Matter in motion with respect to an inertial frame exhibits internal Lorentz contracted moving standing waves. Rest mass and inertia result from confinement of electromagnetic energy as stored energy in standing wave resonances. The inverse effect of self-induced motion of matter may be potentially realized by utilizing synthesized red- and blue-shifted Lorentz Doppler waves in a phase conjugate four-way mixing process using parametrically amplified Lorentz Doppler pump beams to modulate a standing wave generating a matter wave producing self-induced motivided by direct conversion of EM pump energy into the contracted moving standing wave formed within a phase-locked cavity resonator. The imbalance of internal radiation pressure provides the ponderomotive force acting on the resonator. In this inverse effect, application of an external force to induce motion of matter is not required. on of a wave system without expulsion of reaction mass. Kinetic energy of motion is provided by direct conversion of pump beam EM energy into the contracted moving standing wave formed within a phase-locked cavity resonator. The imbalance of internal radiation pressure provides the ponderomotive force acting on the resonator. In this inverse effect, application of an external force or expulsion of reaction mass is not required to induce motion of matter.

1. Matter Wave Propulsion

2. de Broglie matter waves
• Light is a self-sustaining traveling wave of electromagnetic energy.
A photon is described as a spin 1 boson with helicoid geometry and
represents a freely-propagating spin wave disturbance in a polarizable
vacuum.
• An electron consists of an energetic photon confined within a deep
potential well in the quantum vacuum. An electron is described as
as a spin ½ fermion with toroidal geometry and forms a closed-loop
standing wave resonator.
• Matter consists of stored electromagnetic energy topologically bound
within in standing wave resonant structures such as electrons and
aggregate composites such as protons, neutrons, atoms and molecules.
Confinement of radiation creates rest mass and inertia.
• Motion of matter with respect to an inertial reference frame creates
de Broglie matter waves which are contracted moving standing waves.

3. • An external force applied to a standing wave resonator generates internally counter-
propagating Lorentz-Doppler shifted waves resulting in contracted moving standing
waves within the resonator inducing motion due to radiation pressure imbalance.
Velocity is proportional to the phase difference of the red- and blue-shifted beams
while acceleration is proportional to the frequency difference.
• The inverse effect of self-induced motion of matter may be potentially realized by
utilizing synthesized red- and blue-shifted Lorentz Doppler waves in a four-way
mixing process using parametrically amplified Lorentz Doppler pump beams to
generate self-induced motion of a wave system without wheels, friction or expulsion
of reaction mass. Kinetic energy of motion is provided by direct conversion of
electromagnetic energy in the pump beams to the contracted moving standing wave
formed from the signal wave and its phase conjugate wave within a phase-locked
cavity resonator.
• Inverse effects are not without precedent as, for example, inverse Doppler effect,
inverse Sagnac effect, inverse Faraday effect, inverse Compton effect, inverse spin
Hall effect, inverse Cherenkov effect, inverse Raman effect, inverse Cotton-Mouton
effect, inverse Barnett effect, (Einstein de Hass effect), inverse piezo electric effect,
etc.
Matter wave synthesis

4. Confinement of traveling EM waves
• Confinement of traveling electromagnetic waves within a
phase-locked cavity resonator creates rest mass and inertia.

5. Self-referral dynamics of radiation trapped
in a phase-locked resonator

6. Contracted moving standing wave

7. Lorentz contraction of a standing wave
resonator in motion
• Matter in motion undergoes a Lorentz
contraction in the direction of motion
as a result of increased EM flux density
• Inertial mass and gravitation mass are
equivalent as both arise from the same
causal mechanism: Motion into regions
of increased energy density.

8. Equivalence of positive & negative
gravitational and inertial mass

9. Wave motion represented as Riemann
sphere projections onto a complex plane
• Mappings on the complex plane in the form of Möbius transformations
correspond to Lorentz transformations.

