Classifications

• • G—PHYSICS
  • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
  • G21K—HANDLING OF PARTICLES OR IONISING RADIATION NOT OTHERWISE PROVIDED FOR; IRRADIATION DEVICES; GAMMA RAY OR X-RAY MICROSCOPES
  • G21K1/00—Arrangements for handling particles or ionising radiation, e.g. focusing or moderating
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
  • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
  • Y02E30/00—Energy generation of nuclear origin
  • Y02E30/10—Nuclear fusion reactors

Definitions

• the present invention relates to methods and apparatus for providing repulsion, in particular methods and apparatus for providing antigravitational repulsive forces adapted to provide propulsion and levitation.
• G is the gravitational constant, its value being 6.67 ⁇ 10 -11 Nm 2 kg -2 .
• General Relativity is a partial theory in that it deals with matter on cosmological scale, but not an atomic scale. All gravitating bodies are composed of matter and are collections of atoms which are composed of fundamental particles such as electrons, which are leptons, and quarks which make up protons and neutrons. Gravity originates form the fundamental particles.
• the prevailing theory of the properties of atoms and subatomic physics is quantum mechanics, and the unification of quantum theory with General Relativity is a notoriously problematic union. In contemporary theories there is no satisfactory theory of quantum gravity, and even the simplest application of quantum mechanics to the geometric structure of spacetime faces serious conceptual difficulties. Implicit to its success is that the quantum gravity theory must specify the cosmological constant.
• the cosmological constant can be defined most simply as the energy density of a vacuum, that is, the amount of energy in a unit volume of empty space.
• the gravitational equation which contains the cosmological constant is (Eq. 52.08) of Appendix VI. According to quantum mechanics the value of the cosmological constant may not be zero, and in principle, the vacuum energy density can assume any value positive or negative, and current ideas about particle physics and gravity suggest that it is quite large.
• the cosmological constant can be approximately measured by looking for the
• the effects of gravity preclude the existence of inertial frames in a large region, and only local inertial frames, between which relationships are determined by gravity are possible. In short, the effects of gravity are only in the determination of the local inertial frames.
• the frames depend on gravity and the frames describe the spacetime background of the motion of matter; therefore, differing from other kinds of forces, gravity which influences the motion of matter by determining the properties of spacetime is itself described by the metric of spacetime.
• the gravitational method and apparatus of the present invention provides a metric over all scales form atomic to cosmological where the cosmological constant is zero. It is demonstrated that gravity arises form the two-dimensional manifold of the mass of fundamental particles that makes up all matter of the universe.
• the novel model of the atom is consistent with first principles, and is
• the electron is described by the product of two angular functions which are spherical harmonics, a time harmonic function, and a radial delta function forming specific radially quantized orbitals.
• these radially quantified orbitals are referred to as "Mills" orbitals.
• Mills orbitals When applied to atomic structure, Mills orbitals are electron orbitals. Angular momentum and energy are conserved without violation of Maxwell's equations.
• the energy of an electron is the sum of its stored electric and magnetic energies. From the radial delta function, the wavelike properties of the electron arise naturally.
• the angular harmonics give rise naturally to spin and orbital angular momentum, spin-orbital coupling and selection rules for the absorption of emission of electromagnetic radiation.
• a Mills orbital is spherical, and the radius increases with the absorption of electromagnetic energy. When the electron is ionized the radius of the Mills orbital goes to infinity; the electron is a plane wave with the de Brogue wavelength.
• the electric field of an electron of a Mills orbital is zero inside the orbital and is the field at a point charge at the origin outside of the orbital; thus, electron-electron repulsions are naturally eliminated in multi-electron atoms.
• the radii of orbitals in atoms are calculated for each orbital by setting the centripetal force equal to the sum of the coulombic and magnetic forces.
• the result that isolated Mills orbitals are stable where the coulombic attractive force does not cause the electron to collapse into the nucleus arises naturally.
• there exists a central coulombic force acting on each orbital that is proportional to the net charge (that is the charge not cancelled by other electrons).
• a positive central force exists between two unpaired electrons which results in pairing in the same shell with spins opposed.
• the electric field of the electron is spherically symmetric and is that of a point charge for radial distances greater than the radius of the radial delta function and is zero inside the shell.
• This is the basis of chemical bonding and low temperature fusion, as described in the incorporated patent application.
• the nature of the chemical bond is an overlap of Mills orbitals of participating atoms to produce a minimum of the energy stored in the electric and magnetic fields.
• Cold nuclear fusion occurs as a result of cancellation of the coulombic repulsive force between two nuclei for shorter internuclear distances as the shell of the individual atomic electrons decreases by a quantized fraction as an energy hole is resonantly absorbed by the electron.
• the resonance shrinkage energy is n/2 27.21 eV where n is an integer.
• the novel atomic model deals with electrons which comprise the negatively charged fundamental particles, leptons.
• the same principles apply to the other fundamental particles including quarks.
