Very Large Propulsive Effects Predicted for a 512 kV
Rotator
David Maker1
Email: maker3@bellsouth.net
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



 d
1
2 

ve=KVsin 
V   dt

 1  512kV  


(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 g ij 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).

L fractal   i  t N  

N 1

g  , 

N
 m t N  N  g N R N  LSource N

(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
g   ,  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):
  i  0
(3)
we have an infinite succession of such equations:
…., 

 i  0M 1 , 
   i  0M , 
   i  0M 1 ,…
(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  M s with the 1/c serving as the
separation constant. Thus we can write a product function of the ambient M s:


N
 M  M 1  ...  Physical
(5)
N M
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):



 physical  k exp  i1 /    H N t   k exp i1 /  H physicalt 
N M


(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:
  H  1 / g 00  1 / 1  k H / r
(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:
0
0
x x
'
(9)
Z
 Z 00  Z  z



00
00
X X
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 z 00 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:
x
X
0

x
X
0

Z
'
 Z 00  Z
 z  C 00 where C 00  z 00
00
00

(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
ds
2




2
2
2  dr
2
2
2
2
2
2 2 2mr
2
 
 d   r  a sin d  c dt 
a sin d  cdt
2
 





2
r,   r 2  a 2 cos2 , r   r 2  2mr  a 2
(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 g 00  1 
2eV ( x, t )
(A) from our new E&M source. Thus the quadratic formula solution of
2
2m p c
equation 12 in dt is:
dt 
2
 B  B  4 AC
(=Co/c)
(14)
2A
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= 2c
2
a sin 2 
d
 4m 
=annulment

 2
o
 r  2c 1  2m / r  dt
(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
-31
8
(16)
-19
since me=electron mass=9.11X10 kg, c=3X10 m/s and e=1.6X10 C so that mec /e=9.11X10(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:
31
FIGURE 1. Weight vs. Voltage.
2
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 II SC) 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:
o
2
C
2  V  (v / c) r sin d
(17)
 c 2

dt
 512 k  dtc 2 1  V / 512 k


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
o
2
C
2 4m a sin d
So equation 15 becomes:
c

