fine structure constant alpha has numerous interpretations including ratio scaling of tangential velocity v to velocity of light c, electromagnetic force to max. force at Compton radius, impedance of free space to electron impedance, Bohr radius to Compton radius, classical electron radius to Compton radius, Compton radius to electromagnetic radius, etc. The inverse fine structure constant 1/alpha (= 137.035999...) is associated with scaling in mass ratios while the reduced fine structure constant alpha/2pi (= 0.0011614...) is associated with scaling in angular velocity and energy ratios.
The electron charge to mass ratio e/m in mechanical units has the value 1.758820088E11 rad/sec. This angular velocity is quite small in comparison to the Compton angular frequency of 7.76343E20 rad/sec and is interpreted as a precession frequency. The whirl no q equals the inverse fine structure constant. This slight precession arises as a result of imbalance of electrostatic and magnetostatic energy which creates a torsion defect (loop closure failure) with a precession angle (topological charge) of 0.04458 rad (2,62 deg). This topological charge provides an explanation for origin of electric charge of the electron. This precession also results in wave function interference impeding flow of energy, hence providing an explanation of the origin of electron mass which heretofore has likewise been a mystery. A derivation of the fine structure constant and gyromagnetic spin ratio is presented with calculated values of physical properties of the electron corresponding to observed experimental values.
The fine structure constant alpha has numerous interpretations including ratio scaling of tangential velocity v to velocity of light c, electromagnetic force to max. force at Compton radius, impedance of free space to electron impedance, Bohr radius to Compton radius, classical electron radius to Compton radius, Compton radius to electromagnetic radius, etc. The inverse fine structure constant 1/alpha (= 137.035999...) is associated with scaling in mass ratios while the reduced fine structure constant alpha/2pi (= 0.0011614...) is associated with scaling in angular velocity and energy ratios.
The electron charge to mass ratio e/m in mechanical units has the value 1.758820088E11 rad/sec. This angular velocity is quite small in comparison to the Compton angular frequency of 7.76343E20 rad/sec and is interpreted as a precession frequency. The whirl no q equals the inverse fine structure constant. This slight precession arises as a result of imbalance of electrostatic and magnetostatic energy which creates a torsion defect (loop closure failure) with a precession angle (topological charge) of 0.04458 rad (2,62 deg). This topological charge provides an explanation for origin of electric charge of the electron. This precession also results in wave function interference impeding flow of energy, hence providing an explanation of the origin of electron mass which heretofore has likewise been a mystery. A derivation of the fine structure constant and gyromagnetic spin ratio is presented with calculated values of physical properties of the electron corresponding to observed experimental values.
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Electric charge is a fundamental physical property of matter similar to, and inseparable from mass and, like mass, is a conserved quantity. The fundamental nature of electric charge has remained elusive and in standard texts in adopted... more
Electric charge is a fundamental physical property of matter similar to, and inseparable from mass and, like mass, is a conserved quantity. The fundamental nature of electric charge has remained elusive and in standard texts in adopted units of measurement, electric charge is described simply, however opaquely, as [Q] with +/- polarity. Charge has its origin in rotational motion of energy, and is related to topological charge associated with spin precession. Electric charge expressed in units measured in Coulombs may be described in terms of mechanical units of kg rad/sec. The electron is characterized by the fine structure constant in addition to its quantum spin angular momentum. Electric charge arises as a result of a slight precession of the electron with whirl no. q equal to the inverse fine structure constant (=137.0359...). Electron precession arises as a result of an imbalance of electrostatic and magnetostatic energy. Precession represents a loop closure failure (torsion defect). The electron precession angle (topological charge = 0.04458 rad (2.62 deg). This same precession results in wave function interference and is responsible for the concomitant origin of electron rest mass which heretofore has been unexplained in the quantum electrodynamics theory QED and in the Standard Model of particle physics.
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To describe the notion of a connection between topological charge and electrical charge, recourse will be made to use of complex numbers which, unlike real numbers, have magnitude and phase to represent points and position vectors. A... more
To describe the notion of a connection between topological charge and electrical charge, recourse will be made to use of complex numbers which, unlike real numbers, have magnitude and phase to represent points and position vectors. A complex number is of the form z = x + iy where x and y are real numbers with x identified as the real part and y the imaginary part and the symbol 'i' denotes the square root of -1. Multiplying the position vector by 'i' is equivalent to a 2 pi rotation on an Argand diagram in phase. Rotations in the complex plane describe changes in phase. Hypercomplex numbers relate to 4-dimensional and higher dimensional space. The set of hypercomplex numbers are of the form a + bi + cj + dk and encompass the set of complex numbers on the 2D x-plane. Various examples of utilization of complex numbers are illustrated.