• the phenomena of wavelike properties, spin and orbital angular momentum, and selection rules are identical to those of leptons as is the boundary conditions which precludes radiation; thus, quarks have equivalent spacetime charge density functions as leptons.
• the weak and strong nuclear forces are electromagnetic in nature as is the spin-pairing, diamagnetic, and bonding forces of leptons.
• Mass exists as Mills orbitals, each of which comprises the product of two spherical harmonic angular functions, a time harmonic function, and a radial delta function.
• Mills orbitals As leptons and quarks which exist in curved spacetime, all macroscopic configurations of ordinary matter exist in curved spacetime. Furthermore, the total curvature of spacetime is the sum of the contributions from each Mills orbital, termed a "Mills" orbital as defined in the previously filed applications.
• Mills orbitals which comprise mass confined to a three-dimensional spacetime.
• the surface is spherical; thus, the spacetime is curved with constant curvature.
• the effect of this "local" curvature on the non-local spacetime is to cause it to be Riemannian as opposed to Euclidean.
• the effect is a function of the radial distance from the center of the Mills orbital for distances greater than the radius of the Mills orbital and the magnitude of the effect on non-local spacetime is proportional to the total mass of the Mills orbital.
• the effect on spacetime is independent of the Mills orbital radius for spacetime outside of the orbital.
• this feature is symmetrical with the electric field of an electron of a Mills orbital which is that of a point charge at the center for radial distances greater than the radius of the shell.
• the novel atomic theory embraces the postulate that the total mass of the orbital is also equivalent to the inertial mass from which the theory of General Relativity comprising Riemannian geometry of spacetime is derived.
• T ⁇ v is the stress-energy-momentum tensor of matter.
• the Schwarzschild metric is the solution of the boundary value problem of
• the present invention unites the three forces, electromagnetic, gravitational, and mechanical and permits their interconversion.
• the Meisner effect is the phenomenon whereby a superconductor of the present invention converts a gravitational force into an electromagnetic force, and the energy of the strong nuclear force is released as heat during Coulombic Annihilation (cold) Fusion as discussed in the above incorporated prior patent applications.
• the heat produces electricity directly via a thermionic of photovoltaic generator, or the heat produces a
• the electricity provides an electromagnetic, electrostatic, or magnetostatic force which by a device of the present invention warps matter into negative curvature such that an antigravitational force is produced with a gravitating body.
• the antigravitational force provides mechanical force, useful for propulsion or levitation.
• the preferred embodiment of the present invention is a propulsion and levitation device comprising a source of matter, a means to form the matter into a spatial two-dimensional manifold of negative curvature, and a means to produce a force on the negatively curved matter where the force balances the repulsive gravitational force between the negatively curved matter and a gravitating body.
• the matter of negative curvature moves at constant velocity to produce useful work against the gravitational field of the gravitating body where the constant velocity including zero velocity, provides the spacetime manifold of negative curvature which is a solution to the three-dimensional wave equation whose spacetime Fourier transform does not contain components synchronous with waves traveling at the speed of light. Therefore, the manifold is nonradiative.
• the spacetime manifold is based on the present novel atomic model which unites Newtonian mechanics, Maxwell's equations, atomic theory, General
• the present invention of a propulsion and levitation apparatus comprises the conversion of an electromagnetic force to a gravitational force to a mechanical force, which provides a useful
• the electromagnetic force is provided by a generator driven by a mechanical force provided in response to steam, where binding energy of the strong nuclear force is converted to mechanical energy indirectly via steam, for example, or directly via a thermionic generator, for example.
• a generator driven by a mechanical force provided in response to steam where binding energy of the strong nuclear force is converted to mechanical energy indirectly via steam, for example, or directly via a thermionic generator, for example.
• the antigravity propulsion and levitation means comprises a means to inject particles, such as electrons, as plane waves, which serve as the matter, and further includes a guide of the plane waves.
• Negative curvature of the injected and guided matter is effected by applying a force on the matter.
• the applied force is provided by one or more of an electric field, a magnetic field, or an electromagnetic field.
• a second force on the negatively curved matter is applied in the direction of the gravitational force. This second force is provided by one or more of an electric field, a magnetic field or an electromagnetic field.
• the force in the gravitational direction is equal to the repulsive, antigravity force which develops between the gravitating body and the matter due to the negative curvature of the guided matter.
• the repulsive force of the gravitating body is then transferred to the guide (source of the second force) which further transfers the force to the attached structure to be accelerated or levitated.
• a vehicle to be accelerated comprises an antigravity levitating device and a flywheel which rotates about its axis.
