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IOP PUBLISHING SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 24 (2011) 125011 (9pp) doi:10.1088/0953-2048/24/12/125011
Evaluation of enhanced frame-dragging in
the vicinity of a rotating niobium
superconductor, liquid helium and a
helium superfluid
MTajmar
Department of Aerospace Engineering and Department of Physics, KAIST, Daejeon,
Republic of Korea
and
Department of Aerospace Engineering, University of Applied Sciences, Wiener Neustadt,
Austria
E-mail: martin.tajmar@fhwn.ac.at
Received 9 June 2011
Published 8 November 2011
Online at stacks.iop.org/SUST/24/125011
Abstract
To explain a reported Cooper-pair mass anomaly in niobium it has been predicted that rotating
superconductors or superfluids might produce large non-classical frame-dragging fields.
Anomalous gyroscope signals close to the measurement resolution in the proximity of rotating
superconductors or liquid helium have also been reported while trying to investigate this
theoretical concept. Based on lessons from various setups, we succeeded in building an
experimental facility that allowed us to rotate a niobium superconductor, liquid helium,
superfluid helium and low temperature matter with high accelerations at high speed exceeding
all previous efforts. A military-grade SRS-1000 gyroscope at close proximity in different
locations was used to measure any anomalous frame-dragging-like fields. No such anomalies
were found within three times the noise level of our setup (±5×10−8rad s−1). Measurements
with an electric motor at speeds up to 5000 rpm enabled us to set low boundaries for any
coupling or frame-dragging-like effect outside of a rotating niobium superconductor or liquid
helium to 4 ×10−11 and for superfluids to 3 ×10−10. Due to the high speeds used, these results
are up to two orders of magnitude below any previous result.
(Some figures may appear in colour only in the online journal)
1. Introduction
Frame-dragging is a phenomenon in general relativity that
causes rotating matter to drag space–time in its vicinity.
According to Einstein’s theory, this effect is so weak that
it requires astronomical observations and precision tests
with satellites to detect it [1]. Recently, to explain a
reported Cooper-pair mass anomaly in niobium [2,3]which
remains unsolved at present [4], Tajmar and de Matos [5–8]
predicted that rotating superconductors or superfluids might
produce much larger non-classical frame-dragging fields.
Other theoretical concepts were proposed supporting this
conjecture [9–11]. Recently, McCulloch proposed that such
frame-dragging-like fields may be linked to the Pioneer
anomaly [12]. Moreover, it was shown that such fields would
be of great technological interest as they could enable the
creation of artificial gravitational fields to enable, for example,
microgravity research in an Earth-based laboratory [13].
Since 2003, several experiments have been performed at
the Austrian Institute of Technology (AIT) [14–18] to detect
greatly enhanced frame-dragging fields using accelerometers
(dismissed early on due to high vibration sensitivity) and fiber-
optic gyroscopes in close vicinity to rotating matter at low
temperature, including steel, aluminum, Teflon, high and low
Tcsuperconductors, liquid and superfluid helium. Initially,
the sensors were mounted inside the cryostat inside a separate
vacuum chamber, which provided the necessary thermal
isolation to operate them at 25 ◦C. This chamber with the
0953-2048/11/125011+09$33.00 ©2011 IOP Publishing Ltd Printed in the UK & the USA1
Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 1. Experimental setup. (a) Detailed section and (b) overall experimental setup.
sensors was fixed with stainless steel bars to the ceiling of the
laboratory to remain fixed during the tests. When a ring sample
cooled with liquid helium was rotated below the sensors, the
gyroscope indeed seemed to follow the rotating ring with a
coupling factor (gyroscope signal/ring angular velocity) of
about 10−8, mimicking a frame-dragging-like measurement.
Also a parity violation was observed such that clockwise
rotation yielded larger coupling factors than counter-clockwise
rotation. The signal apparently did not decay over the distance
of our vacuum chamber and was independent within a factor
of two of the ring material used. It only decayed with
the temperature of the ring (or with the liquid helium level
in the cryostat) such that only temperatures close to liquid
helium showed an effect. Although the gyroscope signal was
very small, its magnitude was some 18 orders of magnitude
above classical predictions. Of course, this warranted further
investigation into the nature of the signals that we measured.
