Einstein's General Theory of Relativity interpreted in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to an apparent space contraction as a result of a spectral energy density gradient. Matter in motion generates a de Broglie matter wave (contracted moving standing wave). An inverse effect of induced motion of matter by matter wave synthesis is predicted.

1. Gravitation

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

3. Gravitational flux

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

5. Newtonian 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

8. Normalized gravitational potential
Spherical mass M

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

31. Gravitational lens

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

36. Graviton interactions

37. Quantum gravity models

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.

54. Book Details:
Author: Larry Reed
Pages: 710
Publisher: BookLocker
Language: English
ISBN: 978-1-63492-964-6 paperback
Publication date: 2019-01-13

55. 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

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Quantum Wave Mechanics