Time Travel Research Center © 2005 Cetin BAL - GSM:+90 05366063183 -Turkey / Denizli Addendum to the Philadelphia Experiment - The Physics of Time Travel One of the later interviews with Cameron had a chart presented showing a three dimensional hyper space model of a five dimensional universe. This has also been suggested by VLF (1) that a twisted, six dimensional torus makes up our sister universe. The number six for six dimensions means that there are five before and five after (of which the later five was stated as being the contra turn of matter, with the sixth dimension isolated between the first five and the second five, making a total of eleven dimensions, from which the twelfth is resolved as hyper space). This happens to be right out of Einstein's school of thought at Princeton University - the same place where all physics theory emanated from before, during, and after the Philadelphia Experiment, which took place in 1943. The meridians of the torus are divided into Planck lengths, of which the fifth dimension is resolved as units of 0.5 x 10^{-43}sec, which represents each successive turn of the screw, or point on the spiral that circumvents the torus. The meridians are identified with the winding number, n_{i} (described in the section Modeling a Magnetic Monopole, at bottom) with the torus of time identified as the skin of a two dimensional lattice (compactified 4-D subsurface of 26 dimensional string theory). The entire torus circumference is equal to the circumference of the mapped gravitational collapse area of the galactic nucleus onto the torus shaped field. The area of the galactic nucleus sphere is the area that uses the gravitational collapse radius, r_{g} , where: r_{g} = 2GM / c^{2} = (approx) 3 ( M / M_{solar} ) km, where M_{solar} = one solar mass (of our sun), M is equal to the mass of the galactic center, which is said to be about 1 x 10^{9} solar masses, and c = 3 x 10^{10} cm / s is the velocity of light. This formula then equals approximately 3 x 10^{8} km., for the radius of the galactic nucleii collapse radius. Since one complete cycle of the earth's biofield is equal to 40 years, this means that harmonic resonance is achieved every 40 years with the galactic nucleus. During this resonance, the galactic nucleus sphere can be mapped onto a hyperspace torus of time to provide hyperlinks to past and future time frames. On the torus of time, harmonic bleed through between successive turns of parallel realities suffuges our reality with influence of past and future. The reason for our lock in this present reality is because the fifth dimension is curled up into a fantastically small length representing the Planck length, (epsilon)_{o}, which is 1.6 x 10^{-33}cm, and requires an enormous amount of energy to release (on the order of 10^{19}billion ev). This was achieved, however haphazardly, during harmonic resonance with the galactic nucleus, which resonates as a magnetic dipole of 1000 Hz. (It also took 40 years of engineering tests to finally degauss the resonance!) A resonance situation creates intersection with other world lines producing transient mysterious phenomenon such as UFO's, monsters, and hallucinations. Precluding the mysticism and therefore cultish link to licentious interpretation comes the realization that perhaps Adonai Tsebayoth [Lord / God of Hosts of Armies of Angels] provided eternal salvation [now] through a quantum chromodynamic (QCD) harmonic resonant anomaly available to believers in the blood of Christ by confessing Him as Lord and Savior. The neutrino Compton wavelength of one micron, or the size of a living cell, and e-neutrinos, whose Compton radius as big as the universe, allow access thru the ZPE (Zero Point Energy) to eternal salvation thru the blood of Jesus Christ. The spirit of legalised religion comes as a result of the efforts [of antichrist] to imprison the free will of the brothers in Christ with the establishment version of the eternal now, therefore creating false prophets who contest for earthly dominion. World lines existing parallel to ours represent alternative realities where time flows at a different speed than ours. Alternative realities are created by their unique harmonic interval between successive instants, as well as mysterious phenomenal bleed through from alternative realities, producing dreams, art, and other fantastic creations. Changing the helical rate changes the time flow. This was accomplished on the Eldridge by creating a sixth order field which could manipulate the fifth order field, which was t2; or the second order of time. Through our senses, we are familiar with only five dimensions. Putting the Eldridge in hyperspace to solve the problem of resonance required