The document discusses the nature of photons and electromagnetic waves. It describes a photon as a self-sustaining, traveling electromagnetic wavepacket that propagates at the speed of light. A photon is also characterized as a spin wave with quantized spin angular momentum. Photons are interpreted as disturbances in a quantum vacuum composed of Planck mass dipoles, with the electric field representing an alignment of these dipoles and the magnetic field representing their vortical motion. Electromagnetic wave propagation, reflection, refraction, and diffraction are also examined in the context of the quantum vacuum.

1. Photon

2. Freely propagating photon
• A freely propagating photon
is a self-sustaining, traveling
electromagnetic wavepacket
in a polarizable vacuum moving
at the velocity of light.
• A photon is described as a
spin wave of helical geometry
with quantized spin angular
momentum and classified as
a stable, massless, spin 1 boson.
• Photons are elementary
excitations of the normal
modes of the electromagnetic
field with quantized energy.

3. Photon represented as a vacuum excitation
• A photon is interpreted as a spin wave
disturbance in a quantum vacuum
composed of Planck mass dipoles.
• The photon electric field component
represents a synchronous alignment
of positive and negative Planck
masses.
• The photon magnetic field component
represents a vortical motion of Planck
mass dipoles.
• The ratio of curvature and torsion
equals a constant for a freely
propagating photon wavetrain in a
zero curvature vacuum.

4. Wavetrain compression
• Wave pulse compression
results in high frequency
chirp.
• Chirp is produced as a
result of increased
refractive index n (= c0/c
= c0/vp) which is a
measure of increased
energy density.

5. Electromagnetic wave propagation
• Oscillating electromagnetic radiation field of a ½ wave dipole antenna.

6. Electric & magnetic field strength variation
• E and H field phase lag
varies with distance
from emitter.
• Phase lag falls to zero
in the farfield region.
• Electric field E and
Magnetic field H are
orthogonal to each
other but out of phase
in the nearfield region.

7. Radiation field of an oscillating doublet
• Flux lines close off and detach in the nearfield Fresnel radiative zone.

8. Radiation field of a rotating oscillating doublet
• Electric flux lines in the radiation field of a rotating dipole antenna.
• The pair of wavefront spiral arms represent an entangled state.

9. Wave impedance vs. Wavelength
• Wave impedance (Z0) of
electric and magnetic fields
in free space. In the farfield,
radiation resistance ≃ 377 W.
• In the nearfield, impedance
is reactive and E and H fields
are out-of-phase. Once the
flux lines close off, they are
separated from the sources
charges. Farfield radiation
is due to retarded potentials.
• The cutoff wavelength of the
vacuum is taken as the Planck
length lP (= 1.616 x 10-35 m).

10. Wave front propagation
• Plane waves in isotropic
media have in-phase
wavefronts perpendicular
to the direction of
propagation. Wave
vector k is aligned with
the Poynting vector S.
• Plane waves in anisotrpic
media have wavefronts
inclined to the direction
of propagation. Wave
vector k is not aligned
with the energy flow
Poynting vector S.

11. Wave dispersion
• In a non-dispersive medium,
pulse envelope remains
unchanged.
• In a dispersive medium,
pulse envelope is stretched
and amplitude is decreased.
• In an anomalous dispersive
medium, pulse envelope
is distorted with a pulse
peak retardation. Front
velocity of the propagated
signal equals the speed of
light, hence, causality is
preserved.

12. Photon polarization states
• Polarization state represented by a Stokes vector in a Poincaré sphere.

13. Planck quantum vacuum
• Wave dynamics of Planck scale quantum vacuum BEC superfluid composed
of positive and negative Planck masses.

14. Soliton kink spin wave
• Soliton kink spin density
wave in the quantum
vacuum composed of
Planck mass dipoles.
• A photon represents a
self-sustaining spin wave
disturbance in a Planck
quantum vacuum.
• Synchronous alignment
of Planck mass dipoles
generates an E field.
Spin alignment of dipoles
generates an H-field.