Because magnetic or temperature drift effects were soon
ruled out, our main concern was vibration due to the motor
and from the expansion of the liquid helium into gas during
rotation. Our setup was gradually adapted by using low-noise
cryomotors directly below the ring, a military-grade gyroscope
with higher resolution and less vibration sensitivity as well as
trying to move the gyroscope outside the cryostat for optimal
vibration isolation. This resulted in lower rotation speeds and
also smaller anomalous signals with coupling factors now in
the range of 10−9.
Also Graham et al [19] attempted to measure enhanced
frame-dragging from a rotating lead disk at 4 K using the
world’s largest ring-laser gyro and failed to detect a signal
within 1.7±3.8×10−7assuming a dipolar distribution, a
sensitivity which is about two orders of magnitude worse than
our design (their experimental values were re-assessed in [16])
and therefore could not rule out our anomalous gyroscope
signals. Moulthrop [20] investigated frame-dragging-like
signals from rotating superfluid helium and put an upper limit
coupling factor of 0.05 which is seven orders of magnitude
worse than our anomalies.
In order to finally settle the case, we built a new
experiment, where the test sample inside the cryostat can be
rotated at high speeds using an externally mounted motor.
The gyroscope is mounted outside the cryostat, isolated from
the ground, and attached to a structure that allows it to be
mounted at different positions. Our latest setup allows us to
rotate a niobium superconductor and a pot with liquid helium
or superfluid helium at high speeds and accelerations in order
to re-evaluate all theoretically predicted possibilities (whether
the source of the effect is due to superconductivity, superfluid
helium or the liquid helium itself).
2. Experimental setup
2.1. Overview
The main part of our experiment is a large custom-built
cryostat made out of stainless steel (evacuated with multi-
layer-insulation isolation) as shown in figure 1. The cryostat
is mounted on a structure which allows it to be tilted along the
Earth’s north–south axis as we planned to tilt the cryostat in
future experiments to investigate the influence of the Earth’s
spin. However, all experiments performed so far were done
with the cryostat mounted vertically to our laboratory floor.
Inside the cryostat is a pot made out of aluminum with a wall
thickness of 3 mm, which can be filled with up with 1.71 l of
liquid helium. Its outer and inner radii are 173 and 45 mm with
a height of 98 mm. As shown in figure 2, the pot can only be
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 2. Rotating pot with fins (outer walls are transparent).
filled through a ring-shaped hole on the top and it has four fins
that ensure that the liquid is homogeneously rotating with the
same velocity. The fins have a 5 mm gap with respect to the
outer wall and the inner rotating axis in order to allow closed
loops for rotating superfluids to create vortices. In addition,
a niobium ring with a thickness of 10 mm, an outer diameter
of 173 mm and an inner diameter of 77 mm is attached at the
bottom of the pot and fixed with screws.
The pot is mechanically attached to the main axle, which is
stabilized with three ball bearings and extends up to a flexible
coupling that allows any kind of external motor to be mounted
to it. The lower and the middle bearings were low temperature
bearings with solid MoS2lubricants made by KOYO. For
our experiments, we used a compressed air motor (D¨usterloh
PMW 400 Z24) similar to one in our early experiments with
maximum acceleration as well as a brushless servo motor
(Torque Systems BNR3034). The axle also features an optical
encoder to read out the speed as well as a sealing lip that was
inserted during the superfluid measurements which required
evacuation of the chamber. Silicon diodes (Lakeshore DT-
670B-SD) were placed on the niobium disk as well as at the
top of the inner cylindrical surface of the pot (readout via a slip
ring close to the optical encoder as it is rotating with the pot)
and on two positions inside the cryostat to monitor the filling
level of the liquid helium and the temperatures. Great care was
taken for good thermal isolation using Styropor isolation foam
rings as well as protecting the liquid helium in the upper part
of the cryostat from the rotating axle by a shielding tube to
minimize heat and rotation sources, and hence the transition
of liquid into gaseous helium. The helium gas exhaust was
directly connected to a tube that extended through the windows
of the laboratory so as not to influence our equipment.