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A complex number may also be used to represent a vector as a function of time Z(t) and is termed a phasor. Phasors are commonly employed in electrical engineering applications to represent voltage and current sinusoids, Impedance is the... more
A complex number may also be used to represent a vector as a function of time Z(t) and is termed a phasor. Phasors are commonly employed in electrical engineering applications to represent voltage and current sinusoids, Impedance is the ratio of the voltage phasor to the current phasor. Quaternions expressed as ratios, percentages, motion, energy, musical notes, etc varying in time may be represented as angles on a phasor diagram. A wave and phase conjugate as a complex function of time Z(t) is illustrated. Projection of the rotating vector on the real axis represents the physical wave. Motion of a standing wave corresponds to a phasor rotation in the complex plane.
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Quaternions represent a generalization of complex numbers that provide a description in three dimensions just as complex numbers do in two dimensions. A quaternion is a set of four numbers which represent the sum of a scalar and a... more
Quaternions represent a generalization of complex numbers that provide a description in three dimensions just as complex numbers do in two dimensions. A quaternion is a set of four numbers which represent the sum of a scalar and a vector with three imaginary components. The scalar represents rotation about the vector axis. In contrast to complex numbers in which 'i' represents rotation by 90 deg, 'i' represents rotation by 189 deg in quaternion numbers. Quaternions provide an alternative to three Euler angles which, although more intuitive, are limited by gimbal lock when approaching 90 deg. Unlike tensors, quaternions are restricted to four dimensions and may provide an explanation of the four fundamental forces. Quaternions find application in physics, computer graphics, inertial navigation, and robotics for example as coordinates for rotation and orientation.
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In Quantum Mechanics (QM), quaternions can represent particle spin described in Lie Group theory as Sin (n) of dimension n which has elements known as spinors. Spinor rotation operators were introduced by Elie Cartan in 1913. Unlike... more
In Quantum Mechanics (QM), quaternions can represent particle spin described in Lie Group theory as Sin (n) of dimension n which has elements known as spinors. Spinor rotation operators were introduced by Elie Cartan in 1913. Unlike vectors or tensors, spinors change sign when rotated 360 degrees. Spinors were found indispensible to describe the spin angular characteristic of the electron and other spin 1/2 fermions. Spinor rotation operator examples illustrating SU(2) spin group complex vector representation and geometric origin of spin 1/2 characteristic are depicted. Electron 1/2 spin may be understood as a result of poloidal and toroidal spin components.
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Topological and vortex charge are closely related to electric charge providing an explanation for origin of electric charge. Electric charge and topological charge are illustrated as a Tusci couple (2-cusped hypocycloid) with spin 1/2... more
Topological and vortex charge are closely related to electric charge providing an explanation for origin of electric charge. Electric charge and topological charge are illustrated as a Tusci couple (2-cusped hypocycloid) with spin 1/2 characteristic. Similarly, fraction quark charge may be represented as a 3-cusp hypocycloid. Quark decay modes illustrating relation of mass, charge, helicity, curvature and torsion are shown.
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A hypothetical model of a quark with a massless spin 1 gluon field is illustrated as a close-coupled, out-of-phase orbital electron/positron pair with aligned spins. A charge screen of depolarized Planck dipoles prevents Coulombic... more
A hypothetical model of a quark with a massless spin 1 gluon field is illustrated as a close-coupled, out-of-phase orbital electron/positron pair with aligned spins. A charge screen of depolarized Planck dipoles prevents Coulombic attraction and self-destruction. A proton composed of spin-aligned electrons and positrons in tetragonal arrangement is equivalent to the Quantum Chromodynamic (QCD) quark description with 18 gluon fields. A neutron composed of spin-aligned electrons in tetragonal arrangement is equivalent to a QCD quark representation with 15 gluon fields. A vortex spin model of a neutrino is illustrated consisting of toroidal ring composed of spinning Planck dipoles is shown. Electron neutrino spin-flip transformation from LH to RH spin is illustrated
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The Lagrangian function (L) represents a single function description of the differential energy of motion (action) equal to the kinetic energy (T) minus the potential energy (V). The action is equal to the kinetic energy minus the... more
The Lagrangian function (L) represents a single function description of the differential energy of motion (action) equal to the kinetic energy (T) minus the potential energy (V). The action is equal to the kinetic energy minus the potential energy summed over history. The Lagrangian of a free particle path describes a trajectory of least action that follows a world line geodesic independent of coordinate system.
Only when there is an overlap of potential and kinetic energy is there mass-energy interaction. Mass is a measure of wave function dissonance. Least action may be understood as a result of destructive interference of electromagnetic waves. Mass-energy Lagrangian for the electromagnetic field equals the electrostatic energy less the magnetostatic energy. The Lagrangian and Hamiltonian of a de Broglie matter wave system in motion is illustrated.