10. Toroidal electron model
Parameter Symbol Relation Value Units
Electric charge e = F/E = mwC =
√(aqP
2)
1.60217E-19 C
Mass me
= E/c2 = ħc/RC =
e/wC
9.10938E-31 kg
Compton wavelength lC = h/mc = h/p 2.4263E-12 m
Compton frequency fC = mc2/h = c/lC = wC
/2p
1.2355E20 Hz
Compton radius: RC = lC/2p = aa0 =
√(E/mw2)
3.8616E-13 m
Compton angular
frequency
wC = c/RC = mc2/ħ =
e/m
7.7634E20 rad/s
Zitterbewegung angular
frequency
wzbw
= 2wC 1.5527E21 rad/s
Spin angular momentum s = ½ ħ = iw =
½meRC
2w
5.2725E-5 J∙s
Bohr magneton mB = e ħ /2m 9.274E-24 J/T
Rest Energy E = ħ c/RC 8.187E-14 J
• Toroidal electron formed
by a high energy photon
topologically confined
inside the Compton radius.
• Propagation of the rotating
spin wave describes a
current loop equal to ½
of Compton radius.
• Charge path rotation
generates toroidal swept
volume defining a standing
wave resonator. Internal
pressure equals external
vacuum pressure.

11. Electron ring configuration
• Electron depicted as a
precessing epitrochoid
charge path composed of
two orthogonal spinors of
2:1 rotary octave
• Spin ratio of Compton
angular frequency wC and
Zitterbewegung frequency
wzbw (= 2wC) corresponds
to observed spin ½.
• Electric charge arises as a
result of a slight precession
of angular frequency we/m.

12. Electromagnetic energy E vs. Lorentz factor g
After Bergman
The Lorentz factor g is inversely proportional to the Lorentz contraction g.
g = 1/√(1 – v2/c2) = 1/√(1 – b2) = 1/g
Electromagnetic energy of an electron as a function of Lorentz factor g.

13. Electron mass energy MeV/c2 vs. Velocity ratio b
Relativistic increase in electron mass energy as a function of velocity ratio b (= v/c)

14. Contracted moving standing wave

15. Constant wave energy phasor
Traveling wave, standing wave and contracted moving standing waves

16. Contracted moving wave diagram for an
electron moving @ 0.5 c
Compton, Lorentz Doppler and de Broglie wave components

17. EM cavity resonator equivalent LC circuit
• A lossless electromagnetic cavity resonator and equivalent LC circuit.
• The electric and magnetic energy are in phase quadrature.
• A resonant system must contain at least one element in which kinetic
energy is stored and another element in which potential energy is stored.

18. Impedance and energy triangle comparison
• Mass and electrical impedance are measures of resistance to energy flow.

19. Resonator velocity staircase
A Minkowski spacetime diagram illustrating a phased-locked
standing wave resonator in wave resonator

20. Coupled standing wave resonators

21. Mass current effects

22. EM wave reflection/diffraction from
Bragg planes formed by EM wave interference
• Phase conjugate beam formation in four-way mixing of signal & pump beams

23. EM wave-based propulsion
• EM drives have long been envisioned and various forms have been
demonstrated. To realize propulsion without traction or expulsion of
reaction mass what sort of energy conversion would be required? Do
we not understand sufficiently the physics of force fields and wave
mechanics to at least to begin to set forth some notional theoretical
concepts? What sort of energy conversion would be required?
• Energy is a measure of wavefunction curvature and may be conveyed in
waves. Consider what sort of wave transformation is needed. Waves
occur in any of several forms including:
1) traveling waves
2) standing waves
3) transverse waves
4) longitudinal waves
5) partial standing waves
6) contracted moving standing waves
7) coherent waves
8) soliton waves

24. Irradiated phase-locked phase conjugate resonator
• Conceptual diagram for induced motion of a phase-locked resonator with
a phase conjugate reflector irradiated by amplified Lorentz-Doppler shifted
pump beams modulating a standing wave generating a ponderomotive force.