a twelfth order function. The Eldridge was capable of only a 6^{th} order. The Phoenix was capable of an 8^{th} order function. The other four orders came from memory systems and networks; meaning creating a lattice of LC energy storage networks, which could store etheric orders of energy. A 25^{th} order network could store up to 25 orders, or up to the 25^{th} power. In order to prepare for energy storage of this magnitude, the scientists would have to literally travel the entire torus of time (to + and - infinity) to add one order of reality. By leaving the station on for 24 hours, they added one order of reality. After 5 days, they had reached the 12^{th} order. Tesla incorporated gravity field generators on the Eldridge since these generators are capable of drawing on the Tachyon Field energy, or gravitational energy, which is estimated to be 8.8 x 10^{8} volts per cm. (Sieke). The resonance condition that occurred was the result of a standing electromagnetic wave that seemed to disturb a mutual tolerance between the electromagnetic waves and the Tachyon-Field. This led to energy removal from the Tachyons into the electromagnetic field surrounding the Eldridge, which became unsympathetic. This principle was discovered by Nikola Tesla about 100 years ago and was used by him to experimentally extract Tachyon-Field energy and convert it to electrical current. By adopting the term interference, specialists today speak of a Tesla Interferometer. Tesla at that time predicted the technical exploitation of space energy "within a few generations". He was about 100 years ahead of his time. The exeptional importance of this man is only now becoming known. The Tesla principle is considered by specialists today to be a classic example of Tachyon energy conversion. The recently developed Tesla Cannon is based on this principle. The electromagnetic waves are modified in the form of laser bundling, so that they absorb additional Tachyon energy. Such a beam can have a destructive effect in space over hundreds of kilometers and has a very high energy. The American physicist Dr. Moray did not fire Tesla modified waves into space. Instead he directed them into an insulated cable 15 meters long. Inside the cable, energy is removed from the Tachyon-Field. Dr. Moray was able to produce a continuous power of 70kw direct current! This occurred in 1929. Fourty years earlier Tesla directed a Tesla beam over a long distance onto a piece of metal and made numerous electrical bulbs light up. The effective energy was much greater than that emitted by the generator. Geometry of 5 Dimensional Spacetime The fundamental theorem of Riemann states that any reigon with a suitable boundary can be conformally mapped on a circle by means of a simple analytic function. This mapping would occur between gridlines on 5 dimensional hyperspace and an electromagnetic dipole of 1000 hz in a phase locked loop (that would create the hyperspace bubble through harmonic resonance). The side effects of such a resonance on personnel are related to bremsstrahlung, or the electromagnetic radiation produced by the rapid change in the velocity of an electron or another fast, charged particle as it approaches an atomic nucleus and is deflected by it includes electromagnetic fire on the surface of the skin, disorientation, hallucinations, being frozen out of time, and melding into objects (as a result of varying magnetic field strength). Some theory on the effects of strong magnetic fields on atoms follows. First, to determine the amount of curvature in hyperspace requires an equation that describes the energy momentum tensor (2): R_{m}v - ½ g_{m}v R = [ 8(pi) / c^{2} ] GT_{m}v This is an Einsteinian formula applicable for classical physics and also describes the curvature of a 5 dimensional universe in 6 dimensional spacetime, where R = k_{( v,w )} / alpha, k_{( v,w )} = sectional curvature of M at P (Note 1) determined by the tangent vectors v and w. Note 1: If all sectional curvatures, at every P (an element of ) M, have the same value, M is a Riemanian manifold of constant curvature. Constant negative curvature is represented by a torus, as well as constant positive curvature. Alpha depends on the length of v and w and the length between them, g_{m}v = Riemann metric = -2, R = scalar field curvature constant = R_{i}^{i} = g^{ij }R_{ij}, where g^{ij} = G_{ij} / g_{m}v , (I, j interchangable w/ m, v), where G_{ij} = gravitational constant = 6.67 x 10^{-8} cm^{3} / gm-sec^{2}, and T_{m}v is the energy momentum tensor, which measures the matter-energy content. Zamanda yolculuk © 2005 Cetin BAL - GSM:+90 05366063183 -Turkey/Denizli The solution to the above field equation for spherically symmetric mass