PART



Very Large Propulsive Effects Predicted for a 512 kV Rotator

David Maker1

Email: maker3@

Abstract. An equation was developed from an Ungauged GR (Maker 2001) that predicts a negative gravity propulsive force with the pulse speed coming out of the integral of ( times V times d(/dt times sin2( divided by 1-V/512kV. V is the electric potential, ( is the azimuthal angular velocity of the electron cloud, d(/dt the frequency of polar angle oscillation of the electron cloud. Note that if V=512kV this equation is singular implying that large effects are possible near 512kV especially if ( is also large and d(/dt is in phase with V. This equation appears to have been verified in several experiments for both above and below 512kV so there is a high likelihood that these large propulsive effects can be created near 512kV.

INTRODUCTION

An equation was developed (from an Ungauged GR allowing for fractal space time) and shown to be validated in several experiments (Maker, 2001). This equation gave a gravitational annulment (ve that was proportional to

(ve=KV(sin2([pic] (1)

Here K is a constant, V is the electric potential, ( is the azimuthal angular velocity of the electron cloud, d(/dt the frequency of polar angle oscillation of the electron cloud. This equation leads to large propulsive effects near V=512kV.

The underlying Ungauged General Relativity-fractal theory was developed by Dr. Maker (Maker, 2001) and helps solve several problems in physics such as the requirement that General Relativity be gauged and also gives a closed form QED and a resonant term for Z and W in the single vertex S matrix calculation. The conservation of energy is used here to find the optimum conditions for the application of this equation.

THEORY

In this type of General Relativity (GR) the 6 independent equations (with the 10 unknown gij s) are augmented by the 4 physical (not gauged) harmonic coordinate conditions of the Dirac equation zitterbewegung oscillation thereby showing that GR is algebraicly complete (Weinberg, 1972). Augmenting the Einstein equations with the Dirac equation makes the Einstein equations into the Maxwell equations (E&M) in the weak field limit thus implying that we should use a E&M source 8(e2/mc2 (Zoo instead of the usual 8(G( source on the right hand side of the 0-0 component. There is a lot of evidence that this is correct. For example when you substitute back into the Dirac equation, the potentials you get from these new Einstein equations give you the Lamb shift without the need for higher order Feynman diagrams (Bjorken, 1964) or renormalization and the new single vertex Dirac equation S matrix gives the W and Z as resonances (Maker,1999). Note that we are merely saying that GR is complete anyway without adding any new assumptions.

One Less Assumption

In this section we do not implicitly assume that GR is referenced to only one particular scale. Out of the range of observability, in other words on the other side of either large or small horizons, there can be other larger or smaller horizons all over again (fractalness) in this more general general relativity. So there is one less assumption, that GR is referenced to only one particular scale. We simply drop this otherwise implicitly held assumption and write our fractal lagrangian (giving the sum over all fractal scale if we invoke inverse separability) with the sum of the Dirac and Einstein equations (Maker, 1999).

[pic] (2)

(Goldstein, 1980) with the understanding that Zoo(8(e2/mc2, the general covariance implies that E=(dt/ds)(goo =1/(goo, (Sokolnikoff, 1964) and the [pic]term and the equivalence principle applied to electrostatics implies that there is only a single Dirac and Einstein equation with a single physical Hamiltonian) so that inverse separability must accompany the fractalness also.

Fractal Dirac Equation

The equation 1 lagrangian implies that the Dirac equation ( s are also fractal with a (M for each fractal scale M. So instead of just the single scale Dirac equation (Merzbacher, 1970):

[pic] (3)

we have an infinite succession of such equations:

….,[pic],[pic],[pic],… (4)

one for each fractal scale with (((/c. Note from the lagrangian of equation 2 (with the Einstein equation component) the physical regions in which each of these equations apply are separated by an event horizon. The physical (expansion) effects on the cosmological ambient metric vacuum begin with the Mth scale, (here being the electron scale~10–18 m lets say and so we can take the proper time t in equation 2 in its frame of reference) and go to higher M. Also the equivalence principle applied to E&M here implies that there must be only one type of source(and resultant Hamiltonian) and therefore that this sequence of Dirac equations is equivalent to a single separable differential equation in the [pic]s with the 1/c serving as the separation constant. Thus we can write a product function of the ambient (M s:

[pic] (5)

Because these Dirac eigenfunctions have the energies in their exponents (((ei(t=eit/( with H(=E() we can also write (with k a column matrix, ‘t’ the M+1 scale proper time):

[pic] (6)

Additionally the zitterbewegung oscillation will have this same ei(t dependence (as in r=roei(t) from the Heisenberg equations of motion. From dt/ds=1/goo and E(dt/ds(goo, we have H(1/(goo. Thus:

[pic] (7)

Therefore as r becomes smaller than kH the square root becomes imaginary. Thus ( becomes imaginary. Consequently if on the outside (i.e.,r>kH) ((sin(t then sin(t(sin(i(t) =isinh(t as you go to the inside (i.e., r0) (Maker, 1999) to the M+1 th scale fractal object (the recently discovered cosmological acceleration) inside the horizon and represents a metric cosmological expansion occurring at each point.