We used an OPTOLINK SRS-1000 fiber-optic gyroscope,
which is mounted on a support structure outside the cryostat
allowing it to change its position and orientation all around
the cryostat. In addition, a magnetic field sensor (Hon-
eywell SS495A1), high resolution accelerometers (Colibrys
SiFlex1500 and SiliconDesigns 1221) and temperature sensors
were mounted together with the gyroscope. All sensors
are encapsulated under a high permeability magnetic shield
(Permalloy) in order to reduce their magnetic sensitivity. The
support structure was lifted off the laboratory floor by a stiff
structure made out of wood that was connected to the ceiling
of the laboratory as shown in figure 1(b). A gap of about 5 cm
ensured good vibration isolation during rotation between the
vibrating cryostat, which was fixed to the ground by screws and
the actual gyro support structures. In addition, the gyro support
structure was passively damped by rubber sheets between the
gyro support and the wood structure. The gyroscope was
moved along four positions during the experiment, labeled
middle, side, off-axis and off-axis 2 as shown in figure 3,
in order to investigate a possible field distribution of the
anomalous signals.
2.2. Sensitivity and systematic effects
Since we are trying to measure very small rotation rates, it
is important to know the minimum rotation rate that can be
resolved by the fiber-optic gyroscope. For the SRS-1000
gyroscope, the upper limit of the minimal measured rotation
rate, caused by polarization nonreciprocity of a light source
with a Gauss spectrum, is expressed as [21,22]
min λcp
DL λ√ln 2hLp
πλ (1)
where λ=1.55 ×10−6m is the average wavelength of light,
λ =50 ×10−9m is the width of the light spectrum, cis the
speed of light in a vacuum, D=150 ×10−3m is the diameter
of the fiber coil, L=1070 m is the length of the fiber coil,
h=1×10−6m−1is the polarization crosstalk of the fiber coil,
Lp=2.5×10−3m is the beat length of the fiber coil, pis
the residual degree of polarization of the light source and is
the coefficient of the polarizer’s extinction. For typical values
of p≈0.01 and ≈0.01 (i.e. 40 dB), equation (1) gives an
upper limit of min 4.1×10−8rad s−1. This coincides with
the bias drift value specified for the SRS-1000. We also tested
the gyroscope on a piezo-activated nano-rotation table [23]
and could resolve velocity steps of 1 ×10−7rad s−1with
an accuracy of 1.5×10−8rad s−1, which is just below the
theoretically predicted resolution upper limit. No asymmetry
has been seen between clockwise or counter-clockwise gyro
responses.
The magnetic sensitivity along the gyro’s axis is 4.8±
10−3rad s−1T−1. According to our Hall sensor mounted
directly on the gyroscope, the magnetic field changes during
rotation (influence from brushless servo motor and Barnett
effect) were always less than 1 μT. Therefore, the magnetic
influence is about one order of magnitude below our minimum
rotation rate resolution.
3. Experimental results
3.1. Calibration runs
Before going to liquid helium, the whole setup was first
evaluated by filling the pot with liquid nitrogen (for a cold
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 3. Gyroscope positions.
environment—but no superconductivity of the niobium ring or
superfluidity) and then with ethanol as a general electrically
non-conducting fluid at room temperature.
All experiments were done using the same standardized
speed profile which lasts about 200 s. The profile is
subdivided into five sectors with pre-defined time intervals:
rest, acceleration, maximum speed, de-acceleration and rest.
Each profile was performed in clockwise direction (spin
vector points downwards) and in counter-clockwise direction.
Random noise was reduced by applying a 200 point digital
moving average (DMA) filter to the gyro output and motor
velocity. A sampling rate of 13 Hz ensured that the averaging
window is always smaller than the maximum speed time
interval of the profile. After the signal is acquired, it is
normalized by subtracting the Earth’s rotation offset. The noise
was further reduced by signal averaging of at least 10 (up to
more than 50) profiles for each test case which also increases
the statistical significance of our results. For the pneumatic
air motor, the optical encoder data were used for the applied
angular velocity, whereas in case of the brushless servo motor,
the encoder velocity was used. Both were calibrated using
reflection stripes on the axle and an external speedometer.
Figure 4plots the gyroscope response mounted at the
middle position during the rotation of both test fluids. The
gyroscope shows only noise within a boundary of ±5×
10−8rad s−1which is close to the upper limit sensitivity and
the bias drift. We should therefore consider this value as our
noise limit in the further analysis.