• the antigravity force provides pure radial acceleration when the vehicle's
• Fig. 1 is a two-dimensional graph showing the cross-section of the magnetic potential and the corresponding magnetic field lines (arrows) at a point along the channel of guiding and field generating means of Fig. 4;
• Fig. 2 is a three-dimensional graph which shows the magnitude of the electric force in the z direction due to the electric potential function, xyz and the magnitude of the magnetic force in the z direction due to the magnetic potential function, xy where the electron beam propagates in the z direction;
• Fig. 3 is a graph showing the spatial two-dimensional curved manifold which is the Mills orbital that propagates along the channel of the electron guide means of Fig. 4;
• Fig. 4 is a drawing of a system of antigravity propulsion and levitation means according to one embodiment of the present invention
• Fig. 5 is a schematic of forces of gravitation, antigravitation, and angular momentum acting on a vehicle according to one embodiment of the present invention
• Fig. 6 is a drawing of an experimental apparatus according to one embodiment of the present invention to produce electrons of negative curvature with concomitant production of antigravity forces;
• Fig. 7 is a drawing which shows the distribution of negative curvature and antigravitational forces in a relativistic electron beam following a pass through a quadrapole magnetic triplet of the apparatus of Fig. 6;
• Fig. 8 is a block diagram of an antigavitational repulsion device powered by a Coulombic Annihilation (cold) Fusion system according to one embodiment of the present invention.
• the model of fundamental particles i.e., leptons and quarks
• the novel atomic model includes electrons which comprise the negatively charged fundamental particles, leptons.
• the phenomena of wavelike properties, spin and orbital angular momentum, and selection rules are symmetrical with those of leptons as is the boundary condition which precludes radiation; thus, quarks have spacetime charge density functions equivalent to leptons.
• the weak and strong nuclear forces are electromagnetic in nature.
• the nucleus comprises nucleons, the protons and neutrons. Each nucleon comprises three quarks as Mills orbitals analogous to the case of the electrons of the three-electron atom of the novel atomic model.
• the massive vector bosons W + , W-, and z 0 are spin-1 massive photons and are due to the weak nuclear force. W + and W- carry the energy of the spin pairing weak nuclear force and z 0 carries the energy of the diamagnetic weak nuclear force.
• the strong nuclear force binds quarks together in the proton and neutron, and binds the protons and neutrons together in the nucleus of an atom.
• the strong force is due to the field of a spin-1 particle called a gluon.
• the gluon is analogous to the standing traveling photonic wave that exists inside of a Mills orbital of a lepton when it absorbs a photon or an energy hole as described by the novel atomic theory.
• the gluon maintains the quarks in Mills orbitals and is responsible for force balance.
• the nucleon binding energy of the strong force which is released by Coulombic
• Annihilation Fusion of the novel atomic model is analogous to the energy released in the chemical bond as Mills orbitals overlap, and the total energy stored in the electric and magnetic fields is minimized.
• gluons and quarks are red, green and blue.
• Such a triplet constitutes a proton or a neutron.
• Matter/energy are interconnectable and are in essence the same entity with different boundary values imposed by spacetime where the matter/energy has a reaction effect on spacetime.
• the intricacy of the action/reaction is evident in that all matter/energy obeys the three-dimensional . wave equation, and the magnetic, coulombic, photonic, and gravitational fields can be derived as a boundary value problem of the wave equation of spacetime where space provides the respective force fields for the matter /energy. That spacetime is four-dimensional is evident because the fundamental forces of gravity and coulombic attraction which are time dependent have a one over distance squared relationship which is equivalent to the distance dependence of the area of a spherically symmetric wavefront which carries the forces at the limiting speed of light provided by spacetime.
• the action/reaction relationships of the third fundamental force, the mechanical force is given by Newton's Laws which provide the motion of matter including charged matter, which can give rise to gravitational, magnetic, and photonic fields.
• the action/reaction provided by forces in one inertial frame is given in a different inertial frame by the Lorentzian Transformations of Special Relativity which are valid for Euclidean spacetime and are a consequence of the limiting speed of light.
• the magnetic field in on inertial frame is given as a coulombic field, in another as a consequence of their relative motion.
• the presence of matter causes the geometry of spacetime to deviate from Euclidean which is manifest as a gravitational field.
• the gravitational equation is derived for all scales from the present novel atomic model where spacetime is Riemannian.
• a space in which the curvature tensor has the following form:
• the energy of a vacuum is zero; thus, the cosmological constant of the model is zero as demonstrated in Appendix VI.
• the present novel atomic model unifies atomic theory and gravitation on a cosmological scale. It is demonstrated in Appendix VII that the solution of Einstein's field equations as a boundary value problem of a Mills orbital unifies atomic theory and the General Theory of Relativity on an atomic level to provide a completely unified gravitational theory for spacetime of all scales. The application of the relevant equations are provided in Appendices VI and VII.
• the propulsive means comprises a source of fundamental particles such as electrons (which are leptons) where the fundamental particles are forced to be essentially plane waves of matter.
• the plane wave nature of matter results as a Mills orbital absorbs energy to cause the radius to go to infinity as described in the previous patent application.
• the plane waves of matter are accelerated and formed (or warped) into negative curvature by one or more of an electric field, a magnetic field or an electromagnetic field such as a laser beam applied parallel or transversely to the plan wave of matter or such as an evanescent field produced by a totally .internally refracted electromagnetic wave traveling in a fiberoptic cable.
• the antigravity force which arises is transferred to the source means of the fields and is further transferred to the structure to be accelerated or levitated due to the latter means rigid attachment to the structure.