Only when there is an overlap of potential and kinetic energy is there mass-energy interaction. Mass is a measure of wave function dissonance. Least action may be understood as a result of destructive interference of electromagnetic waves. Mass-energy Lagrangian for the electromagnetic field equals the electrostatic energy less the magnetostatic energy. The Lagrangian and Hamiltonian of a de Broglie matter wave system in motion is illustrated.
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In the classical mechanics phase space momentum concept formulated by W. R. Hamilton in 1833, both position and velocity are taken as independent variables. In a closed system, the total energy is represented by the Hamiltonian function... more
In the classical mechanics phase space momentum concept formulated by W. R. Hamilton in 1833, both position and velocity are taken as independent variables. In a closed system, the total energy is represented by the Hamiltonian function H as two equations in terms of position q and momentum p in phase space. Indeterminacy of position and momentum is in accord with the Heisenberg Uncertainty Principle. Te Hamiltonian H is a function of position, momentum and time representing the total energy of a system which is the sum of the kinetic and potential energy (H = T + V). The potential energy represents hidden kinetic energy. Hamiltonians are a method for finding the minimum of a given function and oft used to determine the path of least action.
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The curvature of a wavefunction is measured by the Laplacian and measures the flux density of the gradient of energy flow. Mass-energy and gravitation are associated with positive curvature (compression of spacetime volume). The... more
The curvature of a wavefunction is measured by the Laplacian and measures the flux density of the gradient of energy flow. Mass-energy and gravitation are associated with positive curvature (compression of spacetime volume). The Laplacian may be thought of as a measure of concavity of the wave function. The del operator (Laplacian) equals the divergence of the gradient of a function. Topics discussed include Laplace equilibrium surfaces and Laplace transforms.
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A tensor is a mathematical object that represents the generalization of a vector in which the magnitude and direction can vary at each point in a field independent of any selected frame of reference. The energy tensor can be regarded as... more
A tensor is a mathematical object that represents the generalization of a vector in which the magnitude and direction can vary at each point in a field independent of any selected frame of reference. The energy tensor can be regarded as a provisional means of representing matter. Some tensors are associated with the metric properties of a manifold such as the metric tensor which relates coordinates to the invariant 4D space-time interval or separation between events. Covariance and contravariance refers to how the components of a vector transform under a change in basis. Basis vectors are frame dependent. The one-form and the basis vectors are duals. The Ricci scalar curvature (volume-reducing) tensor is proportional to pressure. In the EGM model, the external quantum vacuum pressure acting on an enclosed mass locally compresses the EM spectrum into higher frequencies and fewer modes. The compressed EGM spectrum within the mass provides an opposing radiation pressure.
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Gravitation in a quantum gravity theory is a result of resonant electromagnetic wave interactions in a polarizable vacuum (PV) with a variable refractive index. Unlike the geometric spacetime curvature assumed in the Einstein theory of... more
Gravitation in a quantum gravity theory is a result of resonant electromagnetic wave interactions in a polarizable vacuum (PV) with a variable refractive index. Unlike the geometric spacetime curvature assumed in the Einstein theory of General Relativity, gravitation is described by variation in EM wave energy and density as measured by local variation in the vacuum refractive index. Variable vacuum electric permittivity and magnetic permeabilty results in alteration in the speed of light providing an explanation for bending of lighr. Gravitational attraction between masses modeled as EM oscillators, as shown by Ivanov, is the result of arrhythmia (frequency pulling effect) due to a difference in frequencies. Mass represents to frequency change. EM wavelength contraction and frequency shift in a polarizable vacuum accounts for mass in motion and gravitational effects including energy change, deflection of light, gravitational frequency shift and clock slowing.
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Something completely new has to be found…something that is somehow based on the ideas of General Relativity. - Albert Einstein A mass object represents an ensemble of one or more autonomous, individual, periodic, self-sustained... more
Something completely new has to be found…something that is somehow based on the ideas of General Relativity. - Albert Einstein
A mass object represents an ensemble of one or more autonomous, individual, periodic, self-sustained oscillators (e.g., electrons, atoms, etc) radiating a broad spectrum of electromagnetic waves. Oscillators constitute clocks which are formed of standing matter waves. In synchronicity, the coupled oscillators reset to common base frequency. Clocks (and standing waves) undergo Lorentz contraction in the direction of motion, slow down in motion, and undergo a time shift due to Lorentz-Doppler effect. In free-fall, the frequency discordance is reduced to zero whereas at a fixed elevation potential, the oscillators are prevented from approaching synchronicity with a net acceleration equivalent to the net frequency difference. Standing wave interference of coupled oscillators can result in repulsion, attraction or cancellation depending on phase difference. Motion of matter arises as a result of dissonance in which the wave system is attracted to wave anti-nodes of out-of-phase oscillator pairs in alternating push/pull fashion.