PROPULSION

Equation 8 [that sinh(t, written out as X((x(-(Msinh((Ht), also from equation 2 we have Zoo=8(e2/2mpc2] implies that to do the physics correctly we must do a radial coordinate transformation to the coordinate system comoving with the cosmological expansion (here the M+1 th fractal contribution to equation 8) giving:

[pic] (9)

That zoo turns out to be the classical gravitational source 8(G( and we can actually derive G here(Maker, 1999). We can then create a ARTIFICIAL coordinate transformation using changing E&M fields that cancels the physical effects of the equation 9 coordinate transformation that gave the gravity term [pic] in equation 9. In that case we could then cancel the effects of the gravitational constant G and so cancel out gravity and possibly inertia or even make G negative! This would certainly be an aid to propulsion technology. So putting in the effects of a annulling C00 into that coordinate transformation X( (x(-(Msinh((Ht) would modify this coordinate transformation to:

[pic] where [pic] (10)

So that X((x(-(Msinh((Ht)-(Msinh((Ht)=x(+0. The zero signifies that our coordinate transformation effect has been annulled and therefore there would be no gravitational contribution zoo in equation 9. Thus our goal is to derive an E&M configuration to artificially create this second

+(Msinh((M+1t) ( Co =cancellation term. (11)

Thus the (Msinh((M+1t) coordinate transformation term in equation 11 (recall X( (x(-(Msinh((Ht) ) will cancel out and the mass zoo term then will be canceled out in equation 10 by that coordinate transformation. To get the artificial equation 11 cancellation term Co we would like the most general (metric) E&M physical configuration available, which includes rotation. We then use it to derive X( ( x(-C(. The most general metric available to do all this is the Kerr metric

[pic] (12)

[pic], [pic] (13)

We will derive equation 11 for the case of the Kerr metric. For that purpose we take the Kerr metric to be a quadratic equation in dt (( Co/c) with B(4masin2(d(/r, A(-c2(1-2m/r) in A(dt)2+B(dt)+C=0. Also we use the ansatz [pic] ((A) from our new E&M source. Thus the quadratic formula solution of equation 12 in dt is:

[pic] (=Co/c) (14)

Note in the discriminant that for A=0 then 4AC=0 and also that C is proportional to the square of already small terms and so is small relative to the d( in the ‘B’ term even where A is not zero. In any case we will be making use of the region for which A(0 so the largest nontrivial component of equation 14 is:

cdt/dto=Co/dto=cB/Adto=[pic]=annulment (15)

where A=c2-(2m/r)c2 and the division by dto is done to get the annulment term into the derivative in equation 9. Also in equation 15 we have m (Zoo/8(=e2/mpc2 and B is carrying the angular momentum term. Notice though that if you varied 2m/r just slightly around this value of ‘1’ you would radically change the annulement and therefor the gravitation since this “A” is everywhere in the denominator with equation 2 metric time component goo=A so there is also a time dilation effect giving “stability” around 2m/r(1. But here mp(me (electron mass) since in macroscopic applications the electron motion will dominate in the geodesic equations. So we make:

2m/r=2e2/2mec2r=2eV/2mec2=V/512kV (16)

since me=electron mass=9.11X10-31kg, c=3X108m/s and e=1.6X10-19C so that mec2/e=9.11X10-31(9X1016)/1.6X10-19 =512,000V. Note that for V=512kV then A=1-V/512kV=0 making equation 15 infinite and so giving a very large contribution to the annulment through equation 15. But in general by keeping ( constant with ( only varying slightly we can plot a graph of equation 15 also here called figure 1:

[pic]

FIGURE 1. Weight vs. Voltage.

EXPERIMENTAL RESULTS

Here we summarize the experimental results for the left side >512kV and the right side 512 kV

A recent superconducting (SC) disc experiment with electron rotation provided by SC vortices was published. Electron cloud stability was indeed noted at ~500kV with the antigravity pulse and rotational (vortex velocity) dependence noted along with observed pulse behavior on both sides of 512kV if the microphone data included. Also very suggestive results have been found from tandem Tesla coil experiments in which the voltage output from one Tesla coil is stepped up even further by another. These experiments involved reproductions of the devices discussed in patents numbered 593,138 and 4,661,747. The electron cloud stability, called cold electrons in this case, and the pulse were both seen also. Also the electron rotation region (Tesla experiments) gives a stable ‘cold’ electron cloud not seen in the section of coil just outside this region. These results also serve as a reality check on the SC experiment.

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