- 1. Graviton
- 2. • The natural force that tends to cause physical things to move toward each other; the force that causes things to fall. – Merriam Webster Dictionary • Gravity is a conservative force field, hence, work performed is independent of the path taken between initial and final positions of an test mass during displacement with the central force field of the active mass. where DU = Difference in potential energy [Joules] F(r) = radial force [Newtons] W = Work (= force x distance) [N·m] G = Universal Gravitational constant [ 6.67428E-11 N·m2/kg2] M = central mass [kg] m = test mass [kg] Gravity
- 4. Gravitational force Newton’s 1st Law F = GMm/r2 [Newtons] where G = Gravitational coupling constant relating curvature and energy density gradient [≃ 6.67428E-11 N·m2/kg2] M = active mass [kg] m = passive mass [kg] r = separation distance between masses [m] Newton’s Law of gravitation assumes instantaneous action-at-a-distance independent of time and, hence, is not relativistic. Gravitational force
- 6. Inertial force Newton’s 2nd Law F = mg [Newtons] Equating F = GmM/r2 = mg [Newtons] Acceleration of gravity g = GM/r2 [m/s2] • Acceleration is a measure of EM wavefront (geodesic) curvature which is a function of an energy density gradient. • Inertial mass mi = Gravitational mass mg (Equivalence Principle) as both arise from the same causal mechanism (i.e., motion though a region of increased energy density). Inertial force
- 7. Gravitational scalar potential (potential energy/unit mass) f = U = -GM/r [J/kg] Gravitational potential is a measure of electromagnetic energy density of mass M of volume V. Near the Earth’s surface, the gravitational potential is linearly approximated as Df = f(R + h) – f(R) = -gh [J/kg] where h = height above Earth’s surface and R = Earth radius Acceleration of gravity g represents the gravitational field strength (= F/m) and is opposite to the scalar gravitational poential f g = -grad f = = -∇f [m/s2] Gravitational force in terms of scalar potential F = -m∇f [Newtons] Gravitational potential energy
- 9. Kinetic energy T = 1/2 mv2 [Joules] Equating gravitational potential energy and kinetic energy -GM/r = 1/2 mv2 yields ve = √(2GM/r) [m/s] where ve = escape velocity of mass m from a central mass M. A black hole is a region of spacetime where gravity is so strong not even light can escape. Gravity is a measure of intrinsic (surface) curvature. The size of a black hole event horizon is described by the Schwarzschild radius rS = 2GM/c2 [m] Escape velocity
- 10. Mass vs. Schwarzschild radius RS of subatomic and astrophysical objects Schwarzschild radius RS = 2GM/c2
- 11. Mass acts as a source of the gravitational field described by Poisson’s equation ∇2f = -4pGr = 4pGM/V [J/kg·m2] where ∇2 = Laplacian operator (divergence of a gradient of a function) [m-2] f = gravitational scalar potential (= -GM/r) [J/kg] M = mass [kg] r = mass density (= mass/volume) [kg/m3] V = mass volume [m3] Gauss’s law of gravity (differential form) ∇·g = -4pGr = -fgr [N/m·kg] where fg = gravitational flux [J/kg] r = mass density [kg·m-1] Laplacian potential
- 12. In terms of the vacuum refractive index KPV of the polarizable vacuum, the time-indepent form is ∇2f = ∇2c0 2/(KPV(r,M) = ∇2c0 2/(1/(1 + 2f/c2) [s-2] A positively curved spacetime corresponds to a converging refractive index (KPV > 1) in which light slows down and material objects contract in size due to increase in EM energy density. For a gravitational potential well, the curvature in tangent space manifold is concave up while the refractive index and frequency hill is concave down. In contrast to GR (with unexplained mechanism for assumed spacetime distortion), gravitational effects in a polarizable vacuum (including length contraction, time dilation, frequency shift, alteration in the speed of light, etc) are EM wave interaction effects due to local variation in the vacuum refractive index KPV(r,w,M) Polarizable Vacuum