distribution at rest is called the Schwartzchild solution. To meet the requirement for spherical symmetry, any solution to the above equation must involve only those combinations of x, y, z, dx, dy, and dz that are left invariant by spatial rotations (1). For the torus screw theory, there are incremental jumps (360^{o} phase at 0.5 x 10^{-43}seconds each, representing our time line on the circumference of a torus) that represent the invariant conditions required for the Schwartzchild solution: ds^{2} = [ 1 - 2GM / r ] dt^{2} - dr^{2} / [ 1 - 2GM / r ] - r^{2}d (theta)^{2} - r^{2}sin^{2}(theta) d(phi)^{2} The value for ds^{2} represents the unit value for fifth dimensional space time curvature, the so-called Riemann curvature ( R_{m}v ), which is the curvature of a space time bubble in hyperspace, whose diameter is equal to the crossectional diameter of one leg of the torus of time. A value for ds^{2} is found so that a spiral 'cutout' for the desired time dialation ( + or - ) is applied using the gravitational collapse radius r for a chosen mass. Theoretically, there exists only an imaginary mass of particles entering a wormhole, but which also contain the minimum negative energy at the event horizon, corresponding to the kinetic and potential scalar energy entering, with simultaneous radiation of total outer shell spectral emission of photon energy over the event horizon (and quite possibly within the ergosphere, described below) taking place. For a rotating black hole, the ergosphere is the region between the event horizon and the static limit, the oblate surface that surrounds the horizon, touching it only at the poles of the rotation axis. Event horizons are discussed regularly when talking about the topology of hyperspace, and how future, past, and present worlds affect each other. There is a growing group of scientists who believe that the properties of the spacetime in which we live are stably causal; that is, ordinary causality has an absence of closed timelike curves. A closed timelike curve has no connections with nearby spacetimes(1), but a connection with nearby spacetimes is physically reasonable if and only if it is stably causal(2). This property of space-time would allow the same particle to exist in two different locations simultaneously (in the fourth dimension), but at different spacetimes (in the fifth dimension), yet even free will could not allow these particles to come in contact with each other without mutual destruction. Of the equipment that was used in the Philadelphia Experiment, much of the generators had originally been designed by Tesla to be for a toroidal shaped field. Ahthough this field was easier to create, there was a problem with an open field in the center which didn't allow uniformity during hyperdimensional translation. This problem could have been eliminated with an oblate spheroid shaped field. If you think about it, the oblate sphereoid field is actually a flattened hyperspace bubble; much like a cigar or saucer shaped field. By reducing the field elevation and flattening it out, problems with teleportation through earth-based elevations-above-sea-level gravitational fields can be overcome, along with a reduction in the diameter or elevation of the torus. Time Travel Research Center © 2005 Cetin BAL - GSM:+90 05366063183 -Turkey/Denizli Tesla, it turns out, was a modulated man, who believed in modulated waveforms. Van Noyman believed in pulsed transmission, in which the transmitters were eventually designed (by Tesla) as 2Mwatt pulsed RF transmission. These transmitters were powered by (2) 75kva alternators, 750 hp Electric motor for driving, (2) right angle gearboxes, electronics pulse generators, oscillators, and amplifiers. (4) rf pulsed transmitters at 2 Mwatt cw output each made the output considerably higher. The time locks or zero time reference described was actually a "Zero-Time Reference Generator", which Tesla invented and was used to set the "time locks" in P.E.-related experiments. A PI / 2 pulse represents a maximum free induction signal. From PART 3-- The Philadelphia Experiment & Nuclear Magnetic Resonance Imaging: "Nuclear magnetic resonance (NMR) is the effect of a resonant ROTATING (or alternating) magnetic field, imposed at RIGHT ANGLES to a typically much larger STATIC field, to perturb the orientation of nuclear moments. First applied to molecular beam "The essence of this methodology is that the nuclear moments u(i) in the specimen under observation are rotated so as to lie at some angle with respect to the applied field B(o). Under these conditions the moments experience a torque u(i) x B(o), "Many techniques have been developed for the observation of NMR signals. These are divided into two