• the force generated by the antigravity levitation/propulsion means can be calculated rigorously by solving Einstein's field equations as a boundary value problem for a three-dimensional spacetime manifold of negative curvature which is produced by the apparatus.
• forces in the limit can be obtained as follows.
• ⁇ of equation (57.37) The negative solution arises naturally as a match to the boundary condition of matter with negative curvature.
• matter having negative curvature would occupy a diminished quantity of four-dimensional spacetime, as compared to matter of positive curvature.
• the surface to volume ratio of a sphere is a minimum.
• ⁇ of equation (57.38) would increase. Consequently, the integral of equation (57.37) is approximately of the form
• s is the space defined by the boundaries of he matter of negative curvature.
• the presence of a three-dimensional spacetime manifold (spatial two-dimensional manifold) in four- dimensional spacetime results in curved nonlocal spacetime which is the origin of gravity
• a two-dimensional spacetime manifold (spatial one-dimensional manifold) in four-dimensional spacetime results in infinite gravity a singularity which is a black hole.
• the sign of the curvature For the case of negative curvature, the antigravity force with a gravitating body can be increased by increasing the intensity of negative curvature.
• the ionization energy can be provided by applying a large potential to or by heating or irradiating a cathode.
• photocathodes irradiated with continuous wave or pulsed lasers can generate very bright, high current density beams of electrons.
• Photocathodes, thermionic cathodes, and cold cathodes are described by Orttinger, P., et al., Nuclear Instruments and Methods in Physics Research, A272, 264-267 (1988) and Sheffield, R., et al., ibid, 222-226 which are incorporated herein by reference.
• the resulting plane waves are caused to propagate through space and to acquire negative curvature by traversing a selected field as created by a field source means.
• the field source means provides one or more of an electric field, a magnetic field, or an electromagnetic field.
• the resulting spacetime manifold is three-dimensional (spatial two-dimensional manifold and time dependent) and is a solution to the three-dimensional wave equation that follows:
• the manifold propagates through space and is decelerated by the antigravity force with a gravitating body and is accelerated by the propagation force provided by the source means.
• the resulting spacetime manifold of negative curvature which arises from the forces acting on the matter is such that its spacetime Fourier transform does not possess waves synchronous with those traveling at the speed of light.
• the manifold is a Mills orbital which provides an antigravitational force.
• Matter (as a Mills orbital) of negative curvature which moves at constant velocity has a spacetime Fourier transform which does not possess Fourier components synchronous with waves traveling at the speed of light.
• F(k x ) and G(k y ) is the Fourier transform of f(x) and g(y), respectively.
• v z is constant velocity in the z direction at force balance.
• the manifold is produced by a quadrapole electric field at infinity or a quadrapole magnetic field at infinity, and a constant force of equal magnitude and opposite direction of the antigravity force; thus, the matter of negative curvature moves with constant velocity v z .
• the apparatus for providing the antigravitational force comprises a means to inject electron plane waves and a guide means to guide the propagation of the plane waves. Acceleration and forming negative curvature is effected in the propagating guided electrons by application of one or more of an electric field, a magnetic field, or an electromagnetic field by a field source means. A repulsive force of interaction is created between the propagating electrons of negative curvature and the gravitational field of a gravitating body which comprises matter of positive curvature where the field source means provides an equal and opposite force to the repulsive force.
• the interactive force is transferred to the field source and the guide which further transfers the force to the attached structure to be accelerated.
• the antigravity means shown schematically in Fig. 4 comprises an electron beam source 100, and an electron accelerator module 101, such as an electron gun, an electron storage ring, a radiofrequency linac, an introduction linac, an electrostatic accelerator, or a microtron.
• the beam is focused by focusing means 112, such as a magnetic or electrostatic lens, a solenoid, a quadrapole magnet, or a laser beam.
• the electron beam 113 is directed into a channel of electron guide 109, by beam directing means 102 and 103, such as dipole magnets.
• Channel 109 comprises a field generating means to produce a constant electric or magnetic force in the direction opposite to direction of the antigravity force.
• the field generating means 109 provides a constant z directed electric force due to a constant electric field in the negative z direction via a linear potential provided by grid electrodes 108 and 128; given that the antigravity force is positive y directed as shown in Fig. 4, the field generating means 109, provides a constant negative y directed electric force due to a constant electric field in the negative y direction via a linear potential provided by the top electrode 120, and bottom electrode 121, of field generating means 109. Given that the antigravity force is positive y directed, the field generating means 109, provides a constant negative y directed magnetic force due to a constant dipole magnetic field in the ⁇ direction for an electron beam traveling in the z direction.
• the field generating means 109 further provides an electric or magnetic field at infinity which warps the electrons of the electron beam 113, into negative curvature to produce the antigravitational force with a gravitating body.
• the electric potential of the warping electric field is given as follows:
• c is a constant and p is either x, y, or, z and is the direction opposite the force of antigravitation; so, the corresponding electric force on the electron is opposite the antigravitational force as described previously.