15. Soliton twisted ribbon model
• Soliton twisted ribbon model of spin aligned Planck mass dipoles.
• A spinning Planck mass dipole constitutes a mass current generating a
magnetic vector potential.

16. Photon wavetrain
• Soliton confinement in an optical
waveguide composed of oriented,
polarized Planch mass dipoles.
• Outside the speed of light boundary
of the wavetrain, the Planck dipoles
can no longer remain synchronized
and become depolarized with
random E-field orientation.

17. Electromagnetic spectrum
• Wavelength, frequency and energy of the electromagnetic spectrum.
• Maximum theoretical vacuum cut-off frequency corresponds to the Planck
frequency (fP = 2.95 x 1042 Hz).

18. Logarithmic spiral
• Hyperbolic energy spiral of of frequency vs. wavelength. Diagonal lines
represent Fibonacci Phi F damping ratios.

19. Logarithmic (Hyperbolic) frequency spiral
• Scaling of frequency & wavelength of matter and energy follows
a logarithmic spiral progression.

20. Photon curvature & torsion
• For a freely propgating photon,
helical curvature and torsion
are equal.
• In a refractive medium of
increased energy density, the
change in index of refraction
n (= c0/c) produces a change
in torsion t and curvature k.
• The effective mass of a photon,
increases in a medium of
increased refractive index
while the torsion and velocity
decreases.

21. Induced polarization
• Comparison of induced polarization due to an applied electric field
for a generalized linear and nonlinear medium.

22. Anharmonic frequency response
• Electric field induced polarization of a nonlinear optical medium
results in anharmonic frequency response distortion.

23. Dielectric frequency response

24. EM wave reflection
Comparison of reflection from a
conentional polished mirror and
a phase conjugate mirror.
• A virtual image corresponds to a
negative location in space.
• A phase conjugate reflection
corresponds to a time-reversed
image.

25. EM wave reflection & refraction
• Reflection and refraction of plane
polarized light from and within an
optically dense medium.
• High reflectance occurs when
incident wavelength >> plasmonic
wavelength of resonant surface
electrons.

26. EM wave polarization & internal reflection
Polarization by reflection and total
internal reflection of light.
• Radiation pressure equals the
energy density of the wave incident
normally on a perfectly absorbing
surface.
• For a perfectly reflecting surface,
radiation pressure doubles.

27. EM wave retro-reflection and
phase conjugate reflection
• Retro-reflection may be effected
by a retroreflector such as a corner
cube, cat’s eye spherical reflector
or phase conjugate mirror.
• Retro-reflection reflects light back
to the source with a minimum of
diffuse scattering.

28. Fabry-Pérot interferometer
• Finesse is a measure of
the measure of the
interferometer’s ability
to resolve closely spaced
spectral lines.
• Internal absorption of
energy reduces the
sharpness of the filter
transmission peaks.
• The distance between
peaks is termed “Free
Spectral Range (FSR)” of
the filter.
• FSR is defined as the
change in wavelength
necessary to shift the
fringe pattern by one
fringe (FSR = l2(2n·d)).

29. Negative refractive index
• Comparison of a phase conjugate mirror (PCM) and a
negative refraction index material (NIM)

30. Bessel beam formation
• Bessell beam produced by diffraction of incident Gaussian beam by axicon lens.

31. Huygens-Fresnel diffraction principle
• Huygens-Fresnel diffraction with secondary wavelets reflecting off
scattering centers generating a deflected wavefront.

32. Bragg diffraction of EM waves
• Bragg diffraction of EM waves by crystalline planes of atomic scattering centers.

33. Bravais lattice formed by EM wave interference
• Bravais lattice reflection by scattering centers formed by EM wave
interference nodes.