A mass object represents an ensemble of one or more autonomous, individual, periodic, self-sustained oscillators (e.g., electrons, atoms, etc) radiating a broad spectrum of electromagnetic waves. Oscillators constitute clocks which are formed of standing matter waves. In synchronicity, the coupled oscillators reset to common base frequency. Clocks (and standing waves) undergo Lorentz contraction in the direction of motion, slow down in motion, and undergo a time shift due to Lorentz-Doppler effect. In free-fall, the frequency discordance is reduced to zero whereas at a fixed elevation potential, the oscillators are prevented from approaching synchronicity with a net acceleration equivalent to the net frequency difference. Standing wave interference of coupled oscillators can result in repulsion, attraction or cancellation depending on phase difference. Motion of matter arises as a result of dissonance in which the wave system is attracted to wave anti-nodes of out-of-phase oscillator pairs in alternating push/pull fashion.
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Gravitational frequencies encompass the entire EM frequency spectrum with energy concentrated in the extreme high frequency range estimated at 10^20 to 10^40 Hz. At the Earth's surface, the bulk of the PV spectral energy is well above... more
Gravitational frequencies encompass the entire EM frequency spectrum with energy concentrated in the extreme high frequency range estimated at 10^20 to 10^40 Hz. At the Earth's surface, the bulk of the PV spectral energy is well above the THz range as estimated by Storti et al. The Earth's gravitational frequency is calculated to extend into the Yottahertz (10^24 Hz) range. The electron Compton frequency (=1.236 x 10^20 Hz( represents the upper frequency limit of electrons and positrons. The Planck frequency (=2.913 YHz) represent the apparent upper frequency limit supported by the vacuum. Gravitational frequencies of astronomical objects are estimated to lie in the lower end of the electromagnetic spectrum roughly in the 10^-16 to 10^10 Hz range.
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The range of mass of the observable universe from the subatomic scale to the galactic scale as a function of the Schwarzschild radius follows a logarithmic progression. The Schwarzschild radius represents the radius of a sphere into... more
The range of mass of the observable universe from the subatomic scale to the galactic scale as a function of the Schwarzschild radius follows a logarithmic progression. The Schwarzschild radius represents the radius of a sphere into which matter must be compressed to form a black hole. Mass appears related to a contraction in radius such that the difference in circumference equals the Schwarzschild wavelength. A logarithmic plot of mass of atoms, planets and galaxies expressed in units of electron mass exhibit a linear relation as a function of radius expressed in multiples of the Compton radius with a grouping that varies in scale multiples of 2^10 = 1024. Oldershaw proposes that aggregates of matter displays a clustering ot fractal characteristic termed Discrete Scale Relativity corresponding to a scale-free resonant coupling of oscillators. The gravitational coupling constant in this model varies with scale.
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A historical account of various proposed gravitational force expressions is summarized including those proposed by Laplace, Barrow, Calder & Lahov, Jefimenko, Lucas and Zel'dovich. A discussion of possible origin of dark energy as an... more
A historical account of various proposed gravitational force expressions is summarized including those proposed by Laplace, Barrow, Calder & Lahov, Jefimenko, Lucas and Zel'dovich. A discussion of possible origin of dark energy as an explanation for apparent expansion of the universe due to gravitational repulsion is included. Estimates of dark energy density are approximately the same order as mass density of the known universe. A dark energy density is equivalent to a negative pressure. Total energy and curvature of the universe equals zero of which half is positive and half negative.
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Gravitation potential (potential energy/unit mass) is a three dimensional scalar function and may be interpreted as a measure of local electromagnetic energy (EM flux) density of a central mass composed of fermionic mass oscillators. The... more
Gravitation potential (potential energy/unit mass) is a three dimensional scalar function and may be interpreted as a measure of local electromagnetic energy (EM flux) density of a central mass composed of fermionic mass oscillators. The local variation in EM energy density results in a reduction of light velocity and deflection of light. The acceleration of gravity g represents the gravitational field strength (= F/m) and is opposite to the direction of the gravitational potential gradient denoted by the Poisson relation.
The Earth's gravitational potential and corresponding gravitational frequency is shown plotted as a function of planet radius. A tangent space representation of the gravitation frequency hill and gravitation potential well for a central spherical mass is illustrated in a flat Euclidean 3D space. Proper length and time in curved spacetime are represented as embedding diagrams in tangent space.
The Earth's gravitational potential and corresponding gravitational frequency is shown plotted as a function of planet radius. A tangent space representation of the gravitation frequency hill and gravitation potential well for a central spherical mass is illustrated in a flat Euclidean 3D space. Proper length and time in curved spacetime are represented as embedding diagrams in tangent space.
