Very Large Propulsive Effects Predicted for a 512 Kv Rotator

Very Large Propulsive Effects Predicted for a 512 kV Rotator

David Maker1

Email:

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 (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).

(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 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):

(3)

we have an infinite succession of such equations:

….,,,,… (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 s with the 1/c serving as the separation constant. Thus we can write a product function of the ambient M s:

(5)

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

(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:

(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., r<kH). Thus for both  and zitterbewegung r=roeit it follows that:

r and Msinht inside, r and Msint outside (8)

Note that equation 8 gives a radial acceleration (d2r/dt2>0) (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:

(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 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:

where (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

(12)

, (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 (A) from our new E&M source. Thus the quadratic formula solution of equation 12 in dt is:

(=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==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:

FIGURE 1. Weight vs. Voltage.

EXPERIMENTAL RESULTS

Here we summarize the experimental results for the left side >512kV and the right side <512kV of the graph of figure 1 confirming the shape of the curve and thereby the validity of equation 15.

Voltage >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.

Voltage<512 kV

Note in figure 1 that for rotating oscillating electrons in a coil lets say that the mass will increase for V<512kV. In that regard note the left side of the curve. This was observed in the $200 A wing 4487 experiment and the John Brandenburg experiment.

Results Above 512 kV for Superconducting Disk

Here we propose these results as a theoretical explanation of a Russian experiment recently completed and published August 3, 2001 (Podkletnov, 2001). We note that the rotational dependence and mg spiking with voltage result was derived prior to August 3 (Maker, 2001). In the Russian experiment as the voltage went through ~500kV (in a type IISC) the combination of microphone and pendulum results imply that a positive and negative gravity pulse was created (recall the above diagram implies this also). The pulse was proportional to the magnetic field put on the superconductor so that it was proportional to the vortex velocity just as the above effect was proportional to the rotational angular velocity . The above equation 15, that gives these results, was presented in the February STAIF 2001 (Maker, 2001). These experimental results were presented in August 3, 2001. The gravity pulse was created by voltage on a superconducting disc. An electron cloud in the form of a disk (instead of a spark! Only sparks occurred below 500kV) left the SC disc and moved rapidly to the anode in a low vacuum chamber. The antigravity pulse (itself) left the chamber and was detected by pendulums (which moved) on the other side of the anode from the disk outside the chamber. The movement was independent of the mass of the pendulum implying that it was a “gravity” pulse. Unattenuated pulses (within measurement error) were detected at 100m from the SC. Claims were made in the paper (Podkletnov, 2001) that the effects of the gravity wave pulse were isolated from those of the sound wave pulse. For example the pendulums were placed in a evacuated bell jar and also measurements taken on the opposite side of a thick wall. Hopefully this was enough. Note that for V above 512kV the curve assymptote is lower so that the antigravity component of the pulse will dominate.

The Integral

Recall from just above equation 15 that A=c2[1-2m/r] with 2m/r=2e2/(2mec2r)=eV/(mec2)=V/512000, so also 4m/r 2 at V=512kV. Also in the classical Kerr solution avr so angular momentumma so area normalized angular momentum = a=(v/c)r with only disc edge electrons contributing to V. The “1” in front of the (v/c)r represents the rotating source magnitude and is less if more than just the rotating source is providing the voltage V. So equation 15 can be rewritten as:

(17)

which is equation 1. The middle of the electron cloud is slightly closer to the anode so it accelerates along the z axis at a slightly greater rate than the outer portion creating a bulge in the middle (so  different on the outside, slightly cusped) that is directly proportional to the voltage traversed by the cloud. So the electron cloud is not flat when it reaches the anode, it has a slight ‘concavity’ to it. Lets say the voltage reaches its final value when  is near 13 (or for the other material 9.2) so for the 13 = 180/C we have that C=14 and so in that case polar angle =/2-(/14)[V/Vf] with (/14)[V/Vf] providing a perturbation from the 90=/2 flat electron disk. So we have the change d=dV/(14Vf). Essentially you then integrate from V=512kV volts up to the final voltage Vf. I assumed a disk that had a bump height/radius large enough to cause a corresponding uncertainty in the voltage around that 512kV value. So the “A” is not precisely zero and is displaced from zero by this small amount. I assumed also that the upper part of the vortex (in the 7X10-7m) contained the contributing rotating electrons. Take the thickness of the SC disk to be 8mm=T and the radius to be 8cm=r, the pulse rise dt=.0001/2sec (Podkletnov, 2001). I assumed that the electron velocity was the classical (e/m)rB=v=(1.6X10-19/9.11X10-31)(7X10-7)(.9)=1.1X105m/s (not much different than the vortex velocity in the superconductor). So the radius normalized angular momentum is a=(v/c)r= (1.1X105/3X108)(.08)=2.9X10-5