3.2. Measurements with the electric motor
We used the brushless servo motor in order to evaluate
the gyroscope response to different speeds rather than only
maximum speed as in our earlier measurements. Two sets of
measurements were taken: one for liquid helium and one with
superfluid He4.
3.2.1. Liquid helium. The cryostat was filled with liquid
helium and a series of measurements was taken with the
maximum speed during our profile measurements varying from
1000 rpm (about 100 rad s−1) up to 5000 rpm. At this
temperature, the niobium ring at the bottom of the cryostat was
also superconducting.
A summary of our measurements is shown in figure 5,
where the average signal and standard deviation was evaluated
Figure 4. Calibration measurements with ethanol and liquid
nitrogen: gyroscope output (middle position) and applied angular
velocity.
during the maximum speed phase of our speed profile. Apart
from the two last high speed points at 4000 and 5000 rpm
(400 and 500 rad s−1) in the counter-clockwise direction,
all measurement data are within our noise limit of ±5×
10−8rad s−1. The detailed plot of the 4000 rpm test run
isshowninfigure6. The gyroscope signal during counter-
clockwise rotation (negative velocities) does not fully follow
the angular velocity profile, and its maximum signal is only
about a factor of three above our gyroscope resolution.
A linear fit through the measurements in figure 5sets a
new limit for a possible coupling factor (or frame-dragging-like
coupling) between the liquid helium/superconducting niobium
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 5. Liquid helium measurement with electric motor: gyroscope output (middle position) versus applied angular velocity.
Figure 6. Liquid helium measurement example at 4000 rpm:
gyroscope output (middle position) versus applied angular velocity.
and a gyroscope in close proximity as 1.9±4×10−11,
which is nearly two orders of magnitude below previous
measurements [17].
3.2.2. Superfluid helium. We also performed test runs with
superfluid helium by filling the cryostat with liquid helium with
the sealing lip on the main axle and subsequently pumping
on it. We could reach a temperature down to 1.8 K in our
pot, well below helium’s lambda point at 2.17 K. The test
runs were done at three maximum speeds ranging from 500,
750 to 1000 rpm, which is an order of magnitude higher
than our previous superfluid helium measurement [18]. Above
1000 rpm we could not keep the temperature below the lambda
point during rotation.
The summary plot is shown in figure 7and shows a similar
picture to the one obtained with the liquid helium only. The
data points are mostly within our noise level with one exception
in the clockwise direction at 750 rpm which is again about a
factor of three above our gyroscope resolution. The detailed
plot from this particular speed is shown in figure 8.
Also here we can perform a linear fit through the
measurements in figure 7and set a new limit for a possible
coupling factor (or frame-dragging-like coupling) between the
superfluid helium and a gyroscope in close proximity as 1.6±
3×10−10.
3.3. Measurements with an air motor
We then performed measurements using the pneumatic air
motor providing very high accelerations and a maximum
angular velocity of around 4300 rpm which is comparable to
the highest speeds that we achieved with the electric motor.
Moreover, it has no electromagnetic noise which may influence
the gyroscope. On the other hand, only one fixed speed is
possible; however, we performed measurements at different
locations as outlined in figure 3.
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 7. Superfluid helium measurement with electric motor: gyroscope output (middle position) versus applied angular velocity.
Figure 8. Superfluid helium measurement example at 750 rpm:
gyroscope output (middle position) versus applied angular velocity.
Two summary plots in figures 9and 10, respectively, show
the results from our air motor measurement on all different
positions for the liquid helium as well as for helium gas
(summarizing temperatures from 6 K up to room temperature)
which we were running as non-liquid helium reference test
runs. Whereas the helium gas reference measurements with
error bars are really all within our noise limit of ±5×
10−8rad s−1, the offset positions for the liquid helium case
appear to show some room for anomalous signals. Also,
the maximum anomalous signal strengths are within three
times our noise level, which is not sufficient. Moreover,
the anomalous signal is not consistent, because for the off-
axis position it is positive and for the off-axis 2 position it
is negative. A similar sign would have been expected for
any frame-dragging-like field at these two locations due to
rotational symmetry. Detailed plots for all gyro positions
during the liquid helium test runs are shown in figures 11
and 12, respectively.