• the electric field is given by the negative of the gradient of the potential.
• the electric warping force in the z direction is shown in Fig. 2.
• c is a constant and p is either x, y, or z so that the corresponding constant dipole magnetic field produces a constant magnetic force in the direction opposite to the force of antigravity as described previously.
• the potential function and field lines are shown in Fig. 1.
• the magnetic field is given by the negative gradient of the potential.
• the z directed warping force on an electric plane wave propagating in the positive z direction is shown in Fig. 2.
• This manifold is shown schematically in Fig. 3.
• the velocity, V, of the manifold is a constant due to the equality of the constant electric or magnetic force and the antigravitational force which arises as an
• the constant force provides constant levitation or propagation work against the gravitational field of the gravitating body as the manifold propagates along the channel of the guide means and field producing means 109.
• the resulting work is transferred to the means to be propelled or levitated via its attachment to field producing means 109.
• the constant electric or magnetic force is variable until force balance with the antigravitational force is achieved.
• the electrons will be accelerated and the emittance of the beam will increase. Also, the accelerated electrons will radiate; thus, the drop in emittance and /or the absence of radiation is the signal that force balance is achieved.
• the emittance and /or radiation is detected by sensor means 130, such as a photomultiplier tube, and the signal is used in a feedback mode by analyzer-controller 140 which varies the constant electric or magnetic force by controlling the potential or dipole magnets of (field producing) means 109 to control force balance to maximize antigravitational work.
• the negative curvature of the electrons of the electron beam 113 is produced by the absorption of photons provided by a photon source 105, such as a high intensity photon source, such as a laser.
• a photon source 105 such as a high intensity photon source, such as a laser.
• the laser radiation can be confined to a resonator cavity by mirrors 106 and 107.
• the laser radiation or the resonator cavity is oriented relative to the propagation direction of the electron plane wave so that the selection rule angular relationship for the quadrapole transition with zero change in angular momentum is maximized for radiation of a given multipolarity. For example, given (that) the direction of propagation of the beam 113 is in the z direction of Fig.
• the radiation is of multipolarity M1 (magnetic dipole radiation)
• the orientation of the laser radiation or resonator cavity is along the x or y axis (i.e., 90° to the electron beam); given the direction of propagation of the beam 113 is in the z direction
• the radiation is of multipolarity E 2 (electric quadrapole radiation)
• the orientation of the laser radiation or resonator cavity is along the z axis (i.e., 0° to the orientation of the electron beam).
• the beam 113 is directed by beam directing apparatus 104, such as a dipole magnet into electron-beam dump 110.
• the beam dump 110 is replaced by a means to recover the remaining energy of the beam 113 such as a means to recirculate the beam or recover its energy by electrostatic deceleration or deceleration in a radio frequency-excited linear accelerator structure.
• a means to recover the remaining energy of the beam 113 such as a means to recirculate the beam or recover its energy by electrostatic deceleration or deceleration in a radio frequency-excited linear accelerator structure.
• the present invention comprises high current and high energy beams and related systems of free electron lasers. Such systems are described in the following references which are incorporated herein by reference:
• Mills orbitals satisfy force balance.
• an electron as a plane wave is accelerated by the force of an electric field, and a nonradiative Mills orbital of negative curvature moves at constant velocity and exists when the forces of absorbed photons, shaping/warping forces, the propagation acceleration forces, and the repulsive gravitational force between the Mills orbital and a gravitating body comprising matter of opposite (positive) curvature exactly balance.
• the Mills orbital does constant antigravity work as it propagates along the guide where the gravitating body's and the Mills orbital's curvatures are essentially constant over the time of interaction of the gravitational forces.
• the antigravity work of the electron is 1 GeV.
• the propulsion power available for guide or a series of guides (109 of Fig. 4) carrying a total of 1000 Amps with a repulsive gravitational interaction force-distance product per electron of 1 GeV is given as follows:
• the time to accelerate a structure such as a vehicle having a mass of 500,000 kg to a velocity of 1000 m/sec is given as follows:
• the antigravity force produced by the antigravity apparatus according to the present invention can be applied to accelerate large vehicles or to levitate any large object.
• the force provided by the antigravity apparatus is central with respect to the gravitating body.
• acceleration in a direction tangential to the gravitating body's surface can be effected via conservation of angular momentum.
• an accelerated structure such as an aerospace vehicle to be tangentially accelerated possess a cylindrically or spherically symmetrically movable mass having a moment of inertia, such as a flywheel device.
• the flywheel is driven with angular motion by a driving device which is powered and energized by an electric motor and an electric energy source means such as a fusion reaction with a thermionic or steam generator, or batteries.
• the driving device provides angular momentum to the flywheel.
• the vehicle is levitated using antigravity means to overcome the gravitational force of the gravitating body where the levitation is such that the angular momentum vector of the flywheel is parallel to the central vector of the gravitational force of the
• the angular momentum vector of the flywheel is forced to make a finite angle with the central vector of gravitational force by tuning the symmetry of the levitating (antigravitational) forces provided by antigravity apparatus.