principle classes, PULSED and CONTINUOUS WAVE (cw) methods..." "Again, borrowing from the terminology of GYROSCOPIC MOTION, the rotation of nuclei about the field B(1) is generally referred to as NUTATION. If B(1) is applied long enough to rotate the nuclear moments into a RIGHT ANGLE with B(o) and then TURNE A pulse twice as long, i.e., a PI pulse, will invert the nuclei to the direction -B(o). THE MAXIMUM FREE INDUCTION SIGNAL IS ACHIEVED WITH A PI/2 PULSE... "Thus, nuclei in solids and liquids are typically very strongly decoupled from their surroundings, making them useful probes of local magnetic behavior. There are two principle types of relaxation process affecting NMR measurements. The first is "The echo decay time constant is usually termed T2.... "...Two-dimensional NMR. This method is a simple extension of the Fourier transform scheme to include a sequence of two PI/2 pulses separated by a variable time t1. Time t1, the 'evolution' time, is varied from zero up to values slightly greater "A three-dimensional object to be imaged is placed in a magnetic field with a field GRADIENT along one axis, e.g., the z axis. A pulsed radio-frequency magnetic field is then applied, exciting the nuclear spins in a planar cross section of small As to the field strength of the main magnet, we read: "MRI equipment consists of a huge, superconducting electromagnet that is cooled by liquid helium. It is constructed as a large tube with an inside diameter of about 1 meter to admit the patient. The electromagnet of a typical MRI system weighs mo the preceding was a compilation of info from several encyclopedias of Scientific terms, most notably Van Nostrand's. One interesting side note: On the one hand we are not taught in school that there is any real danger in being exposed to strong magnetism (except for the current controversy over 60 Hz ELECTROmagnetism from power lines, etc.). Yet, elsewhere in this paper I included the quote "The magnet creates fringe field effects that unless taken into account by designers, stretch far beyond the MRI machine. Although there is no conclusive evidence of harmful effects of magnetic fields, the FDA, feeling it is better to err on the s[ide of]... "Large areas and parking lots surrounding early mobile units had to be roped off to prevent people from straying into the fringe field."-pp 76,77.Just as food for thought: If you strayed too near a mobile MRI unit and soon afterward came down with... Well, there you have it. What are we able to glean from the descriptions of the technology behind the alleged Philadelphia Experiment? In contemporary theory, a waveform which rapidly shifts or chirps its frequency in the ratio of the high infared to the first harmonic of the ultraviolet is associated with growth and self-organization, i.e., the Golden Section (Note 1) by activating natural hyperspace resonance using the twin magnetic field generators operating at the chosen chirp frequencies. An induced hyperspatial resonance would interact and orthorotate the ZPE (Zero Point Energy) flux, causing the bending of fabric of spacetime. Teleportation results when the bending becomes induced by a 25^{th} order of energy over a period of 12 days. This is accomplished thru the use of chirping twin generators described above that are similar to the gravity field generators of Tesla. Note 1: The Golden Section can be percieved as the addition of a sequence of number ratios, that when added together (in an infinite series) is equal to the value of: ( sqrt [5] -1 ) / 2 The sequence used is called the Fabonacci sequence, named after an international merchant born in Pisa, Italy (1180 - 1250). The sequence is: 1,1,2,3,5,8,13,21,34,55,89,144,... If one takes the ratio of two successive numbers in the sequence, i.e., 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/55, 55/89, ... the numbers tend to the value of ( sqrt [5] -1 ) / 2. This is the Golden Section. The Golden Section appears naturally, and beautifully, in the organisation of flower petals, sequences of leaves on a branch, and the central sunflower seeds in a spiral arrangement. How this has anything to do with the flow of time is anybody's guess, except that the idea for growth and self-organization is represented by a waveform that shifts or chirps its frequency in the ratio of the Golden Section, and the spiral shape of the geometry represented is related to Diophantine equations, which have been around for centuries (17.5 to be exact), and are still being used in mathematics today. For interesting reading, refer to Fermat's Last Theorem: Unlocking the Secret of An Ancient Mathematical Problem, Amir D. Aczel, Delta Trade Paperbacks, Dell Publishing, Copyright 1996. There seems to