In this paper, we formulate a percent mass change equation based on Woodward's transient mass shift and the Cavendish balance equations applied to superconductor Josephson junctions, A correction to the transient mass shift equation is presented due to the emission of the mass energy from the superconductor. The percentage of mass change predicted by the equation was estimated against the maximum percent mass change reported by Podkletnov in his gravity shielding experiments. An experiment is then discussed, which could shed light on the transient mass shift near superconductor and verify the corrected gravitational potential

Robertson, Glen A.

English

NASA Technical Reports Server

j, /j
On the Mechanism for a Gravity Effect using Type II Superconductors
Glen A. Robertson
Advanced Systems and Technology Office, NASA-Marshall Space Flight Center, Huntsville, Alabama 35812
ABSTRACT
In this paper, we formulate a percent mass change equation based on Woodward's transient
mass shift and the Cavendish balance equations applied to superconductor Josephson junctions.
A correction to the transient mass shift equation is presented due to the emission of the mass
energy from the superconductor. The percentage of mass change predicted by the equation was
estimated against the maximum percent mass change reported by Podkletnov in his gravity
shielding experiments. An experiment is then discussed, which could shed light on the transient
mass shift near superconductor and verify the corrected gravitational potential.
INTRODUCTION
Eugene Podkletnov has reported that a gravity shielding effect was seen above a YBCO
superconductor being rotated by a magnetic field and irradiated by RF energy. I11 The mechanism
for this phenomenon is as debatable as the test itself. Independent of Podkletnov and about the
same time, Torr and Li published several papers on the possible connection between gravity and
superconductors. I2-41 These papers suggest that the gravity mechanism arise from the spin of the
lattice ions aligned by an applied magnetic field. In 1995, Becker a student of Torr, showed
mathematically that a significant size gravito-magnetic field could exist along with a magnetic
field.whenever there is flux pinning or other forms of flux trapping in a type II superconductor. [sl
Modanese, a close contact to Podkletnov, has presented a theoretical model from Podkletnov's
experimental results. [61. The model, which is based on the "anomalous" coupling between Bose
condensate and the gravitational field, suggests that the essential ingredient for the shielding is
the presence of strong variations or fluctuations of the Cooper pair density in the disk.
The behavior of the Bose condensate of Cooper pairs within superconducting materials in an
external gravitational field has been the subject of some study in the past. I71 M. Casas, etal,
recently suggested that Cooper pairs lead to Bose condensation at temperatures substantially
greater than those of the BCS theory of superconductivity. [81 In an unpublished paper presented
to the author for review, Noever and Bremner suggest such a connection by indicating that
superconductors could modulate the background quantum ZPF. [91 Stirniman presents a related
historical overview leading up to gravity's relationship to the superconductor. II°l Other papers
have even suggested a connection between gravity and electrons. [l 1,121
In this paper, it is suggested that a combination of flux pinning and Cooper pair fluctuating
across Josephson junctions produce a mass change about the superconductor. An equation for
the mass energy produced across the Josephson junctions and an equation for the percentage of
mass change is derived from Woodward's transient mass shift equation. {i31 A correction to the
gravitational potential Woodward used in the equation is presented. The correction implies the
emission of mass energy from the superconductor. The percentage of mass change predicted by
this equation was estimated against the maximum percent mass change reported by Podkletnov
in his gravity shielding experiments. An experiment is then discussed, which could shed light on
the transient mass shift near superconductor and verify the corrected gravitational potential.
https://ntrs.nasa.gov/search.jsp?R=19990046249 2020-06-18T01:04:19+00:00Z
BACKGROUND
Of what is known of the type II, YBCO superconductor disk used in the Podkletnov
experiments; it seems certain that a large number of superconductor-oxide-superconductor
Josephson junctions exist within the disk. In the general sense, Josephson junctions are very
small capacitors with the electrodes composed of superconductor material and the dielectric
composed of an oxide layer. [14' pg 196-286] Unlike normal capacitors, Josephson junctions exhibit a
unique property. They radiate RF energy when traversed by a current and generate a current
when radiated with RF energy. This would indicate a fluctuation of energy across the junction.