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The gravitation Gamma conversion constant (nondimensional) relates transformation of physical units and constants in a gravitational field in terms of proper length and time. Gravitational Gamma represents the strength of the... more
The gravitation Gamma conversion constant (nondimensional) relates transformation of physical units and constants in a gravitational field in terms of proper length and time. Gravitational Gamma represents the strength of the gravitational field independent of the acceleration of gravity and is equal to the local vacuum refractive index. Conversions for Gamma are shown in terms of coordinate time (remote observer)/proper time (local observer, vacuum refractive index, gravitational potential, General Relativity GR metric coeff., and escape velocity. The gravitational Gamma is comparable to the lower case gamma (Lorentz factor) of Special Relativity which relates transformation of relative motion in flat space of inertial (non-accelerated) reference frames. A plot of calculated variation in Earth's gravitation Gamma and vacuum refractive index is shown as a function of planet radius.
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The Vis inertiae is a passive Principle by which bodies persist in their Motion or Rest, receive Motion in proportion to the force impressing it, and resist as much as they are resisted.- Isaac Newton The inertial force due to gravity... more
The Vis inertiae is a passive Principle by which bodies persist in their Motion or Rest, receive Motion in proportion to the force impressing it, and resist as much as they are resisted.- Isaac Newton
The inertial force due to gravity in terms of the gravitational gradient, in accordance with the modern day interpretation of Newton's second law of motion, is defined as F = ma = W = mg where: F (= W) Force (or weight) , m = inertial mass and a = acceleration. An explanation for the origin of Newton's 2nd law was derived by Jennison and Drinkwater for a phase-locked cavity model of a wave system resonator representing a fundamental particle (fermion). A trapped standing wave exhibits not only rest mass but also intrinsic inertia. Rest mass arises as a result of electron wave function self-interference due to a slight precession with whirl no. equal to the inverse fine structure constant owing to an imbalance of electrostatic and magnetostatic energy. Electric charge of the electron arises from this precession which results in a torsion defect (topological charge). Hence, rest mass and electric charge are intimately related.
Ivanov derives an expression for acceleration of a wave system of coupled oscillators in terms of phase shift and frequency difference of forward and backward travelling waves within a resonator. Thus, inertia may be seen as a near instantaneous local electromagnetic interaction with 100% negative feedback. The acceleration of gravity is proportional to the frequency shift of a standing wave system restrained from free-fall. The frequency difference is the result of a Lorentz-Doppler shift of counter-propagating travelling wave components of a contracted moving standing wave. In a free-fall, weightless condition, this beat frequency difference is reduced to zero. The acceleration of gravity and associated frequency difference of the Earth's gravitational field is illustrated.
The inertial force due to gravity in terms of the gravitational gradient, in accordance with the modern day interpretation of Newton's second law of motion, is defined as F = ma = W = mg where: F (= W) Force (or weight) , m = inertial mass and a = acceleration. An explanation for the origin of Newton's 2nd law was derived by Jennison and Drinkwater for a phase-locked cavity model of a wave system resonator representing a fundamental particle (fermion). A trapped standing wave exhibits not only rest mass but also intrinsic inertia. Rest mass arises as a result of electron wave function self-interference due to a slight precession with whirl no. equal to the inverse fine structure constant owing to an imbalance of electrostatic and magnetostatic energy. Electric charge of the electron arises from this precession which results in a torsion defect (topological charge). Hence, rest mass and electric charge are intimately related.
Ivanov derives an expression for acceleration of a wave system of coupled oscillators in terms of phase shift and frequency difference of forward and backward travelling waves within a resonator. Thus, inertia may be seen as a near instantaneous local electromagnetic interaction with 100% negative feedback. The acceleration of gravity is proportional to the frequency shift of a standing wave system restrained from free-fall. The frequency difference is the result of a Lorentz-Doppler shift of counter-propagating travelling wave components of a contracted moving standing wave. In a free-fall, weightless condition, this beat frequency difference is reduced to zero. The acceleration of gravity and associated frequency difference of the Earth's gravitational field is illustrated.
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Equations for calculation of the Newtonian Gravitational constant G advanced by various researchers are reviewed and compared. Implications of spatial and temporal variation in G on the evolution of the universe are described.... more
Equations for calculation of the Newtonian Gravitational constant G advanced by various researchers are reviewed and compared. Implications of spatial and temporal variation in G on the evolution of the universe are described. Conversions relating the Gravitational coupling constant G to Planck mass, length and time, effective permittivity and gravitational gamma are provided. Dimensionally, G is equal to c^2 (Runiverse/Muniverse). Hence, the so-called 'Mach Effect' is already incorporated into the gravitational constant G. Variation in empirical measurements of G may be attributed in part to stray capacitances (electrostatic leakage) in experimental test measurement layout.