dt
r dtc 2 1  2m / r 
 v   2    V

r sin

8 
 2 14 V
o
3
X
10




f
C

2 V 
 c 2

2
dt
 512 k 
dtc 1  V / 512 k 

c
2
V 
2

 512 k 



    dV
 
 14  V f


14 V f   dV


v / c r  cos 2  
V
2
dtc 1  V / 512 k 
14 V f
5
V
 2   V
 2  2.9 X 10 X 



 cos  14 V
 512 k  ..0001 / 2 V f 14  1  V / 512 k  
f


 V
7
 5.14 X 10 
 V f
dt
C
o




 cos 2  / 14  V / V f


1  V / 512 k




dV


dV
(18)
We next integrate this equation. Define
Integral= 5.14 X 10
7
 V


512 k   V f

Vf
cos

2  V
 14 V
f




dV


 1  V / 512 k 

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
ve  2 gh
v
(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.
Tandem Tesla ~512 kV
Patents 593,138 and 4,661,747 involve tandem Tesla coil apparatus. The voltage is stepped up by a first
Tesla coil and then stepped up again by a second coil to a very high voltage. The pulse and the electron
cloud stability are seen, and in that respect are even called “cold electrons” here. They are “characterized by
voltage drop in the spark gap”, ~400kV has been mentioned as the voltage this happens at, the pulse “leaves
wires and other circuit components perpendicular to the current flow”, pulse effects “penetrate all
materials”, effects “propagate instantaneously as a light like ray”. The very suggestive (near) 500kV voltage
requirement for this effect, electron cloud stability, pulse penetration of materials, pulse leaving at 90
degrees to the current (in this SC this means 90 to the current in the disc) all are common characteristics to
the above SC experimental results and so constitute at least a qualitative double checking of its validity. .
<512 kV Experiments
In a AC coil the current can increase in angle  from the coil mid plane since in that case the case the coils
are oriented that direction. Thus d/dt is positive lets say. When the current reverses itself (so  becomes
opposite sign) the angle  then is becoming smaller and so d/dt becomes the opposite sign, negative lets
say. Thus the product of  d/dt will always have the same sign in the equation 1! Also the terms
approximating the geodesics the 2m/r do cancel but the (m/r)adtd rotational term does not cancel. Thus a
net static charge does not have to be on the conductor to see this effect. So (Given that negative electrons
in the current are always involved here also) below 512kV these three phase electric motors will always
have positive gravity since there can be no sign change for in this equation for V crossing 512 in that low
voltage region since the voltages are far below 512kV. In that regard experiments were done in 1997 in A
wing 4487 of NASA MSFC on a coil suspended from a string on a balance. The stator coils were powered
by two phase, 400 Hz, ac, to generate a rotating magnetic field. The weight of the coil was measured for AC
current in the coil. Note here there is the voltage, electron rotation and oscillation all required in our
annulment equation to make it nonzero. But the voltage was clearly far less than 512kV so from the curve
on the left side of figure 1 it appears that mass (in the mg) should increase slightly. In this experiment there
was no magnetic shield but the ac effectively averaged out the effect of the earth’s magnetic field. The table
itself was about two feet away. A net weight gain of about 1% was seen. John Brandenburg of the
Aerospace Corporation did an experiment in the Space Sciences building at MSFC in front of an audience
that same year. He also used an ac current in a coil and saw a net weight gain also. Apparently Lenz’ law
was not the culprit here because that would have made the device appear lighter instead. By the way that
the Faller experiment (Faller, 1990) (that was supposed to prove no weight gain) did not use electrical
currents, it was purely mechanical, even used compressed air jets to rotate the gyroscopes. That makes it
irrelevant since with no net charge moving, there is no effect here. That annulment equation predicts no
weight change in this case also. A unpublished GSFC experiment using the Mettler mechanical balance is
somewhat of a question mark however and was contradicted by that MSFC experiment. The GSFC
experiment used electrical power to cause the gyroscopes to move but gyroscopes require very little power
to keep them moving. So the relevance to oscillating charges moving in a circle here is not clear: If the