With this in mind, it must be noted that the procedure for making the superconductor disk,
including the pressing and sintering of varying size SC grains, produces a structure having many
flux pinning sites around which exist the Josephson junctions. Flux pinning is a well-known
phenomenon associated with Type II superconductors where magnetic flux is trapped inside a
superconductor. Flux pinning results from any spatial inhomogeneity of the material, such as
impurities, grain boundaries, voids, etc. To be most effective, these inhomogeneities must be on
the scale of the order of the penetration depth or the coherence length, i.e. -10 .6 to 1 04 cm, rather
than on the atomic scale where inhomogeneity causes electronic scattering which limits the mean
free path. I14' pg 166] This so happens to be in the range of the size superconductor powders used to
make Podkletnov's disks.
In order for the magnetic flux to remain trapped, a current loop forms around the holes
created by the superconductor particles. It would therefore seem that Podkletnov has produced a
device that allows flux pinning to enhance the production of RF energy and RF energy to
enhance the production of superconductor currents. These reinforcing phenomena should lead to
high electron densities or super currents in the superconductor disk. These currents are focused
between the superconductor particles, which are Josephson junction sites.
TRANSIENT MASS SHIFT
During a review of current literature for clues on the connection between mass energy and
superconductors, it was found that Woodward, who has done some very interesting work with
capacitors, both theoretically and experimentally, has come up with an equation for a transient
mass shift derive from Mach's Principle. L131 Mach's Principle explains inertia - the tendency of
an object to resist acceleration - by the sum of the gravitational attractions of all objects in the
universe. Woodward presented the transient mass shift dmo as
flw& (1)
c_mo - 27cGpoc2
Where dmo is the transient mass shift; fl is the ratio q_/ c 2 (9 is the gravitational potential due to
all the matter of the universe) and is approximately 1 and unitless; w is the frequency of the
driving voltage into the capacitors in radians per second; Po is the power applied to the capacitors
in ergs/s (10 7 ergs/s = 1 Watt); G is the gravitational constant = 6.67xl0 8 dyne cm2/gm2; po is
the density of the capacitors; and c is the velocity of light in cm / s = 300x108 cm/s.
A Cavendish balance, which is routinely used to measure the gravitational constant G allows
for the expression of G in terms of measurable quantities, which are
G = ¢ _ (2)
Where M is the test mass (superconductor), b is the distance between the center of a known mass
m and the test mass M, 1 is the separation distance of the masses m on a torsion bar, T is the
period of the damped harmonic motion of the torsion bar, and 0 is the angular displacement of
the torsion bar caused by the motion of the test masses. Note that the result is independent of the
value of m and can be written in the following simplified form
= L,GM (3)
Where Tc = (8/b2l)(T/2,rc) 2 is a proportionality constant associated with the torsion balance
characteristics.
If perceptible transient mass shift could be demonstrated with a Cavendish balance, the
change in the measured angular displacement of the torsion fiber will be directly proportional to
the test mass change, assuming the gravitational constant is unaltered. For example, the change
in angular displacement dO associated with an effective change in test mass dM due to
gravitational modification is given by
Oq5= Tc Gc3M (4)
By combining equations 4 with equation 1, the change d0 in the angular displacement ¢ due
to a mass change dM can be expressed in engineering terms as
c3O - Tc flJ;.,P' (6)
Po c
Wheref is the frequency (in Hz) of the effective input power Pi (in watts).