• a torque is produced on the flywheel as the angular momentum vector is reoriented with respect to the said central vector due to the interaction of the central force of gravity of the gravitating body, the force of antigravity of the antigravity means, and the angular momentum of the flywheel device.
• the resulting acceleration which conserves angular momentum is perpendicular to the plane formed by the centred vector and the angular momentum vector.
• the resulting acceleration is tangential to the surface of the gravitating body.
• ⁇ is the tilt angle between the central vector and the angular momentum vector
• g is the acceleration due to gravity of the gravitating body
• 1 is the height to which the vehicle levitates
• ⁇ is the angular procession frequency resulting from the said torque.
• the linear velocity is the radius times the angular frequency which is given as follows:
• rapid long distance transport may be realized where the propelled means, such as a space vehicle, is accelerated to enormous velocity by executing a hyperbolic trajectory around a gravitating body wherein the force of gravity of the gravitating body and the antigravity force of the vehicle provided by the antigravity means of the present invention accelerate the vehicle to high velocity.
• the propelled means such as a space vehicle
• One embodiment of the antigravity propulsion and levitation means of the present invention comprises the apparatus of Fig. 6 with the absence of the wiggler and the spectrometer. But, in addition the device of the present invention comprises an electron guide means comprising a channel for the electron beam and a field generating means 109 of Fig.
• the maximum vertical deflection of the relativistic electrons by the antigravitational forces is approximately 5 centimeters over a displacement in the direction of the electron beam of 50 centimeters.
• antigravitational forces comparable to the electrostatic and electromagnetic forces of the apparatus were achieved.
• the current dependence of the efficiency of negative curvature production resulted from increased electron-electron interactions with higher beam current which prevented efficient coupling of the electrons with the quadrapole triplets.
• significant antigravity was produced at currents of several hundred amperes.
• the present experiment indicates that antigravitational work of the order of 1 GeV per electron is achievable by the methods and apparatus of the present invention.
• the present invention unifies the three forces, electromagnetic, gravitational, and mechanical and permits their interconversion.
• the Meisner effect is the phenomenon whereby a superconductor of the present invention converts a gravitation force into an electromagnetic force, and the energy of the strong nuclear force is released as heat during Coulombic Annihilation (cold) Fusion of the present invention which produces electricity directly via a thermionic or photovoltaic generator, or the heat produces a mechanical force via steam which turns a generator to create electricity, as illustrated in Fig. 8.
• the electricity provides an electromagnetic force which by a device of the present invention warps matter into negative curvature such that an antigravitational force is produced.
• the antigravitational force provides useful propulsion or levitation as a mechanical force.
• the fusion reactor 210 provides heat via Coulombic Annihilation Fusion which is converted to steam in heat exchanger 214.
• the steam is transferred by connection 216 to turbine 218 which is driven by the steam to produce electricity to supply the electrical load of the antigravity apparatus 224.
• the heat is transferred by connection 212 to thermionic power converter 226 which directly converts the heat to electricity to supply the electrical load of the antigravity apparatus 224, where the unused heat is returned via connection 213.
• the electrical energy is converted into antigravitational energy by antigravity apparatus 228 which provides propulsion and levitation to the vehicle to which the antigravity apparatus 228 is structurally attached by structural connection 206.
• the fusion reactor 210, the heat exchanger 214, the turbine 218, the power generator 220, and the thermionic power converter 226, are also propelled or levitated with the vehicle by their respective structural connections 201-206 to the vehicle.
• the transformation described corresponds mathematically to passing to a locally geodesic system of coordinates.
• Fermi it is possible to introduce coordinate systems which are locally geodesic not only at one point but also along a time-like world-line.
• Einstein illustrated his "equivalence hypothesis" with the example of a laboratory inside a falling lift. All objects within such a lift appear bereft of their weight, they all fall together with the lift, with the same acceleration, so that their relative accelerations vanish even when they are not fixed to the walls of the lift.
• Einstein two frames of reference, one inertial, or almost inertial, fixed to the Earth and another accelerated, fixed to the lift. In the first, inertial frame, there exists a gravitational field - in the second, accelerated frame, it is absent.
• an acceleration can replace gravitation or at least a uniform field of gravitation.
• Einstein develops this idea further. He proposes to consider bot the accelerated and the unaccelerated frames to be physically completely equivalent and points out that from such a point of view the concepts of inertial frame and absolute acceleration cease to have any meaning.
• Galilean space can be defined in the infinitesimal. However this in no way justifies conclusions about the equivalence or indistinguishability of fields of acceleration and of gravitation in finite regions of space. To illustrate the nature of the error
• ds 2 c 2 df' 2 - (dx' 2 + dy' 2 + dz' 2 ) (61.01)
• harmonic coordinates can be defined uniquely apart from a Lorentz transformation.
• Einstein's theory of gravitation does not reduce to a formulation of the law of equality of the masses; it embraces essential new physical principles.