- 13. Non-rotating black hole in a polarizable vacuum • Geodesic curvature is produced by gradient in energy density
- 14. Mass induced EM wavefront curvature • Acceleration is a measure of wavefront curvature induced by an electro- magnetic spectral energy density gradient in the vicinity of mass
- 15. In the Einstein General Theory of Relativity (GR), gravity is represented mathematically as a curvature of spacetime. GR gravitational field equation equates curvature to sources of stress-energy momentum Gmn = Rmn – ½gmnR = -(8pG/c2)Tmn = -kTmn where: Gmn = Einstein tensor [m-2] Rmn = Ricci curvature symmetrical tensor (contracted from Riemann tensor = Rabc b) [m-2] gmn = Lorentz spacetime metric tensor (= nmn + hmn) [ - ] R = scalar curvature defined as trace of Ricci tensor [m-2] G = Newtonian gravitational constant [≃ 6.67384E-11 nt·m2/kg2] c = velocity of light (= l/f = c0/n = 1/√(e0m0)) [≃ 2.997924E8 m/s] Tmn = stress-energy-momentum tensor [kg/m3] k = Einstein’s constant (= -8pG/c2) [m/kg] curvature source Einstein field equation
- 16. In the Einstein General Theory of Relative (GR), no physical mechanism is defined as to how matter is said to ‘bend’ spacetime or how spacetime alters the motion of matter. GR represents a metaphysical mathematical coordinate description of space (relative location of objects) and time (ordering of events) in terms of curvature of geodesics without a quantum mechanical description of the underlying physical vacuum. The Einstein equation is equivalent to a statement that energy density equals pressure, hence, gravitation is related to vacuum energy/pressure. Tmn = (1/8p)(c4/G)Gmn = k∙FP Gmn where: Tmn = stress-energy-momentum tensor [N/m-2] c = velocity of light (= c0/G = 1/√(e0m0)) [≃ 2.997924E8 m/s] G = Newton’s Gravitation constant [≃ 6.67428E-11 N·m2/kg2] Gmn = Einstein tensor [m-2] k = Einstein constant (= -8pG/c2) [N·m2/kg2} FP = Planck force (= c4/G = mPlP/tP 2) [= 1.210E44 N] Stress-Energy-Momentum tensor
- 17. Geodesic deviation in a gravity field
- 18. • In an optical theory of gravity, the vacuum refractive index KPV(r,w,M) is a measure of the local energy density . The acceleration of gravity g is a measure of the spectral energy gradient. The Gravitation Constant G is a constant relating curvature and energy-momentum density. • Gravity represents a frequency arrthymia between mass oscillators as they attempt to synchronize. The acceleration of gravity g is equivalent to a frequency shift Dn in a standing wave system restrained from free fall is given by g = 2cDn. In free fall, the frequency difference is reduced to zero. • Effects of change in gravitational potential on motion of matter in terms of spacetime curvature may be described equivalently in terms of changes in frequency and phase of de Broglie matter waves. A moving wave system undergoes a Lorentz contraction g (= √(1 – v2/c2) and Lorentz- Doppler shift Dl in the direction of motion. Acceleration is proportional to the frequency difference Dn while velocity is proportion to the phase difference Df. Vacuum refractive index
- 19. Gravitational acceleration is equal to the negative of the gravitational potential (g = -∇f) and is proportional to the EM frequency gradient (g = 2cDn·ru) Tangent space
- 20. Gravitational potential well • Earth mass ≃ 5.972E24 kg • Earth mean radius ≃ 6,378 km • Acceleration of gravity @ Earth’s surface ≃ 9.8 m/s2 • Escape velocity of Earth ≃ 11.2 km/s
- 21. Gravitational potential well & Frequency hill
- 22. Variation in Earth’s gravitational gamma & Vacuum refractive index
- 23. Acceleration of gravity g and frequency shift Dn vs. distance from Earth
- 24. Nonuniform gravitational well and frequency hill of a spherical mass
- 25. Frequency shift in a gravitational field
- 26. Gravitational effects on EM fields • Wavelength increase corresponds to apparent time dilation • Frequency increase corrends to apparent space contraction
- 27. Gravitational field standing wave pattern of a central mass