By setting equation 3 equal to equation 4 through the constant TcG, a relationship between
the two angular displacements and the masses can be made. From this relationship, a percent
change in mass can be expressed by
M% = __aM*100 -- --c30*100 (7)
M 0
Using dO as defined by equation 6 and 0 as defined by equation 3, the percent change in mass
can be expressed as
=I PJ;g
M% LGMpoc 2 *100 (8)
In the Podkletnov experiments, the percent change in mass of an object placed above the
superconductor disk was maximized at 2%. Assuming the same for equation 8, then Mpo is on
the order of 1012 kgZ/m 3 withf = 10 6 Hz and Pi = 100 watts. Then it is easily seen that this
equation does not make much sense if M po is that of a typical mass and mass density of a YBCO
superconductor (M- 2 kg and po- 50 kg/m3). Therefore, what are these quantities? It is argued
that the mass change is due to electrons, which somehow affects the total mass. It is then stated
that in the superconductor po is the density of the superconductor (given by psc) and M is the
mass of the electrons (given by Me) involved in the phenomena given by
I_ A j; (9)
Where6j is thecurrentperareaassociatedwith the superconductorJosephsonjunctions,Ajj is the
sum of the magnitudes of the normal vector to the cross sectional area of the Josephson
junctions, f j is the Josephson junction frequency, and qJm_ is the ratio of charge to mass of an
electron (= 1.759x10 tl coulombs/kg). By incorporating equation 9 into equation 8, then for a
superconductor with Josephson junction sites, equation 8 is rewritten as
• *100 (10)M,_%=
• Gl_jAt_p.,.cc 2
Given the analysis, from which equation 0 was derived, the transient mass shift expression
in equation 1 is modified for the superconductor to produce an energy E,o equation as
am_,c 2 : E, c - flf*P" (11)
P._C
Where Esc is the energy released during the mass change of the superconductor. Lettingf = 106
Hz, P, = 100 watts, p,c = 48 kg/m 3, G = 6.673 x 10 tl N mZ/kg 2, the mass energy radiated by the
motion of the electrons across the Josephson junctions is about 10 _6Joules. Noting that 1 Watt =
1 Joule/s, then the emitted power P,o associated with the mass energy E_c emission can be
expressed as
(12)
The frequencyf. 2 of the electrons fluctuating across the Josephson junctions is used. Since,
the mass energy is being created at this frequency. Lettingf =_j., the Power P_c emitted is about
1022 Watts. How can 100-Watts input produce 1022-Watts output? It is argued that the
gravitational potential _babout the superconductor is changed due to the emission of the mass
energy (E_). This change results in a change (A) in the dimensionless constant/3', expressed as
Where a is defined as the new gravitational potential due to the emission of mass energy E,o
from the superconductor. Redefining ,8 in equation 10 with Aft in equation 13 and regrouping the
terms, equation 10 can be simplified in terms of the power input and the superconductor
properties as
M,.,.% =y, *[LP,]* af,j *100 (14)
It. A.i, P.,_.
Where _'k = (qJme)/(Gc4) • Now an approximation of the percent mass change in terms of input
power and the superconductor can be made. The estimation is presented in figure 1 where ot =
.03, qJm_ = 1.7588 x 1011C/kg, G = 6.673 x 10-11 N m2/kg 2, c = 2.9979 x 108 m/s,f =fs= 106
Hz, p,_ = 48 kg/m 3, and/jj = 10 3 amps/cm 2, Ajj = 0.001 cm 2. The term a was chosen to make Pso
100 Watts and the magnitude Asj of the Josephson junction cross-sectional area was chosen to
make the 2% mass change fall at 1O0 watts.
600
5OO
400
3OO
200
100
0
0%
% Mass Change Per Input Power
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11%
% Change
Figure 1
TESTING FOR A TRANSIENT MASS SHIFT
The corrected gravitational potential a can be perceived as the only unknown in equation 14.
However, the values for/a) and Ajj were chosen to fit the predetermined notion of Podkletnov's
experiment. With this in mind, the ratio cr,/(6j Ajj) is the real term in question with respect to a
transient mass shift about a superconductor as just changing one of these terms without changing
the others could implies an energy loss or gain. Reproduction of the YBCO disk used in
Podkletnov's experiments should lead to reasonable values for /j). and Ajj. In addition, the
direction of the vector sum of the magnitude of Aii should be predominately in the plane
perpendicular to the direction of the pressuring force applied to make the disk. The pressing
plane used to make Podkletnov's disks was in the plane of rotation, which is perpendicular to the
effective force seen on the test masses. Given this assumption the pointing vector associated
with the Josephson junctions would be in an upward or downward direction. Due to the two-
layer arrangement of the disk and the fact that no change in mass was seen for a mass placed
below the disk, it is argued that it is upward. Also worth mentioning is that/jj was chosen for
this estimate as the critical current density of small grain YBCO superconductors produced by
the author. It may very well be that /j:/ is the current density across the junction and not the
critical current of the superconductor grains.