• the first is already contained in the ordinary theory of relativity: the unification of space and time into a single four-dimensional manifold with an indefinite metric. This principle is related to the limiting nature of the velocity of light and, closely connected with this, to the more precise specification of what is meant by a sequence of events in time and also by cause and effect [(Section 12)].
• the second principle establishes the unity of metric and gravitation; it is the very essence of Einstein's gravitational theory.
• ds 2 c ⁇ dt' 2 - (dx 2 + dy 2 + dz 2 ) (35.02)
• An independent set of conditions is, for instance (35.25), the first inequality of (35.26) and the first of (35.27).
• ⁇ x , ⁇ y , ⁇ z , and ⁇ t denote the derivatives of ⁇ with respect to x, y, z and t.
• equation (35.30) can be solved for the time and written in the form
• Equation (35.38) assigns to every point in space a definite instant of time in such a way that all the four-dimensional "point -instants" are quasi-simultaneous. Such an equation may be called a "time-equation.” [We recall that] also time equations occurfred] [in Section 3] in connection with the question of the characteristics of Maxwell's equations.
• Newtonian mechanics In classical Newtonian mechanics one often uses a time dependent coordinate transformation which is interpreted as passing to a moving frame of reference. In comparing coordinate transformations in Newtonian mechanics with the transformations of time and space coordinates in the Theory of Relativity it is essential to realize the following. Firstly, in the general case of accelerated motion the very notion of an accelerated frame of reference in Newtonian mechanics is not the same as in Relativity. The Newtonian concept involves the idea of an absolutely rigid body and the instantaneous propagation of light.
• variable xo can characterize a sequence of events in time and the variables x1, x2, and x3 their location in space.
• ⁇ 0 - H ( ⁇ 1 , ⁇ 2 , ⁇ 3 ) (36.07)
• Section 35 In addition to the g ⁇ we shall consider the g ⁇ , their connection being (36.04).
• the conditions under which the g ⁇ can be represented in the form (36.03) [will be] is established in Section 42 of the following reference which is herein incorporated by reference in its entirety: The Theory of Space, Time and Gravitation, V. Fock, the MacMillan Company, New York, 1964. In particular.
• Section 20 of this reference gives the definition of a four-dimensional vector: Section 21 describes four-dimensional tensors; Section 22 describes pseudo-tensors: Section 37 describes the definition of a vector and of a tensor in terms of tensor algebra; Section 42 describes the transformation law for Christoffel symbol, and the locally geodesic coordinate system, conditions for transforming ds 2 to a form with constant coefficients; Section 43 describes the curvature tensor; Section 44 describes the properties of the curvature tensor, and Section 31 describes the mass tensor. Also Section 39 describes the parallel transport of a vector; and Section 40 describes covariant differentiation.
• the coefficient of can be symmetrized with respect to ⁇ and ⁇ ; if we
• dp is considered to be the differential of the independent variable p.
• the first four equations of (38.40) have already been given in Section 36. Writing the righthand sides explicitly we get
• F is constant, a geodesic retains its character for its entire length; it may always describe the motion of a point with a speed less than that of light or it may be a null-line or, finally, it may be everywhere space-like.
• the Hamilton-Jacobi equation is obtained by the usual rule of expressing p1, p2, p3 and H as partial derivatives of S with respect to the spatial coordinates and to time, as follows:
• the relativity principle in general form then reduces to the Galilean relativity principle.
• Inertial mass is the measure of the ability of a body to resist acceleration; for a given force the acceleration is inversely proportional to the inertial mass.
• Gravitational mass is the measure of the ability of a body to produce a gravitational field and to suffer the action of such a field; in a given field the force experienced by the body is proportional to the gravitational mass.
• the atomic basis for Galileo's law is that all matter is composed of fundamental particles comprising matter with mass that is confined to three-dimensional space-time.
• the two-dimensional spatial manifold of ordinary matter is a spherical shell. Such a manifold possesses positive curvature.
• Einstein's field equations are solved by equating the discontinuity of mass as given in the two-dimensional spatial manifold with the discontinuity of curvature of Riemannian spacetime. It will be demonstrated that the resulting gravitational equation contains the entire mass of the manifold which is also the inertial mass.
• Einstein's field equations are derived on the basis of this equivalence, and they are solved by matching boundary conditions at a Mills orbital.
• the gravitational field can be characterized by the gravitational potential U(x,y,z).
• the gravitational potential produced by an isolated spherically symmetric mass M at points exterior to itself is
• the required generalization of Newton's theory of gravitation must be covariant with respect to arbitrary coordinate transformations. Therefore, it is impossible to regard as a generalization of the Newtonian potential a term in the coeffident g 00 or this whole coeffident; instead the whole set of coeffidents g ⁇ v must be taken into consideration and must appear as the generalization of Newton's potential.
• the fundamental metric tensor must satisfy a set of equations that are generally covariant and in the Newtonian approximation one of them must go over into Poisson's equation for the potential U. The total number of equations must, generally speaking, be equal to the number of unknown functions, i.e. to the number of components of the tensor g ⁇ v , which is ten.