25. Phase-locked phase conjugate resonator
induced motion
• Simulated Lorentz-Doppler effect results in a contracted moving standing wave.
• The internal radiation pressure imbalance results in a net ponderomotive force.
• Pump beam energy input provides the kinetic energy of motion.

26. Wave system resonator at constant velocity
• Displacement of phase triggers shifting of standing wave nodes.
• Mass transport is a result of node displacement of contracted
moving standing waves.

27. Induced motion of wave system resonator
• Contracted moving standing waves created by superposition
of Lorentz-Doppler shifted modulated standing waves.

28. Self-induced motion of wave system resonator
• Velocity v is proportional to
phase difference (= Df·c/p)
• Acceleration a is proportional
to frequency difference (= 2c·Dn)
• Energy flow is in the direction of
the frequency gradient. Pump
beam energy is converted directly
into kinetic energy of motion.
• Very high velocity and acceleration
possible with no expulsion of
reaction mass
• Electromagnetic energy contained
within resonator(s). Low external
observables.

29. Phase conjugate resonator array

30. Push-pull cavity phase conjugate resonator
• Direction of motion may be rapidly changed by redirecting the vector
orientation of the incident and phased array conjugation beams enabling
levitation and high acceleration, darting, zigzag motion without expulsion
of reaction mass. Amplified pump beams provide energy of motion.

31. Broad band frequency phase conjugate
resonator system
• High internal radiation pressure
provided by high frequency
standing wave modulation over
a wide frequency range.
• Amplified synthesized Lorentz-
Doppler shifted pump beams
modulates a standing wave in
a phase conjugate resonator to
generate a matter wave inducing
motion of the wave system.
• Energy of motion is proportional
to the number of frequency pairs
DEi = nhDni.

32. Gravitational spectral energy density gradient
subject to electronic augmentation and control
• Acceleration is proportional to the frequency differential Dn.

33. Paired overlapping multi-band swept frequencies
with discrete frequency differential
• Available energy is proportional to the number of frequency pairs (DEi = nhDni)
• Acceleration induced inertial strains are reduced by minimizing jerk (Da/Dt)

34. Inertia control
• Under uniform acceleration, there is no relative movement of particles
of matter. As a result, stresses and strains due to changes in acceleration
are zero. In a free-fall weightless condition, residual stresses are due to
tidal deformation.
• Application of an external force results in a localized impact wave of
progressive acceleration/deceleration inducing localized stresses and
strains. Sudden acceleration or deceleration as in a collision can result
excessive strains above the elastic limit leading to catastrophic structural
failure, e.g. “Humpty Dumpty” problem.
• Effects of sudden acceleration or deceleration may be mitigated by
absorption of energy by shock absorbers to prevent localized yielding or
buckling or by inertial dampers converting linear momentum into angular
momentum or vice versa.
• To prevent excessive acceleration or deceleration forces, the time
rate-of-change of acceleration , i.e. jerk (= Da/Dt) must be minimized.
Using paired, overlapping, swept EM frequencies, acceleration and
acceleration rate may be controlled to minimize stresses and strains.

35. Inertial damper
• Linear momentum converted
to rotary momentum in a
whispering gallery mode (WGM)
resonator.
• Electro-optic analog of a
mechanical rack & pinion
or shock absorber. Electro-
magnetic wave energy is
temporarily stored in the
resonator and released.

36. Inertia control using overlapping EM waves

37. Contra-gravity & inertia neutralization

38. Acceleration induced thermal spectrum
• Intensity of observed EM spectrum is greater in an accelerated frame than
one at rest and is proportional to the cube of frequency.

39. Phase conjugate simulated Doppler shift
• Phase conjugate by degenerate
four-wave mixing requires a
signal, phase conjugate and two
pump beams.
• Pump waves at simulated Doppler
red- and blue-shifted frequencies
acting on a phase conjugate
reflector in a nonlinear medium
may be used to modulate a signal
beam standing wave to generate
a matter wave to induce motion
of a resonator.
• Synthesis of de Broglie matter
waves to induce motion is the
inverse effect of motion of matter
inducing matter waves.