Utilizing the previous equations, the ratio a/(/:j Ajj) can be defined in measurable terms as
a _ 1 ,] p,_, a_, (]5)
1l,.4,, r, LZ_/,j P,
Where d_¢, can be experimentally derived using a properly' designed Cavendish balance.
Figure 2 shows the effect on the transient mass shift changes with the ratio ct/(Ic A/j) (= 0.003,
0.03 & 0.3). As seen, percent mass change is very sensitive to this ratio.
%Transient Mass Shift vs Power
24%
22%
20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
0 100 200 300 400 500
Watts
Figure 2
Such an experiment would utilize properly constructed high-Tc oxide superconductors
containing multiple Josephson junction sites between superconductor grains. The fabrication of
the superconductor would be such that the pressing force was applied perpendicular to the
applied magnetic field. This will insure alignment of the Josephson junction predominately in
the plane of the magnetic field. Cooper pair super-currents would then be induced across the
many Josephson junction sites that are distributed about the flux pinning vortices and modulated
by the RF input. A sketch of the proposed experiment is given in Fig. 3. As shown, U-shaped
permanent magnets with poles of high field, rare-earth permanent magnets are arranged such that
the magnetic field is through a high-To oxide superconductor like YBCO. The RF coils are
shown for representation. The actual configuration may vary dependent on the frequency
required.
From equation 4, an estimate the sensitivity to a transient mass change can be made by
making reasonable assumptions for the various balance parameters. Based on the published
characteristics of commercially available Cavendish balances, where T-- 120 sec; l -- 30 cm; b =
3 cm a numerical estimate for the sensitivity is given as
0_b _ 0.7 microradians / gram (5)
c_M
Thus, the sensitivity of a Cavendish balance to small transient mass change effects is generally
somewhat limited, and successful detection of these effects will require painstaking efforts in the
design and fabrication of the instrument. It will be necessary to push every parameter toward its
extreme values in order to achieve the highest possible sensitivity. For example, for a 500 gram
superconductor test mass, where the density of the YBCO ceramic is approximately 4.8
gram/cm 3, -then a I% change in effective mass (dM = 5 grams) due to transient mass change
effects would yield a torsional displacement of d_ = 3.5 microradians. This is within the
established sensitivity of state-of-the-art torsional displacement transducers, which can easily
resolve displacements of less than 1 microradian. Such a Cavendish balance is commercially
available from Tel-Atomic.
Permanent Magnets
Superconductor
! \ ....
N ] _'_ S' I
_'_---v--I
"'LI\. \.
RF Power
^ RF Power ^
T ,-, _ ,\1I L\..\...
i
I
Electronic Scale
Figure 3
CONCLUSION
Much of the material presented in this paper is clearly hypothetical. The equations are a first
order approximation that needs further refinement. For example, the corrected gravitation
potential ot may also involve an efficiency of the power inputted into the superconductor or the
conversion of the power to currents across the Josephson junctions. Although, should a transient
mass shift be seen by the described experiment. It would provide the necessary foundation for
further work in this area.
This research was supported in part by NASA's Advanced Space Transportation Research,
Breakthrough Propulsion Physics. The author wishes to thank R. Litchford for help in the
sensitivity analysis of the Cavendish balance and R. Koczor, W. Brantley, and J. Cole for helpful
discussions.
References
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gravitation shielding properties of composite bulk YBa_2Cu 30 {7-x} superconductor below 70 K
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On the Mechanism for a Gravity Effect Using Type 2 Superconductors

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