be a relationship between the application of the Golden Section and the solution to Fermat's Theorem, which encompasses nearly all branches of Mathematics. A very powerful application is suggested here. The Unified Field Theory may indeed be related to applications of Golden Section equations in hyperspace resonance theory! If the frequency of gravitational radiation from the galactic center resulting from a rotating black hole; i.e. next to pulsars, the entire electromagnetic spectrum would become radiated at the frequency of a rotating dipole of 1000 hz (9); 1943 technology limited the magnetic field generators to about 15,000 rpm. Alternating between 2 generators with a 180^{o} phase differential overcame the mechanical limitation of field generation. By application of certain perturbation methods in quantum theory, the effect of the atom on the field can be replaced by an equivalent set of linear oscillators, associated with the various transitions that are allowed by Planck's relation. Each oscillator has a resonant frequency given by one of the allowed transitions. With N atoms per unit volume, however, we do not have the equivalent of N oscillating electrons per unit volume of each of the frequencies; we have instead only Nf, where f is a fraction, sometimes called the oscillator strength and which can be calculated by quantum mechanics. We further find that the oscillators not only have resonant frequencies, but also damping terms, which can be correlated with the broadening of the upper and lower states, by collisions with other atoms and other perturbing processes. Thus, the net result of the quantum discussion is a theory mathematically equivalent to the one developed for classical theory, but with a different physical interpretation. In metals, quantum theory also leads to quite a different picture from an elementary classical theory. Electrons are not governed by classical statistics, but by Fermi Statistics, as a result of which the electrons are in continuous motion with a very high velocity. In the absence of a field, there is no net current. In the presence of a field, the electrons gain an average acceleration, and have an effective mass that is different from their classical mass, because of the structure of the energy bands of the metal. For conductors, the general complex is: gamma = (+ or -) jw sqrt [epsilon - ( j (omega) / w) m] (1) where w = frequency in radians / sec, epsilon = dielectric constant, k_{e}
( epsilon)_{o}, where the dielectric constant k_{e} = n^{2},
where n = refractive index, or the ratio of the speed of light in a vacuum
to the speed of light in the material (if magnetic susceptibility is small
in a dielectric), and (epsilon)_{o} is equal to the capacity of a
condenser whose plates are 1 square meter = 8.85 x 10^{-12 }farad /
m, m is equal to the total magnetic permeability, which is equal to
k_{m}m_{0}, where m_{0} = magnetic
permeability of free space (4(pi) x 10^{-7}henry / m), measures the
self-inductance, per meter length, of a transmission line, consisting of two
parallel plane conductors, each 1 meter broad, spaced 1 meter apart, k_{m}
= magnetic permeability of material in henry / meter, and omega =
conductivity. Each of these definitions, of course, implies suitable
conductors outside those in question, such as waveguides (Note: The
divergent zone, the so-called photons, are identified with local cells of
wave guides confining the amount of energy hY (h = [1 / 2 (gamma)] x
sqrt [ mue / epsilon ] x e^{2} , where Y represents the propogation
constant in a waveguide, when multiplied by h is the resultant energy that
has experienced diminution in magnitude and retardation in phase experienced
by current of specified frequency in passing along a unit length of
transmission line or waveguide; Given by the natural logarithm of the ratio
of output to input current (3), insofar as no intense external electric
field interferes and separates the pairs into particles and antiparticles at
high energy (4). In the case with the Eldridge, the two men who jumped
overboard (and had leaped forward in time to 1983) had created a hyperspace
bubble (monopole) that was within the positive (probably because they were
within the positive part of the magnetic dipole when they did it) Tachyon
energy field, described later; and insulation of the potential
conductors to prevent fringing of fields. There are also the effects of
gravity anomalities to take into consideration. This consists of the seven
parts of gravity effects including:
Apart from the gravitational anomalies,we are also looking for frequencies, w, of conductors which would, in a five dimensional translation, be protected with the use of magnetic shielding of the potential molecular magnetic oscillations, and frequency control (of the generators) as pictured in the following schematic: Analysis of the Circuit