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Calculation of the gravitation force between electrons according to the Macken model is described in terms of strain amplitude relating the nonlinear vacuum energy resonance at the Compton and Planck scales. Diagrams of the vacuum... more
Calculation of the gravitation force between electrons according to the Macken model is described in terms of strain amplitude relating the nonlinear vacuum energy resonance at the Compton and Planck scales. Diagrams of the vacuum nonlinearity and electron vacuum resonance are illustrated. Electric charge results from a slight spin precession of the electron with whirl no. equal to the inverse fine structure constant. Electrostatic and gravitation force between electrons are compared. Gravitation force arises as a result of a gradient in the EM spectral energy density gradient. Both light and matter are subject to gravitational scalar and vector potential effects. The generalized Newtonian force equation advanced by Jefimenko includes scalar and vector potential components. The gravitational vector potential is proportional to the velocity of the gravitational scalar potential. The gravikinetic field opposes changes in mass motion. Photon wave function interference produces an effective mass due to change in momentum in regions of increased EM energy density. Similarly, matter wave interference is responsible for relativistic mass increase of a moving standing wave due to change of momentum in regions of increased EM energy density.
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The Einstein GR gravitational field equation equates curvature of a 4D spacetime metric to sources of stress-energy-momentum. The stress-energy tensor T is identified as the source of the gravitation field rather than mass. The Einstein... more
The Einstein GR gravitational field equation equates curvature of a 4D spacetime metric to sources of stress-energy-momentum. The stress-energy tensor T is identified as the source of the gravitation field rather than mass. The Einstein equation is equivalent to a statement that energy density equals pressure, hence, gravitation is related to vacuum energy (pressure). In the limit of maximum curvature, the maximum force possible is the Planck force. Spacetime metric, stress-energy-momentum and electromagnetic tensor components are illustrated. The 5D Kaluza-Klein metric and 5D Heim energy density action tensor components are likewise illustrated for comparison. The Evans-Cartan curvature tetrad is described which includes curvature associated with gravitation and torsion associated with electromagnetism. Electric charge is described as a torsion defect, e.g., loop closure failure.
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Graviton vertex interactions are illustrated in terms of Quantum Field Theory, Quantum Mechanics sine-Gordon solitons, and Quantum Gravity bosonic closed-loop strings. Quantum diagrams of symplectic structure spin networks are depicted... more
Graviton vertex interactions are illustrated in terms of Quantum Field Theory, Quantum Mechanics sine-Gordon solitons, and Quantum Gravity bosonic closed-loop strings. Quantum diagrams of symplectic structure spin networks are depicted as well as Quantum Field symmetry breaking representations. Vorticity, helicity and chirality of soliton-soliton interactions are compared.
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The hypothetical graviton is described as a spin 2 boson posited as the carrier of the gravitation force. In the proposed model, the graviton is averred to be a resonance interaction of a spin 1 boson and its phase conjugate. The phase... more
The hypothetical graviton is described as a spin 2 boson posited as the carrier of the gravitation force. In the proposed model, the graviton is averred to be a resonance interaction of a spin 1 boson and its phase conjugate. The phase conjugate photon is generated upon reflection from a EM wave interference pattern in a nonlinear polarizable vacuum with nodal spacing comparable to the wavelength of the incident photon. The phase-conjugate photon is not an anti-particle as the spins are in the same direction and, hence, are additive. The momentary graviton interaction is not directly observable, however, the gravitation effects may be observable. The effect of the resonance interaction is to locally increase the energy density of the Planck vacuum increasing the refractive index and gravitational gamma. Graviton formation from a counter-propagating photon and phase conjugate are illustrated in terms of Whittaker scalar potentials. Spin angular momentum is additive while linear momentum and helicity cancel to zero. Graviton (helicoid), photon and conjugate (helices) curvature and torsion characteristics are illustrated.
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For a central mass, the associated gravitational field has negative energy density equal to the positive energy density of matter. Condensation of matter produces an equal and opposite reaction: extraction of mass-energy from the... more
For a central mass, the associated gravitational field has negative energy density equal to the positive energy density of matter. Condensation of matter produces an equal and opposite reaction: extraction of mass-energy from the vacuum. EM wavelength increase in a gravitational field corresponds to apparent time dilation while EM frequency increase corresponds to apparent space contraction of GR theory which posits curvature of a metaphysical spacetime. The polarization of a physical vacuum may be understood as an effect of polarization of Planck mass dipoles comprising the vacuum resulting in a modification of the local vacuum refractive index. Plots of the Earth's mass-energy density and gravitational field mass-energy density are compared.