34. Fresnel zone plate
• A zone plate is based on diffraction rather than refraction or reflection
and selectively blocks incident radiation for focusing.

35. Spherical Luneberg lens
• A Luneberg lens is a type of GRIN lens
formed of concentric graded dielectric
shells, metallic/ceramic matrix or
printed circuit metamaterials and able
to focus planar wavefronts to a point
or convert spherical wavefronts to
planar wavefronts.
• An invisible lens refracts an incident
planar wavefront a full turn such that
the transmitted beam is in the
direction of the incident beam with
the same phase.

36. Spherical Eaton lens
• An Eaton lens is a type of gradient
refractive index lens that is an
omnidirectional retroreflector.
• A spherical Eaton lens has a radially
symmetric refractive index of one
at the outer boundary and high
refractive index which can approach
infinity at the center singularity.

37. Phase conjugation
• Under FWM, interference of a pump beam A1 and opposing pump (or signal)
beam A2 create a refractive index of grating of alternating grid of variation of
refractive index in a nonlinear medium as a result of Kerr/Pockels effects.

38. • An electromagnetic wave is propagating wave disturbance of a polarizable
quantum vacuum.
• 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

39. Non-rotating black hole in a polarizable vacuum
• Geodesic curvature is produced by gradient in energy density.

40. 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.

41. 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

42. 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

43. • 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 conversion factor 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

44. 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

45. 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

46. Gravitational potential well & frequency hill
• Tangent space representation of EM frequency hill and gravitational well.

47. Variation in Earth’s gravitational gamma
& Vacuum refractive index
• Calculated gravitational gamma G, gravitational magnitude bg and vacuum
refractive index KPV(r,w,M) as a function of Earth radius Re.

48. Acceleration of gravity g and frequency shift Dn
vs. distance from Earth
• Variation of acceleration of gravity g and standing wave frequency shift
Dn as a function of Earth radii.

49. Nonuniform gravitational well and frequency hill
of a spherical mass

50. Frequency shift in a gravitational field
• Acceleration of a standing wave
oscillator pair in a gravitational
field g = 2cDn.
• In the Pound-Rebka experiment
utilizing the Mössbauer effect,
the gravitational shift of emitted
gamma rays is offset by the
relativistic Doppler shift of the
source resulting in a frequency
ratio Dn/n – gDH/c2 = 2.46 x 10-15.

51. Gravitational effects on EM fields
• Wavelength increase corresponds to apparent time dilation.
• Frequency increase corrends to apparent space contraction.

52. Gravitational field standing wave pattern
of a central mass

53. Gravitational lens
• Gravitational lensing by an obstructing mass in the line of sight of a
radiation source can produce an Einstein ring distortion or arc around
the obstruction as seen by an observer.

54. Graviton interactions
• Quantum vertex diagrams
of a massless spin-2
graviton formed by
interference of a photon
and a counter-propagating
phase conjugate photon.

55. EM standing wave interference lattice
• Interference anti-nodes act as scattering centers for an incident EM wave

56. Spin 2 Graviton gg*
• Graviton formed by coupling of photon and counter-propagating phase conjugate

57. Graviton curvature and torsion
• Graviton gg* is of helicoid geometry whereas photon g is a helix

58. Confinement of light
• Confinement of a traveling wave in a standing wave results in rest mass and inertia.
• Bosons are traveling waves while fermions are standing wave resonant structures.

59. Transformation of traveling wave into a standing wave
• A photon is a traveling wave of
helical geometry whereas an
electron is a standing wave of
toroidal geometry.
• Photons and electrons/positrons
may be interconverted in processes
of pair production & annihilation.

60. Electron/Positron formation from a photon

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

63. 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 of 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

64. To order print copies of this book, contact:
https://booklocker.com/10176
https://booklocker.com/books/10176.html
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https://www.amazon.com/Quantum-Wave-Mechanics-Larry-Reed/
dp/16349249640
Quantum Wave Mechanics