If, for example, the frequency decreases slightly the tuned circuits provide a control m.m.f. which is amplified in the transductor and the output controlled the field of the motor in such a direction as to cause an increase of speed. The windings (b) are feedback windings which stabilizes the system by applying an m.m.f. proportional to the rate of change of field current through the capacitor C_{b}. The output from the alternator is approximately 150 VA. at 42 volts r.m.s. and 500 c/s. According to tests made on the system, the alternator frequency can be maintained to within 0.1% of the demanded value. gamma = (+ or -) jw sqrt [epsilon - ( j (omega) / w) m] (1) Referring back to the above equation, it is surmised that as the
frequency approaches zero, the second term in the radical becomes infinitely
greater in magnitude than the first. Thus at low frequencies the optical
properties of a conductor are determined entirely by the conductivity, and
not the dielectric constant; in fact, there is no experimental way of
finding the dielectric constant of a conductor at low frequencies. The
values of omega for conductors, such as metals, are such that sigma /
epsilon does not become comparable with w until frequencies in the visible
part of the spectrum. It is found experimentally that the optical properties
of metals are well described by this simple theory through the radio-frequency,
microwave, and infared parts of the spectrum, and that the dielectric
effects begin to be important in the visible reigon. By then, both epsilon
and sigma vary in complicated ways with frequency. The variation with
epsilon with a metal is not unlike that for a dielectric; there is anomolous
dispersion, and consequent absorption, superposed on the conductivity. From
the ultraviolet to the X-ray region, the effect of conductivity becomes
negligable, and metals are no more absorbing than other materials. There are
frequencies ( 38 - 40 Khz, 150 - 160 Khz, 1.1 - 1.3 Mhz, 1.057 Ghz - 1.067
Ghz (Lamb Shift), and in the near ultraviolet frequency). These frequencies
represent enhanced channels between subquantal (virtual) and spatial (observable)
states. A particularly good magic window exists when the infared and
ultraviolet bands being utilized are phase-locked so that the ultraviolet
represents a first harmonic of the infared (6).; Me^{jwt} = [ e^{2} / m ] [ E_{0}e^{jwt} / [w_{0}^{2} - w^{2} + jwg] ] Where w_{0}^{ }= resonant frequency chosen to be within the magic window, And plugging into the formula for the resulting magnetic field: H_{phi} = [ jwMk^{2} / 4(pi) ] [ e^{ j (wt - kr)} sin(theta) [ j / kr + 1 / (kr)^{2} ] The shape of the field of expanded space near the wormhole through spacetime would conform to a Riemann type curvature of a pseudosphere of pseudoradius b, with ground zero at the top surface as shown, and with z set to less than zero only, a line through the center of the vortex a function of (5): z = integral [ sqrt [ 1 - b^{2} [ c_{1} exp (u / b ) - c_{2} exp ( -u / b ) ]^{2} ] du with curvature k = - b^{2} less than 0 for a space curve The above value of k is related to R_{m}v, mentioned at the beginning, as R_{m}v = k _{( v, w )} / gamma where k _{( v, w )} is the sectional curvature of M at P (Note 3) determined by the tangent vectors v and w, and gamma depends on the length of v and w and the length between them. Note 3: If all sectional curvatures, at every P an element of M, have the same value, M is a Riemannian manifold of constant curvature. (Constant negative curvature is represented by a torus, as well as constant positive curvature). The c_{1} and c_{2} constants are picked off the geometry for torus screw construction of 5 - dimensional space from the small torus radius : sqrt [ (c_{1} cos u)^{2} + (c_{2} cos u)^{2} ] where, for a torus wormhole, c_{1} = c_{2} . To navigate galactic hyperspace would require tracing a line, or torsion, corresponding to the rate of change in the direction of the binormal, or lamda, represented by d(phi) / ds, where (phi) is the angle through which the binormal turns, and ds is the time increment. The timelike vector, also called the null vector, can be either future directed or past directed. By adding boundaries to a set of spacetime manifolds, it is possible to define past (and future) null infinities for such systems. Recall the null vector is the time vector. With 1 / (phi) the radius of torsion, which is equivalent to the amount of time dialation for respective wave numbers, a torsion line is traced through a pseudosphere vortex that is wide enough (because of the