electrical current was extremely small then that annulment equation predicts a very small (unobservable?)
weight change here also. Additionally this method did not use a mechanical arm to separate the gyroscope
from the scale making the GSFC experimental results questionable. In any case I was a witness to both the
MSFC experiment and Brandenburg’s and noted then that perhaps they did not sufficiently take into
account possible environmental effects by doing the experiments at different vertical heights above the
possibly small ferromagnetic content of the table or floor. But Brandenburg did a later experiment with a
mechanical arm with the sample far above the floor (the GSFC experiment can be discounted because it
hadn’t done this necessary thing) and the MSFC people claimed that the experiment worked even with a
conducting aluminum sheet separating the table and coil. So these results are suggestive that there is a small
but increased weight gain below 512kV for rotating charge in a coil such that d/dt is also not zero which
is seen in figure 1 consequence of equation 17.
Finally we note that the superconductor just provides the initial conditions for the later discharge. The
high velocity vortex currents and the coherent phasing are two such conditions. The coherent phasing is
probably responsible for the beam collimation since then the classical =1.22/D equation can be used to
calculate the beam divergence. An analogy is parallel wavefront light beaming entering a circular aperture.
The 1.22/D equation can then be used here also because of this initial condition of assumed coherence at
least over a modest distance in the aperture (so the same physics can be used as in the superconducting case
in calculating the beam divergence). Thus we can have the narrow observed beam divergence because of the
large D (8cm)..
Note that in that equation:
Vsin2(d/dt)(1/(1-V/512)). Note that the effect in this equation is proportional to V (voltage) and w, the
angular rotation and a change in sign in V (charge).
From European patent# EP 0 486 243 A2 done by Yamashita, Haruo of Japan:
"The amount of the generated vertical force or thrust depends on the magnitude of the charges and/or the
rotational speed. Whether the generated vertical force or thrust is directed upwardly or downwardly
depends on the polarity of the electric charge generator 9 but does not depend on the direction of rotation of
the rotor"
In any case there are at least 10 different correspondences between those equation 17 predictions and
these clearly relevant experiments: 1) Stable electron cloud in SC experiment, 2) near 512kV, 3) effect
dependence on rotation, 4) attractive pulse below 512kV, 5) antigravity pulse above 512kV, 6) antigravity
pulse dominates if V ramped far above 512kV since curve assymptote lower there, 7) acceleration
magnitude1000gs, 8) Equation 17 predicts the disk electron shape (/2) seen by the experimenter at the
onset of the phenomena, 9) electron rotation region (Tesla experiments) gives stable cold electron cloud not
seen in the section of coil just outside this region, 10) one free parameter () gives correspondence over
entire curve (for pendulum heights). In most other types of scientific experiments you are deemed fortunate
to obtain even one such correspondence with theory, there are at least 10 here.
LARGE EFFECTS
Recall from equation 17 we obtained the equation 1 annulment = KVsin2
d  1 
  , with A1-V/512kV.
dt  A 
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. Note that if V=512kV this equation is
singular (1/A=1/(1-1)=1/0=) implying large effects are possible (note singularity of figure1 at 512kV).
Below 512kV the force is attractive, above 512kV the force is repulsive (note sign change) with a rapid
ramping up of voltage far above 512kV giving a net antigravity force because of the then higher value of V
in the numerator and the lower assymptote. Electron cloud stability is provided by the E&M metric time
component goo=A in this theory. Both the >512kV repulsive and <512kV attractive effects with electron
cloud stability have been seen in the above experiments. The rotation was provided by electron motion in
superconducting vortices in the SC published experiment and by electron motion from tandem Tesla coils
where this repulsive effect was seen for >512kV. The rotation was provided by electron motion in motor
