Matter Wave Synthesis

1. Matter wave synthesis

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 as a result of • wave function interference. • Motion of matter with respect to an inertial reference frame creates • de Broglie matter waves which are contracted moving standing waves.

3. Matter wave synthesis • 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.

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 • Gravitational and inertial mass result from acceleration into regions of • increased EM energy density and represent EM wave interference.

9. Falling resonator matter wave

10. 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.

11. Toroidal electron model Toroidal electron model

12. 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.

13. Electromagnetic energy E vs. Lorentz factor g Electromagnetic energy of an electron as a function of 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

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

16. Contracted moving standing wave

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

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

19. 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.

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

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

22. Coupled standing wave resonators

23. Mass current effects • Gravitational field of a mass in motion undergoes a Lorentz contaction. • Mass motion represents mass current analogous to electric current

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

25. 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.

26. Lagrangian and Hamiltonian • Representation of a deBroglie matter • wave (contracted moving standing • wave). • Lagrangian interaction energy equals • kinetic energy minus potential • energy. Mass is a measure of wave • function interference. • Trajectory path is a geodesic in which • the action is minimized. Action is • defined as the integral of velocity • along spacetime interval. • Least action path is the result of • destructive interference of EM waves.

27. Standing wavefront aberration • A standing wave resonator in motion • undergoes aberration altering the wave • front direction of transverse traveling • waves toward the direction of motion. • A standing wave system in motion travels • at velocity < c due to the longer zigzag • light path travelled than a freely • propagating wave at velocity c. Hence. • a decrease in resonator size is required • for increased velocity, e.g, fermionic • matter.

28. Lorentz Doppler shift and co-moving aberration Lorentz Doppler shift of a moving object @ 0.5c compared to relativistic aberration as observed in a co-moving reference frame.

29. Matter Wave Resonator • Mass oscillator wave • system consisting of two • interacting source • oscillators generating a • standing wave. • Once disturbed from an • equilibium, consonant • rest state to a dissonant • state, the nodal end • point(s) undergo phase • displacement towards • the displaced toward • potentialminima to re- • establish resonance.

30. 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

31. 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.

32. 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.

33. Example wave types

34. Comparison of traveling, standing and moving standing waves • Motion of the driven quantum system alters the internal wave function. • A phase-locked state has identical mean phase velocities. • Lorentz-Doppler frequency shift alters the accumulated phase of the matter wave • function resulting in a change in resonator motion.

35. Standing wave resonator set in motion by external force The impulse generates an internal radiation pressure imbalance inducing wave system motion.

36. Standing wave resonator set in motion by internal force A ponderomotive force results from an internal radiation pressure imbalance.

37. Shepard-Risset-glissando phased matter waves • Shepard-Risset-glissando phased matter waves allow increased thrust and control of rate-of-change of acceleration. • Overlapping matter waves allow uniform acceleration/deceleration and minimization of catastrophic jerk and avoidance of excessive stresses and strains.

38. Matter wave propulsion characteristics • De Broglie matter waves are physical and are the result of motion of matter. • The inverse effect of self-induced motion of matter may be realized by matter • wave synthesis without expulsion of reaction mass.

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

40. 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.

41. Phase conjugate resonator array

42. 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.

43. 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.

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

45. 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)

46. 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.

47. 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.

48. Inertia control using overlapping EM waves

49. Contra-gravity & inertia neutralization

50. Matter wave propulsion flight vehicle concept Phase conjugate push-pull cavity resonators and phase conjugate push-pull grappler