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For mass in motion, the gravitational field undergoes a Lorentz contraction in the direction of motion. Mass motion constitutes a mass current analogous to an electric current. As a result, there is a circumferential gravitomagnetic... more
For mass in motion, the gravitational field undergoes a Lorentz contraction in the direction of motion. Mass motion constitutes a mass current analogous to an electric current. As a result, there is a circumferential gravitomagnetic field similar to the magnetic field of an electric current albeit much weaker to the large gravitomagnetic permeability. Relative motion generates a cogravitation field K in the Jefimenko model exerting a force F (= m(v x K) on a moving mass with velocity v in the direction of motion. A gravikinetic field is analogous to an electrokinetic field opposing motion. The cogravitation force associated with Lagrange orbital positions is illustrated.
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Wavefront interference patterns of interacting oscillators are depicted illustrating a quantized wave interference metric and Fresnel zone effects. Gravitation is viewed as entirely electromagnetic phenomena whereas spacetime is merely a... more
Wavefront interference patterns of interacting oscillators are depicted illustrating a quantized wave interference metric and Fresnel zone effects. Gravitation is viewed as entirely electromagnetic phenomena whereas spacetime is merely a mathematical abstraction describing electromagnetic wave curvature. In the polarizable vacuum PV model, gravitation is the result of variation in local electromagnetic energy density equivalent to a gradient in the vacuum refractive index. The gravitational field EM standing wave interference pattern is illustrated for an isolated mass as well as a pair of interacting mass objects. The local geodesic relative acceleration of free-falling masses is shown. The gravitational Poynting energy flux is associated with the Ricci tensor..
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A photon (boson) ascending in a gravitational field loses energy and undergoes a gravitational frequency redshift and while descending exhibits a blueshift gaining in energy. Conversely, an electron (fermion) ascending in a gravitational... more
A photon (boson) ascending in a gravitational field loses energy and undergoes a gravitational frequency redshift and while descending exhibits a blueshift gaining in energy. Conversely, an electron (fermion) ascending in a gravitational field gains energy undergoing a blueshift and descending loses energy exhibiting a frequency redshift . Equations describing this phenomena are reviewed. Conversion formulas for gravitational redshift in terms of gravitational potential, vacuum refractive index and gravitational gamma are detailed as well as de Broglie matter wave phase shift.
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A generalized Fourier representation of the gravitational frequency spectrum of a mass object in a polarized vacuum as developed by Storti et al is illustrated. Various estimates of the Earth's gravitational frequency spectrum are... more
A generalized Fourier representation of the gravitational frequency spectrum of a mass object in a polarized vacuum as developed by Storti et al is illustrated. Various estimates of the Earth's gravitational frequency spectrum are compared. According to the electro-gravi-magnetic EGM polarized vacuum construct using the Buckingham II theorem, all mass radiates a spectrum of wave functions w PV (1,r,M) ≤ w ≤ w W (r,M)… At each frequency wave functions are propagated with positive and negative amplitudes. A Fourier representation of graviton wave packet is illustrated.
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Phase-locking synchronization of interacting mass oscillators associated with gravitation is discussed. Gravitational acceleration as shown by Ivanov results from a frequency discordance or arrhythmia creating an asymmetry of the... more
Phase-locking synchronization of interacting mass oscillators associated with gravitation is discussed. Gravitational acceleration as shown by Ivanov results from a frequency discordance or arrhythmia creating an asymmetry of the standing wave interference pattern. A standing wave system undergoes a nodal compression of standing waves as well as an internal phase shift that varies with velocity. Motion of matter represents a continuous symmetry transformation through wave function translation minimizing the frequency difference. Phase and frequency difference of counter-propagating travelling waves within a resonator generates a moving standing wave. A standing wave resonator may be set in motion by external or internal force. A ponderomotive force results from an internal radiation pressure imbalance of disparate source oscillators.
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Anti-gravity concepts and means are reviewed including: 1) EM alteration of local gravitational potential, 2) spectral density modulation, 3) matter wave cancellation, 4) nullification of naturally-occurring gravito-Poynting energy influx... more
Anti-gravity concepts and means are reviewed including: 1) EM alteration of local gravitational potential, 2) spectral density modulation, 3) matter wave cancellation, 4) nullification of naturally-occurring gravito-Poynting energy influx countering conversion of gravitational potential energy into kinetic energy, 5) synthesized Lorentz-Doppler and inverse Doppler utilizing phase-locked resonators, phase conjugation, and negative refractive index metamaterials, 6) augmented gravitomagnetic field utilizing negative index metamaterials altering gravitomagnetic permeability, 7) Gravitic drives employing artificially created negative mass. Quantitative design examples are illustrated.