coils for the <512kV added small attraction results seen in several (<512kV, left side of figure 1)
experiments discussed above; both cases together verifying (quantitatively in one and qualitatively in the
others) the validity of the equation 17 in both regimes of figure 1.
To obtain large effects we artificially make the electron cloud oscillate in the polar angle =sin(t) so
that d/dt=cost. Also we need to make the voltage oscillate around 512kV so that for example
V=512kV+(V)sin(t+) where  is a phase constant. We set  so that A1-V/512kV (the reciprocal 1/A
of which is huge if V is close to 512kV) is in phase with cost (which is huge if  is huge, perhaps in
the kilohertz range) so that the sign on the annulment equation is constant (i.e. the sign at repulsion). Thus a
very large quantity  multiplies a very large quantity “1/A”, making equation 17 singular (1/A=1/(11)=1/0=), implying large effects are possible. Given that the equation apparently works we can use it to
predict a very large propulsive effect caused by an artificial electron cloud polar angle oscillation (e.g..
perhaps even with a microwave transmitter) about o artificially making =0+sint so that a HUGE
propulsion antigravity effect, millions of times larger than seen even in those experiments since  can be in
the kilohertz range (even for high voltage) and the voltage uncertainties of the Podlektnov apparatus near
512kV appeared to be only in the 10kV range.
In practice here d/dt even at 1000Hz will probably be order of 100 because the angle change is only on
the order of 2/100 for this concave shape. Also at these >500kV voltages there is approximately 10kV
uncertainty so that perhaps on the average 517 or 507 voltage will really occur so that A term even here
will be on the order of 100(e.g.,1/(1-507/512)) . Also because of material strength limitations for a 5 meter
diameter rotator nothing more than /2 100 times per second is to be expected. However the voltage will
be on the order of 512,000 V so that the net effect will still be huge. Thus a
512,000X100X100X1005X1011 effect. So that if this is set up as a tank circuit then very little energy
input gives a huge effect only limited by the conservation of energy.
Conservation of Energy
The conservation of energy leads to some very interesting consequences here. Note that if energy is
conserved and very little energy is being put in (for a tandem Tesla LC tank circuit setup this would be the
case) then the work done is (near) zero. W= Fdx0. If this is work being done against gravity (so net
vertical force) then this very huge antigravitational effect has to be constrained to do little or no work so
that the vertical forces (Fy) on the rotator exactly balance (Fy0 ), so the device must have a very stable
hover. In fact since this antigravity effect is so strong very heavy objects would then have a very stable
hover.
Conservation of Energy Application For Low Velocity Vertical Motion
We call the antigravity force upward (due to ve) Fup and gravity Fg down so the net vertical force is Fup–
Fg.=Fnet. Even allow the weight to be extremely large so that Fg is extremely large. But ve and therefore Fup
is (otherwise) unlimited due to the ease of getting that oscillation phased near the 512kV. But Fnetdx=Enet,
which is the propulsion energy input which could be due to Fup, chemical, ion propulsion, etc. with the
energy coming from combustion, nuclear reactor, solar energy, etc.. For vertical motion then Fnetdx=
½mv2=Enet. So for small Enet and nominal displacement ‘x’ then Fup–Fg.= Fnet must be small and therefore
FupFg. Thus the force up and force down cancel for small energy input. But again F up is unlimited allowing
Fg to be very large even for small energy input! Thus a huge weight (which could even be living quarters)
can be made to hover in midair with this 512kV rotator technique without violating the conservation of
energy.
Conservation of Energy Application for High Speed Propulsion
Propulsion to earth orbit is possible even if Enet is small, so even for small power input. As an example for
100kg =m, v=8km/sec (orbital v) and a 1000watt solar array (3mX3m solar array) on the rotator we can
calculate the time to orbit. For example Pt=KE= ½mv2=½100(8000)2=1000t. So t=3.2X106sec= 37 days 1
month to orbit. So we can attain earth orbit in a reasonable amount of time (~month) with the power input
equivalent of the space heater in your bathroom!
 v   2    V