stretched space), to accommodate a magnetized shell capable of withstanding the centripetal acceleration outside of a given gravitational collapse radius. The shell, in this case, refers to the formula for H_{phi}, mentioned above. This means that the magnetic confinement should also have controls that are delicate enough to accommodate easy passage through wavenumber flux generated between the outside edge of the wormhole vortex of the galactic nucleus and the ship hull's outer skin, which is subject to a Planckian magnetic field. It should be noted that natural anomalies exist with the frequencies associated with the magic windows, mentioned earlier, and that there is a natural branch within the spacetime continuum, which allows hyperdimentional translation during resonance in a 40 year galactic biofield. Thus calculations need to be made for adjoining latitudinal and longitudinal sectors of the vortex, and mapped to its corresponding wavenumber grid on the ship's hull: The timelike vector, also called the null vector, can be either future directed or past directed. From sources: The conformal treatment of null infinity was introduced by Roger Penrose; see Penrose (1964, 1968). To define a manifold-with-boundary we consider first the n-dimensional half-space H^{n} an element of R^{n}. This consists of all real number n-tuples with non-negative first element. The boundary of H^{n } (in R^{n}) is the (n-1) manifold-{0} x R^{n-1}. We view H^{n}as a topological space with the topology induced by the standard (Euclidean) topology of R^{n}. An n-manifold -with-boundary M is defined like an n-manifold, except that the of M are bijective mappings of subsets of M onto open sets of the half-space H^{n}. A point P (an element of) M belongs to the boundary d(dM) an element of M, or the partial derivative of M (an element of) M if and only if P is mapped by a chart on a point of the boundary of H^{n}. (The reader ought to satisfy himself that this property of being charted onto the boundary of H^{n} is invariant under coordinate transformations).(9) A Fortran program that calculates wavenumber coordinates for each element of a rectangular grid from the discrete Fourier transform and inverse Fourier transform of an N - dimensional array is given as subroutine fourn.htm. Some theory of Fourier transforms might help make the connection to the formula for H_{phi} for wave number clarification. The variable k is called the wavenumber and has units of inverse distance; it is analogous to angular frequency in time-domain Fourier transforms, which has units of inverse time. For a magnetic dipole, which is a generator-driven field, the Fourier transform of a uniformly magnetized sphere observed on a horizontal plane is the total field anomaly: F[delta T] = 2(pi) C_{m}m ()_{m} ()_{f} abs[k] e^{abs[ k ] (Zo - Z')}, z' > z_{o}, where ()_{f }= ( ^ f_{z} ) + i [ ( ^ f_{z} ) k_{x} + ( ^ f_{y} ) k_{y} ] / abs [k] For the dipole, the maximum energy-density spectrum occurs at a value of k that depends on the depth of the dipole in the exponential term ( z_{0} - z' ). But in order to selectively choose a value of k such that when multiplied by 2 ( pi ) / k^{2}c, where c is the velocity of propogation, results in the wave period, or time (per cycle). In this case, the actual velocity of propagation is not limited to the photon speed or the c of relativistic mechanics. The value of the c in this formula refers to any velocity greater than the photon speed and outside the light cone of Tachyon Physics. (The light cone represented by pure photon energy is represented geometrically by the event horizon, or gravitational collapse radius, which becomes enlarged at Planck field strength to allow phased transitions to past and future events around the corkscrew. At between 45^{o} and 135^{o} phase angle, a positive as well as negative fraction of the mass becomes imaginary, with the equivalent balance of mass to rest mass. Complete translation has not occurred until this remaining rest mass becomes imaginary (in this Planck dimension), and completely phased into either a past or future 40 year order of reality. This event would take place in a portable stage ejection from a degaussable Planckian magnetic field within a phase locked loop resonance (somewhere between 90^{o} and 135^{o} for a fourty year future dimension), or between 45^{o} and 90^{o} (for a fourty year past dimension). The solution for dipole moment equation, mentioned earlier, uses the phase relationship (wt) for determining phase angle for selected frequencies. The energy required for these two conditions is solved for using Tachyon particle theory for v > c (4): E = (plus or minus) m_{o} c^{2} / ( i [ ( v / c )^{2} - 1 ]^{1 / 2} Which is complex and could not be measured unless m_{0} is imaginary. Note: Relativistic mass remains real even though rest mass is imaginary. It is important to note that time reversal occurs for negative energy Tachyons, but also that for positive energy, forward motion in time occurs. By reverse engineering this value of time, one could alter the value of k for positive and negative values of time. Other terms on the Fourier transform such as c_{m}, ()_{m}, ()_{f}, and ( z_{0} - z' ) could be forced to accommodate the altered values of k, where c_{m}, the proportionality constant, is equal to m_{0} / 4(pi) = 10^{-7} henry per meter, where m_{0} is equal to the permeability of free space. This value for c_{m} is in the SI, or System International units, or, depending on the units used, may be in emu, where m_{0} = unity ( or 1 ) in the CGS system (centimeter-gram-second). ()_{m} is a complex function of k_{x} and k_{y} that depends only on the orientation of the dipole and is equal to: m_{z} + i [m_{x}k_{x} + m_{y}k_{y}] / abs[k] where m_{x}, m_{y}, and m_{z} are the unit vector components of the dipole moment, m is the magnitude of magnetization potential of a uniformly magnetized sphere, ()_{f} is another complex function of k_{x} and k_{y}, depending on the ambient field componentsf_{x},f_{y}, and f_{z}, which comprise the unit vector f (parallel to the ambient field), and (z_{0} - z') is the dipole thickness, or pole separation. The shape of the field of the starship could fool mother nature into believing that the geometry of the expanded space conforms to the shape of an electron (sideways teardrop) or cigar-shape (proton or nucleus). In the case of the Eldridge, a hyperspace bubble was created as a result of an intense disturbance of the magnetic field between the magnetic generators on the Eldridge and the earth's biofield, which came in a standing wave resonance with each other. The bubble was, in effect, a magnetic monopole in standing wave resonance with the earth's biofield, and was continuing to grow in size and strength and could have "removed the entire northern techtonic plate from the earth's crust" unless a way was found that would dampen the resonance. As it turns out, the resonance can be avoided by either 1) Destroying the equipment responsible for creating the resonant radiation, or 2) Providing a string singularity as a means of containment. The first option was used for the Eldridge. The second option remained undiscovered by physicists until the mid-1980's and is described below. Preamble to Magnetic Monopoles In present-day electromagnetics theory, charge and charged mass are falsely made identical. Actually, on a charged particle, the 'charge' is the flux of virtual particles on the 'bare particle' of observable mass. The charged particle is thus a 'system' of true massless charge coupled to a bare chargeless mass. The observable mass is static, three dimensional, and totally spatial. Charge is dynamic four dimensional or more, virtual, and spatiotemporal. Further, the charge and observable mass can be decoupled, contrary to present theory. Decoupled charge, or the absence of mass, is simply what we refer to as vacuum. However, vacuum, spacetime, and massless charge are not identical, although they may become interchangeable, and therefore identical, through what we now call non-Abelian gauge theory. The symmetry of integer charge and mirror planes allows the translation of metrics through non-Abelian gauge theory between different spacetimes, using a highly stretched space for intermediate vector boson particle model, and given a QED (Quantum -Electro-Dynamic) photon interaction with beaded plasma to tunnel the ZPE vacuum of outerspace. Modeling a Magnetic Monopole Electron-positron pairs create a cloud of particles at energies associated with stretching the space of 10^{-11}cm to human proportions. Between 10^{-11}cm and 10^{-13}cm., the color magnetic field can be screened out utilizing the non-abelian gauge theory of QCD (quantum chromodynamics). At 10^{-16}cm., the weak interaction (with the 10^{-28}cm. X boson) causes coupling to the W and Z bosons. Note than a pair of bipolar bosons constitute a graviton, or unit of gravity. Since bosons can be interchanged through a symmetric wave function, a hyperfine energy shift can be induced by beading projected plasma for the required transition. The resultant energy shift opens to nearly a Planck core (10^{-28}cm.) of X boson, for an SO(3) non-abelian gauge transformation to rotate the scalar field (phi) to a standard direction.
Next, the off-diagonal components giving rise to the Killing Vector (or
time vector) become
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