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Motion of a mass object through a gravitational field produces ultrahigh frequency tones as the mass moves through EM wave resonance points. The chord progression corresponds to the trajectory path through a tone net. An inverse effect... more
Motion of a mass object through a gravitational field produces ultrahigh frequency tones as the mass moves through EM wave resonance points. The chord progression corresponds to the trajectory path through a tone net. An inverse effect may be demonstrated in motion of objects on a vibrating Chladni plate in which motion may be controlled by a melody of note progression. Musical pitch, ratios, and rate of change define harmony, melody, meter and rhythm invoking a sense of motion. Musical intervals are apparent in the EM spectrum of oscillation modes of standing waves. At nodal points, kinetic energy of material particles is minimum and at anti-nodes is maximum. Wave motion transfers energy from one point to another. Nodal displacement induces mass transport. Standing wave resonance results in localized concentration of matter density at nodal points. Resonance occurs at simple, whole number ratios requiring the least energy per oscillation period. Dissonant musical intervals such as tritones require more energy than octaves with thirds, fourths and fifths in between. Equal temperament divides the octave into twelve equal semitones described as the chromatic scale. The number twelve is of special significance in music and represents the sum of the three smallest integers 3 + 4 + 5 = 12 and relates to the Pythagoras Theorem (a ^2 + b ^2 = c ^2) for a 3:4:5 right triangle. The EM frequency range of the Earth's gravitational field is estimated to extend up through 520E24 Hz (C 77) or ~77 octaves. For comparison, the electron Compton frequency is 1.2356 x 10 20 Hz (C 18). The overall EM frequency spectrum extends up through C 138 (2.913E43 Hz) which corresponds to the Planck frequency where the number of octaves = log(f2/f1)/log(2). Pythagorean tuning logarithmic spiral of perfect fifths (3:2) is mapped onto a 12-note equal temperament circle of fifths. Twelve major keys in ascending fifths and minor keys in descending fourths correspond to even (sine) and odd (cosine) frequencies. The frequency spiral corresponds to a golden mean pathway of harmonic cascade energy flow.
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An emphasis has been placed in this book on geometrical and dimensional descriptions of electromagnetic and gravitational quantum fields. A variety of geometrical relationships between physical quantities and fundamental interactions in... more
An emphasis has been placed in this book on geometrical and dimensional descriptions of electromagnetic and gravitational quantum fields. A variety of geometrical relationships between physical quantities and fundamental interactions in physics are apparent such as in group theory with the Lie E 8 group being a prominent example. Dimensions for various physical quantities and MKS derived units are detailed in Table 54-1 and fundamental definitions and relationships are briefly summarized. Scientific International SI units (rationalized MKS) are used throughout unless otherwise noted. The term "rationalized" refers to the inclusion of the factor 4pi into equations involving point quantities and thus 2pi involving line quantities and disappears in uniform fields as well as Maxwell's equations. Use of 'geometrized' units where fundamental constants G = c = 1 and nondimensionalized Planck units where k = ħ = 1 is, in general, avoided due to quantitative misrepresentation, obfuscation of physical meaning, dimensional error check, and labor of reconversion for practical use. An example visual summary of an organizational structure is an illustration of a hypercube ordering of physical quantities based on four dimensions of length, time, mass and angle represented as matrix elements [L T Q M] including derived dimensions for mechanical and electromagnetic quantities such as momentum, angular momentum, charge, action, energy, etc together with physical constants c, G and h is depicted. The hypercube is illustrated as an extension of a Bronstein-Penrose cube revealing the interrelationships of quantum mechanics, classical mechanics, relativity theory, quantum field theory and quantum gravity.
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A dimensionless quantity described as a fundamental physical constant characterizing the coupling strength of the electromagnetic interaction. Introduced by Sommerfeld in 1916 to describe the spacing of splitting of spectral lines in... more
A dimensionless quantity described as a fundamental physical constant characterizing the coupling 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 four physical constants: electric charge, speed of light in vacuo, Planck's constant and electric permittivity of free space.
The inverse fine structure constant (=137.035999...) represents the spin precession whirl no. of the electron. The electron exhibits a slight precession due to an imbalance of electrostatic and magnetostatic energy levels. Electric charge is a result of this spin precession and represents a loop closure failure (torsion defect) similar to topological charge.
Rest mass results from quantum wave interference due to precession. Hence, electric charge, rest mass and the fine structure constant are interrelated and directly calculable.
The inverse fine structure constant (=137.035999...) represents the spin precession whirl no. of the electron. The electron exhibits a slight precession due to an imbalance of electrostatic and magnetostatic energy levels. Electric charge is a result of this spin precession and represents a loop closure failure (torsion defect) similar to topological charge.
Rest mass results from quantum wave interference due to precession. Hence, electric charge, rest mass and the fine structure constant are interrelated and directly calculable.