r sin

8 
 2 14 V
o
3
X
10




f
C
V


2
 c 2

2
dt
 512 k 
dtc 1  V / 512 k 




    dV  dt o
 
dt
 14  V f
ct o
t
(23)
v=1.1X105m/s,V=522kV, 8cm=r, the pulse rise dt=.0001/2sec so that from equation 23 and given
experimental parameters:
 1.1X 10 5   2   
.08 sin  

8 
3
X
10
 2   522000    1
xo C o
2
522
k
 

 
c ' 
 3 X 10 8  2


 
dt
xo
 512k  3 X 10 8 2 1  522k   .00005  14  512k


 512k 




(25)
Cancel the c2 s and plug in the numbers:
2.9 X 10 5
m
1.044 X 1010 4.38 X 10 7  13.9 =v
 .0195
s
v
13.9
m

 27800 2 . Let m=2kg. But the impulse is given by Ft=mv and operates over only
t .00005
s

2.04 X
.0005sec so that




Ft  2 27800 .0005  27.8  mv  2v so v=13.9m/s
But if this same oscillation occurred continuously, in the way discussed above for the HUGE effect, then
there would a velocity of
m
m
 1 
 27800
after one second. But this translates into a kinetic energy gain of

13.9
sec
sec
 .0005 
1 2
mv  KE =( ½)2(27800)2 J=7.7X107 J which is more than even needed for low earth orbit. But as
2
we noted above the energy is constrained by how much energy can be put into the device, nonetheless, if we
put a huge amount of energy in we would get a huge amount of propulsive energy out and moreover the
”hovering” would be easy since it doesn’t require that any work be done at all.
Energy Source for Propulsion
A tandem Tesla LC tank circuit can provide the electrical oscillation if non drift electron flow is utilized
such as vortex electron flow. So if there is very little electrical resistance in the system this kind of hovering
requires very little energy. It would then be possible for the object to go into space at a slow rate (perhaps
take a week to orbit), with the thrust coming from whatever energy source is available, even solar power
supplied to an ion engine. For a kilogram of payload then a week to orbit would only require a continuous
power input of 60watts, enough to operate a light bulb.
Again the tandem Tesla coil method by itself provides far too little rotation rate in the coils for large
propulsion since electron drift velocity is so small in typical conductors. So it is best to make use of the SC
vortex rotation as a first step and proceed next to an actual physical charged rapid rotator. Also if an attempt
to duplicate this huge effect at 512kV is done without regard to voltage and phase accuracy (recall that )
all that will be observed is ordinary sparking, no propulsive effect. The voltage ramping up method (Taylor,
2002) is easier to accomplish in that regard but hasn’t near the propulsion capability of this 512kV rotator
since it does not make nearly as much use of the V=512kV singularity, just ramps up rapidly through it.
In this diagram these double concave plates (when completely expanded near the edges) engage in a J o
mode Bessel function 1st harmonic oscillation so that as the upper plate is increasing in  the lower one is
decreasing in , thus always keeping d/dt opposite sign for the two plates and so making it look like they
have the same charge since equation 1 will then have the same sign for both plates. The d/dt signs are also
phased to make sure that 1/(1-V/512kV) always opposite sign as V crosses back and forth across 512kV so
that the net sign on each plate stays a constant.
Thus the plates can have opposite charge and still the equation 1 left hand side will still have the sign for
both plates and at all points in the oscillation cycle if these double concave capacitor plates are used.
Development Plan of 512kV Rotator Oscillator
1) Set it up with pods capacitors and the SC and again find the pulses at for voltage ramped up to >500kV.
Perhaps then demonstrate it to get backers. Then proceed to step 2.
2) Use coils and full wave rectifiers (instead of Pods capacitors) to have the voltage vary back and forth
across 512kV (not ramped then) in phase with pulse shape change. Note the pulse strength and pulse
duration then, (it should be a machine gun type set of repeated pulses) and note the impulse forces on
objects and therefore the (antigravity) propulsive effects (then get more backers).
3) Instead of a superconductor have the electrons rotate in a ordinary conductor (flywheel) at very high
angular velocity for two oppositely charge double concave plates with a piezoelectric oscillator between
them that also doubles as the capacitor dielectric. The piezoelectric oscillator changes the capacitor plate
shape (this electron cloud shape change is needed just as in Pods pulse case) therefore the electron cloud
shape (here however enclosed inside the conductor). The plates oscillate in the fundamental Jo mode with
the antinode along the edge as the voltage is also changed back and forth across 512kV using two full wave
rectifiers 90deg out of phase with one another. The effect will then essentially be continuous instead of
pulsed. The (antigravity) effect should then be continuous on these plates.
4) Build a working model. Things should then snowball.
Annulment
To demonstrate that we are at least close to annulment you must demonstrate numerically that the dt/dto
using the T=+Msinh(M+1t)/c  Co actually cancels the derivative term equation 9. The derivative term in
equation 9 can be calculated by taking the derivative of the r  ro 
 M 1
1.57c
cosh  M 1t  with