So equation 15 becomes:

(18)

We next integrate this equation. Define

Integral=ve (19)

Close to the 512kV singularity the V is not infinitely well defined because of the SC surface irregularities. Also this integral was taken numerically and Podkletnov claimed that the pulse started at 500kV instead of 512kV so we take =12kV. Thus for 500<V<512 we use the integrand value at 500kV and for 520>V>512 use the integrand value at 520kV. The rest makes normal use of the integral. Note here that the entire electron density (giving the charge) was on the exterior here. If there had been a lower density than the charge that created the voltage then the rotational term would have been correspondingly smaller.

Comparison to Pendulum Tests

A pendulum in an evacuated chamber was situated on the line connecting the anode and the cathode but on the other side of the anode from the cathode, outside the experimental apparatus. At various distances from the cathode its displacement was measured due to the pulse. A repulsive pendulum movement was observed that was independent of the type of material or the mass the pendulum was constructed of. The pendulum displacement was measured (and so the final height) as a function of the applied voltage V at the cathode. To help determine the nature of the effect of this voltage we look at the data presented in the aforementioned impulse experiments. Recall that ve is the voltage integral with Vf being the integration variable in equation 19. So here the acceleration is

a(c)ve/ t (20)

where again ‘t’ is the impulse time given by Pod-Mod pulse rise time of t.0001/2sec. The velocity applied to the pendulum mass by the impulse is given by

(21)

So that

(ve)2/(2g)=h (22)

This is the equation used to calculate the pendulum height as a function of Voltage applied to the SC at two different pulse curvature (or cusp)  s differences from the /2 flat case. Putting the integral of equation 19 into equation 22 we get for individual final heights (using a numerical integration fortran code) as a function of voltage and plotting the results along with the experimental (Podkletnov, 2001):

FIGURE 2. Height vs Voltage

Thus by only varying one parameter in equation 17, the value of  at the anode, we find a fit over the whole experimental curve. This is clearly suggestive since intersection with only one or two discrete points would be expected from a mere coincidence. In any case it may be possible to photograph the (luminous) electron cloud in which case  itself would no longer be a free parameter. Also Podkletnov noted that pendulum accelerations on the order 1000gs were observed and here at 600kV there is about a 1000g acceleration using equation 20.

Microphone Results

Note also the (Podkletnov, 2001) microphone results (up and down dips in pressure) that can be inferred to be the results of the up and down mg spike predicted above given the pendulum results. There is ambiguity in the microphone results to a 180 phase uncertainty that can be resolved if these data are also viewed in the context of the pendulum results. The first spike (in the microphone results) must have been the attractive pulse below 512kV since the antigravity (lower spike) dominated in the pendulum experiments. Thus the Podkletnov results (if you also include the microphone data) predict the curve of figure 1 over the whole range!

Electron Cloud Stability In SC Experiment

Also in the experiment a stable electron cloud was observed to leave the disk above 500kV (below 500kV there were only sparks). But electron cloud stability is provided by the E&M metric time component goo=A=1-V/512kV in this theory. Both the >512kV repulsive and <512kV attractive effects with electron cloud stability have been seen in the recent experiments discussed in the previous section. The effect was roughly proportional to the B field imposed on the disk (Podkletnov, 2001) and the superconducting vortex velocity is directly proportional to this B field. So the rotation was provided by electron motion in superconducting vortices. The electron cloud stability and rotation dependence of this effect (which is implied by the  term in figure 1) provide additional evidence that equation 17 serves to explain the outcome of the SC experiment. Also the theoretical shape goes from complete disk 0-25, still pretty much a (slightly concave) disk. But the shape was identified as a disk leaving the superconductor so this is further confirmation of equation 17.