• Such tensors are the curvature tensors (either of second or fourth rank).
• the fourth rank curvature tensor R ⁇ v, ⁇ is unsuitable because its components do not contain expressions which could be generalizations of the Laplace operator acting on U. Also has too many components, the number being twenty, twice as many as there are unknown functions2. Therefore, there remains the second rank curvature tensor which has just the right number of components.
• the metric tensor g ⁇ V itself also satisfies (52.05); therefore, we could add to the conservative tensor on the left-hand side of (52.06) a tensor of the form 1gmn where ⁇ is a constant , without violating (52.03).
• the constant a depends on the choice of energy unit, the constant ⁇ also on the conditions at infinity. If in supplementation of the local conditions one demands
• the absence of a gravitational field signifies the absence of deviations of the geometry of space-time from the Euclidean, and therefore also the vanishing of the curvature tensor R ⁇ v and of its invariant R.
• the energy of a vacuum is zero; thus, the cosmological constant of the model is zero.
• the model unifies atomic theory and gravitation on a cosmological scale. It is demonstrated in Appendix VH that the solution of Einstein's field equations as a boundary value problem if a Mills orbital unifies atomic theory and the General Theory of Relativity on a atomic level to provide a completely unified gravitational theory for spacetime of all scales.
• the equation of the characteristics represents the propagation law for the wave front of a gravitational wave.
• the last term in (53.04) does not involve second derivatives but is a homogeneous quadratic form in the ⁇ v ⁇ ⁇ and hence also in the first derivatives of the metric tensor.
• the r ⁇ v are obtained from the ⁇ v by the rule which is formally identical with the rule for forming the symmetrical contravariant derivative of a vector:
• Einstein's equations are generally covariant and therefore permit coordinate transformations involving four arbitrary functions.
• the equations are solved in some arbitrary system of coordinates.
• We can then go over to other coordinates by taking as independent variables four solutions of the equation ⁇ ⁇ 0.
• Equation (53.17) for the propagation of a gravitational wave-front is the same as the corresponding equation for the front of a light wave in empty space on which the whole theory of space and time was based 3 . Briefly one can say that gravitation is propagated with the speed of light.
• M is the total mass of all the bodies of the system in question and is equal to
• ds 2 c 2 dt 2 - (dx 2 + dy 2 + dz 2 ) (54.05)
• Newtonian theory is non-relativistic and in passing from a relativistic theory to a non-relativistic one, it is especial to single out the speed of light as a large parameter. Therefore we shall no longer introduce the quantity c into the parameter; instead of (35.03) we shall now write
• ds 2 c 2 dx 0 2 - (dx 1 2 + dx 2 2 + dx 3 2 ) (54.07)
• n is a unit vertor with th e components
• f is an arbitrary function.
• the function / and its derivatives with respect to all its arguments are assumed finite.
• the argument n gives the dependence of f on the direction along which a point recedes to infinity.
• Equation X 0 means simply the time and not ct; therefore, the notation T 00 will presently be equal to c 2 T 00 ; and T 0i of equations (32.34) will presently be equal to cT 0i , and T ik is unaltered.
• Equations (55.03) and (55.04) enable us to calculate the approximate values of the tensor components entering the right-hand side of Einstein's equations written in the form
• U has the dimensions of a velodty squared and the U i the dimensions of a velodty cubed.
• U has the dimensions of a velodty squared and the U i the dimensions of a velodty cubed.
• the set of quantities a ik may be interpreted as the three-dimensional spatial metric tensor, but only its algebraic properties are of importance to us here.
• V 2 we shall consider the quantity V 2 to be a three-dimensional scalar and the quadratic form
• the four-dimensional Christoffel symbols and the curvature tensor can be expressed in terms of the corresponding three-dimensional quantities.
• equations (56.25), (5628) and (5629) lead to the following expression for the invariant (R) g :
• V e - ⁇ (56.46)
• H ik - 2 ⁇ i ⁇ k - h ik ( ⁇ j ⁇ j) h - xT ik (56.50)
• radius-vector r will be "non-harmonic", in the sense that it is not related to the harmonic coordinates, x 1 , x 2 and x 3 by equations of the form (57.03). But having formed Laplace's equation for the quantities (57.03) with r * replaced by r one can always go over afterwards to a "harmonic" radius vector r *.
• the invariant of the three-dimensional curvature tensor can be calculated from the formula
• ⁇ is the Newtonian gravitational constant, related to x by (56.51).
• M is the mass of the gravitating body; in] In going over to the case of a concentrated mass this quantity, and with it ⁇ , remain finite and positive.
• the dimensions of ⁇ are those of a length, which is why it is called the gravitational radius of the mass.
• ⁇ ' ⁇ ( ⁇ 2 + ⁇ 2 ) (57.41)
• d ⁇ 2 dr 2 + (r 2 - ⁇ 2 )(dv 2 + sin 2 u d ⁇ 2 ) (57.45)
• equation (57.45) shows that the components of the metric tensor of ds2 have relative deviations from their Euclidean values of the order

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