1.57
sinh  M 1t  which is
 M 1
2
  M 1 , Thus
 5.6 X 10 40 , and therefore
18
4.3 X 10
1.57c
=2.67X10–31 m/sec. In this regard note that radial expansion effects of V, r and v (recall in equation 17
that rv/c=a=angular momentum term) scale down tremendously in going from the ring of electric current on
the edge of the disk and superconducting vortex radii respectively to the 10 –13 m radius scale of the
zitterbewegung oscillation needed to calculate the derivative. Recall for one large value of the final
voltage in equation 17:
a sin 2 
d
 4m 
ve  2c 2 
 14m / s for the electron cloud over
 2
o
 r  2c 1  2m / r  dt
the whole width .008m. But since this is a radial velocity the effect over 10 -13 m is proportionally smaller.
Thus m/r=VV(10-13/.008), SC vortex r(10-13/.0001)r, v(10-13/.008)v. The Vrv factor in the numerator
of equation 17 then is reduced by 1.56X10–31 over the zitterbewegung distance which is 1/(8X1011 ) times
the width of the superconductor (about 8cm). So 1.56X10 –31 times 14m/s is the result which is thus close
to annulment of =2.67X10–31 m/sec in equations 9-11.
Figure 2
SUMMARY
An UNgauged general relativity (with harmonic coordinates provided by Dirac zitterbewegung, so
<H>=E=(dt/ds)goo, goo= 1-k/r) implies the source is Zoo =8e2/mc2. In a ungauged GR it is also possible to
limit the number of implicit assumptions by allowing for fractalness within unobservable regions, within
horizons. In combining the set of such Dirac equations, one for each fractal scale, one gets (using
separability) a physical wavefunction which is a product of the time dependent Dirac eigenfunctions over
fractal scales. Propulsion applications arise in introducing an artificially created Kerr metric structure with
the above 8e2/mc2 source: same math as Kerr metric, new source. We use this artificial metric to cancel the
effect of the zoo created by the radial expansion implicit in that fractal wavefunction. In doing so we find a
zoo annulment term that has an angular momentum in the numerator and a A=1-e2V/2mc2 =1-V/512kVterm
in the denominator if m is the electron mass. For rotating charge there is a large (repulsive) gravitational
propulsion effect if A=0 (=1-V/512kV) so for V=512kV. Also if the voltage is increased fast enough there
will be a consecutive repelling and attractive propulsive pulse released. If the voltage V is varied around
512kV such that 1/[1-V/512kV] is in phase with d/dt (with the product then a constant) then a very, very
powerful propulsion is a consequence with the conservation of energy constraining the propulsion to a
‘hover” for small energy input. Experiments have been done that spectacularly verify equation 17 in the
<512kV and >512kV regimes so this extremely large propulsion effect is to be expected.
ACKNOWLEDGMENTS
It was Glen Robertson’s idea to integrate that negative gravity equation. At about the same time he also was
first to learn of the superconducting experiment confirming the validity of this equation several years after
it was discovered (in the equation 17 form) and presented in other forums by Dr. Maker much earlier in a
BPP proposal in 1997 and a STAIF 2001 paper. Nathan Hanesh brought to our attention those tandem
Tesla experiments that appear to lead to the same experimental results.
REFERENCES
Bjorken, Drell, Relativistic Quantum Mechanics, McGraw-Hill (1964).
Faller J.E. et al, “Gyroscope Weighing Experiment With a Null Result,” Phys.Rev. Lett., 64(8), (1990) pp.825.
Goldstein, Herbert, Classical Mechanics, 2nd Ed, Addison Welsey, 1980 pp.594.
Maker, David, “Quantum Physics and Fractal Space Time,” Chaos, Solitons, Fractals, 10(1), (1999).
Maker, David, “Propulsion Implications of a New Source for the Einstein Equations,” in proceedings of Space
Technology and International Forum (STAIF 2001), edited by M. El-Genk, AIP Proceeding 552, AIP, NY, 2001,
pp. 618-629.
Merzbacher, Quantum Mechanics, 2nd Edition, Wiley, New York, New York, 1970, pp.574.
Podkletnov, E,” Impulse Gravity Generator...” arXiv:physics/o108005, LNL Archives, 3Aug 2001.
Sokolnikoff, Tensor Analysis, Wiley, (1964).
Taylor, C, Evaluation of An Impulse Gravity Generator Based Beam Propulsion Concept, American Institute of
Aeronautics and Astronautics, 2002.
Weinberg,S., Relativity and Cosmology, Wiley, (1972).pp.254.
STAIF 2003 Site
http://content.aip.org/APCPCS/v654/i1/958_1.html
.Appendix A From Meteorology article:
In both tornado and thunderhead storm systems -- start from the same early structures:.the
hammer-head formation which are around 300kv. Tornado clouds have been termed as
a low voltage thunderheads. When a certain voltage is reached, the cloud undergoes a dynamic
change in the basic structure. Interestingly, tornados haven't been seen over a maximum of
600Kv. In contrast, thunderheads start at over 1Mv and never develop the rotor motion... There