40. Tractor/repulsor beam operation
• Phase conjugate standing wave levitation with multi-phase, multi-frequency
oscillator array.
• Levitation is accomplished by neutralization of the gravitational frequency
differential Dn = g/2c.

41. Synthesized Doppler frequency
phased array antenna
• Synthesized Doppler phased
emitter array antenna disc
with agile beam steering and
focusing.

42. Tractor/repulsor beam generated by
phase conjugate phased array antenna
• Attraction and repulsion is
determined by direction of
contracted moving standing
wave vectors.
• Direction is controlled by
relative phase and frequency
of the synthesized Doppler
signals fed to the emitter
array.
• The phased array allows
control of the beam boresight
direction, focus length,
intensity, and wave front
contour.

43. Tilt-edge suspension modes
• Tilt-edge & on-edge suspension
hover modes enabled with
opposed, contracted moving
standing waves in a
tractor/repulsor, tractor/tractor
or repulsor/repulsor mode
configuration.
• Chromatic focusing results in a
frequency gradient along the
boresight augmenting tractor/
repulsor beam effect.

44. Triangular plan form vehicle
concept
• Phase conjugate push-pull
cavity resonators and phased
array push-pull phase conjugate
grappler beam

45. Nonlinear ultra-wideband fractal
cross-field antenna concept
• Endfire cross-field fractal antenna with rectangular waveguide

46. Augmented spectral energy density profile
• Modification of naturally occurring spectral energy density enables alteration
of local acceleration of gravity

47. Neutralization of gravity by EM
energy density gradient inversion

48. Phase array beam operating modes
• Horizontal and vertical flight
accomplished with either
repulsor or tractor beams or
in combination.
• Sustained hover accomplished
with a combination of tractor
or repulsor beams, dual
repulsor or dual tractor beams.
• Near the ground, intensity of
phase conjugate beam is
augmented by reflected ground
return.
• Objects located within the beam
focus will tend to attracted or
repelled with the tractor/repulsor
engaged

49. Phase conjugate cavity resonator cell
• Double-ended phase conjugate
cavity resonator includes a
nonlinear, high K, polarizable,
phase conjugate medium.
• EM radiation may be confined
within a dielectric resonator by
abrupt change in permittivity
and reflected by the large
change in conductivity by the
walls of a metallic cavity
resonator.
• Nonlinearity may be augmented
if the energy input interval is on
the order of the system critical
reaction time.

50. Horizontal motion – level flight
• Planar array wave system
composed of n-element
phase conjugate, phase-
locked resonators.
• Horizontal velocity is
controlled by varying the
relative phase of two
counter-propagating
moving standing waves.
• Horizontal acceleration
is controlled by varying
the frequency difference.

51. Induced gravitomagnetic field
• Radially outward directed EM
waves creating a synthesized
gravity-Poynting energy flow
Sig (= - gi x Hg) opposing the
gravito-Poynting energy influx
Sg (= - g x Hg).
• Angular rotation of a standing
wave corresponds to a mass
current loop gravitomagnetic
field. Result torsion field is
equivalent to a co-gravitational
field K inducing an acceleration
in the axial direction perpendicular
to the disc plane. K = (g x v)/c2 =
(2cDn x c)/c2 = 2Dn

52. Gravitational dipole self-induced motion
• Hypothetical gravitational
dipole of positive and
negative mass accelerates
in the direction of the field
gradient from negative and
positive mass.
• A changing gravitomagnetic
mass current loop generates
a net acceleration from the
virtual negative mass pole
towards the virtual positive
mass pole.
• Two coupled, coaxial,
gravito-magnetic loops
generates a net acceleration
in the direction of the
inertial moment.

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 occurring 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