- 28. Keplar’s Laws of orbital motion
- 29. Keplerian & non-Keplarian motion Orbital motion of mass m about a large, central mass M (scalar potential effect) Orbital motion of diffuse, spin density waves (vector potential effect)
- 30. Lagrange points Lagrange (libration) points are orbital positions where gravitational force equals centrifugal force L1 – L5 = Lagrange points M1 = central mass M2 = orbital mass
- 32. Co-gravitation • Mass current generates a gravitomagnetic (co-gravitation) field K (= ∇ x Ag)
- 33. Motion induced gravitomagnetic field • Mass motion constitutes a mass current with an induced gravitomagnetic field analogous to an electric current with an associated magnetic field
- 34. Gravitational field variation @ relativistic velocities
- 35. Gravitational wave effects • Gravitational waves exhibit quadrapole polarization
- 38. EM standing wave interference lattice • Interference antinodes act as scattering centers for an incident EM wave
- 39. Phase conjugate wave reflection • EM Fresnel zones of interacting mass oscillators result in phase conjugate wave reflection in a polarizable vacuum
- 40. Standing wave interference • Standing wave interaction of a pair of oscillators of equal frequency in an idealized, nondissipative elastic medium results in attraction or repulsion depending on phase synchronization. • Force imbalance is proportional to the difference in wave energy density between oscillators and inversely to the wave velocity.
- 41. Quantized wave interference metric • Wavefront interference of mass oscillators result in a quantized field metric
- 42. Spin 2 Graviton gg* • Graviton formed by coupling of photon and counter-propagating phase conjugate
- 43. Graviton curvature and torsion • Graviton gg* is of helicoid geometry whereas photon g is a helix
- 44. Fourier representation of gravitational frequency spectrum
- 45. Oscillator frequency synchronization of coupled mass pair
- 46. Vacuum spectral energy density modulation • Mass induces a local recompression of the vacuum spectral energy density. Acceleration of gravity is a measure of the spectral energy density gradient.
- 47. Polarized vacuum response due to presence of mass
- 48. Spectral energy density of Earth’s gravitational field • The spectral energy density rSED(w) represents the energy density per frequency mode. The number of mode of the PV spectrum increases with radial distance from a mass object and decreases in energy. Ref: QE, Storti et al
- 49. Anti-Gravity • Acceleration of gravity varies as the spectral energy density gradient. Inversion of the naturally occurring spectral energy density gradient offsets the local acceleration of gravity equivalent to anti-gravity effect.
- 50. Gravitational field energy vs. Fundamental frequency
- 51. Augmented spectral energy density profile
- 52. Induced motion of matter wave system • Synthesized matter wave (contracted moving standing wave) generated by amplified Lorentz-Doppler pump beams modulating a signal beam in 4-way phase conjugate mixing results in radiation pressure imbalance. • Matter in motion generates a de Broglie matter wave. • The inverse effect of matter wave synthesis generates induced motion.
- 53. Inertia control using overlapping EM waves
- 54. Contra-gravity & inertia neutralization k phase conjugate
- 55. Phase conjugate phased antenna array • EM energy density gradient creates radiation pressure differential across disc • Energy gradient augmented by graviton beam formation beneath antenna disc
- 57. Book Details: Author: Larry Reed Pages: 710 Publisher: BookLocker Language: English ISBN: 978-1-63492-964-6 paperback Publication date: 2019-01-13
- 58. 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. Quantum Wave Mechanics
- 59. To order print copies of this book, contact: https://booklocker.com/10176 https://booklocker.com/books/10176.html or https://www.amazon.com/Quantum-Wave-Mechanics-Larry-Reed/ dp/16349249640/ref=sr_1_1 Quantum Wave Mechanics