4. Discussion and conclusion
Our latest setup enabled us to perform high acceleration and
high angular rotation of a niobium superconductor, liquid and
superfluid helium together with a military-grade fiber-optic
gyroscope mounted outside the cryostat and isolated from
vibration. No anomalous signals were found up to within three
times the noise level of our gyroscope (±5×10−8rad s−1)
which puts new bounds on any coupling or frame-dragging-like
effect from superconductors, superfluids or low temperature
matter. In addition, our accelerometers (mounted in tangential,
radial and vertical directions) did not record any anomalous
result within a noise band of ±10μg.
Our electric motor measurements at different speeds
enabled setting very low standard deviation boundaries for
external coupling effects (space–time like dragging of rotating
matter) for superconductors and liquid helium to 4 ×10−11
and for superfluids to 3 ×10−10 outside their boundaries.
This is orders of magnitude below both previous theoretical
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 9. Liquid helium measurements with an air motor: gyroscope output at different positions versus applied angular velocity.
Figure 10. Helium gas measurements with an air motor (reference): gyroscope output at different positions versus applied angular velocity.
predictions and measurements. A short comparison is given as
follows:
•We speculated earlier that a frame-dragging-like field
could account for a reported Cooper-pair mass anomaly
in niobium. A coupling factor of the order of magnitude
of 10−4was predicted [6] in this case. In accordance with
our previous measurements, such a possibility can be ruled
out by some seven orders of magnitude.
•Another prediction was that superfluid helium may
produce frame-dragging-like fields with an even higher
coupling factor of the order of unity [6]. Although
Moulthrop [20] had already ruled out a coupling factor
down to 0.05, we can rule out such a possibility by some
10 orders of magnitude.
•All previous measurements which were performed outside
the cryostat (setup C [17]andsetupD[18]) recorded
anomalous signals up to 1.5×10−7rad s−1similar to
the maximum signals that we have seen in the present
tests. However, the tests in this paper were performed at
nearly 50 times the speed in our previous setups. Since the
anomalous signals did not increase at higher speeds, they
are most probably noise and data analysis artifacts.
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Supercond. Sci. Technol. 24 (2011) 125011 MTajmar
Figure 11. Liquid helium measurements with an air motor:
gyroscope output at middle and side position versus applied angular
velocity.
Although conclusions can be drawn for all results obtained
previously and now outside the cryostat, an explanation for
the large anomalous signals with up to 1.4×10−5rad s−1
reported from gyroscopes inside the cryostat (setup A and B
in [17]) is still missing. Our results, however, suggest, that
the liquid helium expansion during rotation created an acoustic
noise environment that may have influenced the gyroscopes.
This needs to be confirmed by future measurements.
This leaves the following conclusions:
•Since our earlier speculation about non-classical frame-
dragging fields from superconductors and superfluids can
be ruled out, the starting point of the reported Cooper-pair
mass anomaly in niobium is still not solved. That leaves
the possibility for a weak-equivalence-principle (WEP)
violation of Cooper-pairs or an unknown experimental
error that was not accounted for in the setup from Tate
et al [2,3]. Both possibilities should be pursued and
first theoretical concepts [24] as well as experimental
assessments for WEP violation in superconductors [25]
have been reported in the meantime. Tate’s experiment
should be repeated in order to further investigate the
Cooper-pair mass anomaly.
•Attempts to replicate our frame-dragging experiment
should concentrate on our earlier setups A and B [17] with
the gyroscope embedded around a cold environment in
order to either confirm them or identify the source oferror.
Figure 12. Liquid helium measurements with an air motor:
gyroscope output at offset positions versus applied angular velocity.
Recent theoretical work points to the necessity for a cold
environment to measure the effect [12].
Acknowledgments
This work was funded jointly by the Austrian Institute of
Technology and Hathaway Consulting Services. I would like
to thank F Plesescu and B Seifert for their technical and
electronics support, respectively. Moreover, I would like
to thank all supporters and collaborators that enabled me to
perform this work including C J de Matos, E Semerad, E Kny,
E Gornik, T Sumrall, T Lawrence, M Fajardo, G Hathaway and
M Millis.
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