seems to be something happening at the lower voltages which drastically alters the course of the
cloud's nature..."
At 100kV insulating capability per meter go a few meters deeper into the tornado (instead of at
the 300kV surface) and we see 500kV instead of 300kV. Thus these rotating and oscillating
objects (tornados) have a optimum voltage of formation of around 500kV.
>>>>>>>>
Note that "when a certain voltage is reached” comment with that voltage being around 500kV. Also
“thunderheads over 600kV never develop the rotator motion” comment. Also note the comment that “There
seems to be something happening at the lower voltages which drastically alters the course of the clouds
nature” . It appears the cloud becomes very dynamic around 500kV and is not so way above or way below.
But I would have expected that given that singularity at 512kV, rotation w, oscillation dtheta/dt, etc..!!!!
(in that regard recall:effect=V(d/dt)[sin2][1/(1-V/512kV)])
Perhaps thunderhead meteorology is the best experiment
Sparks at 512kV
In that LargeP paper note that equation 12 is the GR Kerr metric generalization of the Pythagorean
theorem for a rotating object in 4 dimensions where time is considered the 4 th dimension. The standard GR
representation here is to take the 'm' to be mass times a constant (here classically 2G) and the 'a' to be
angular momentum. Note that for zero velocity and small angular momentum 'a' then ds2 =(1-m/r)dt2 so
that when m=r then ds is zero and time slows down. The corresponding situation in that 'Ungauged GR
paper in the context of fractal physics' gave us the proton stability discussed in section 4 of that paper. Thus
in a black hole the time slows down(the clocks are observed to slow down) with respect to an external
observor, the light is red shifted,etc, the person lives longer relative to the external observer, etc..
But here in the LargP paper we replace the right hand side of the G oo component of the Einstein equations
with 8e2 /mc2 and do not use the 8piGrho as in the traditional GR equations (recall this is consistent with a
complete set of GR equations, etc.). Thus the mathematical symbolism of the traditional Kerr metric has a
E&M source instead of a gravity source here. But the meaning of dt2 stays the same so that
ds2=(1-m/r)dt2 ds2=(1-V/512kV)dt2 for our spherical static electric source and time slows down just as in
the classical case. Thus for the electrons and currents flowing at 512kV there is more 'stablility'. Such
currents are harder to shut down thus in open circuits electrical currents (sparking across gaps) would
persist longer (see insert), pod's 500kV disk of electrons is stable and less likely to disperse (see pod's
paper), that "cold electricity" quiet type static sparking that has been observed by others near 500kV is less
likely to jump around and cause a lot of noise (I have some literature on this subject), etc..
Sound oscillation of a ring instead of piezoelectrics
displacement of air sm with 120dB sound (so loud it is painful). That loudness corresponds to a deltap of
28pascals and so at 1000Hz , sm= deltap/vrhow=28Pa/[(343m/s)(1.21kg/m^3)(2pi(1000Hz)]=11microns
which clearly isn't any better than piezoelectrics. But the actuator must only be displaced that amount there
won't be much dtheta/dt unless the ring is very small..
Recall impulse integral =integral V(d/dt)[sin2][1/(1-V/512kV)])dt, In that regard one could use
just one rapidly rotating oscillating plate in this capacitor, with the other plate stationary.
The(negative charged) flourine would be rotating and also moving back and forth along the z axis
with changes in the applied potential. One way to get a really monster-huge effect is to put a
CONSTANT 512 DC on these two plates (with the negative on the flourine side of course) and
then flutter the voltage (by perhaps plus or minus 120V) with microwaves! The flourine gas will
move easily so d/dt will be huge and in phase with the 1/[1-V/512]. since V will be moving above
and below 512 in phase. Both V and w in the numerator will be approximately constant giving us
the correct phasing. Anyway billions of cycles per second microwave will make this thing rock and
roll, do big things. Of course the conservation of energy will make it so it will hover, but any excess
energy will send it up in space.(you need to solar panels for that also).Thus there is only one
oscillating and rotating plate. The other (positive) plate is stationary but still has opposite charge of
the active plate. This is far easier than rotating two plates and still makes it so the passenger of
the prototype only sees zero voltage since the charge on both plates cancels! The 500kV won't be
a danger any longer with the electrons in that plate doing the heavy lifting, the electrons in the
other plate aren't rotating, contribute nothing to the lift process.