Anomalous weight reduction on a gyroscope’s right rotations around the vertical axis on the Earth

VOLUME 63, N U M B E R 25 PHYSICAL REVIEW LETTERS 18 DECEMBER 1989
Anomalous Weight Reduction on a Gyroscope's Right Rotations
around the Vertical Axis on the Earth
Hideo Hayasaka and Sakae Takeuchi
Department of Radiation Engineering, Faculty of Engineering, Tohoku University, Sendai 980, Japan
(Received 7 March 1988; revised manuscript received 9 August 1989)
The weight change of each of three spinning mechanical gyroscopes whose rotor's masses are 140, 175,
and 176 g has been measured during inertial rotations, without systematic errors. The experiments show
that the weight changes for rotations around the vertical axis are completely asymmetrical: The right
rotations (spin vector pointing downward) cause weight decreases of the order of milligrams (weight),
proportional to the frequency of rotation at 3000-13 000 rpm. However, the left rotations do not cause
any change in weight.
PACS numbers: 04.80.-fz
To confirm the reflection symmetry relating to the ro-
tational motion of objects in the gravitational field of the
Earth, the weight of each of three spinning mechanical
gyroscopes has been measured during left (spin vector
pointing upward) and right (spin vector pointing down-
ward) inertial rotations around the vertical axis by
means of a chemical balance. The experimental ap-
paratus and method are as follows.
Each gyroscope is composed of the stator, rotor, and
rigid frame. Rotors of 139.863, 174.882, and 175.504 g
are used, and their diameters are 5.2, 5.8, and 5.8 cm,
respectively. The materials of the rotors are brass,
aluminum, and silicon-steel. The dynamic balance,
which is the criterion of the maximum deviation of the
center of a rotor's mass associated with rotations, and
the fluctuation of the rotational frequency of each gyro-
scope are 0.3 mm/s and ±0.2%, respectively, for both
rotations. This means that the dynamic characteristic,
i.e., the synthetic criterion of the stabilities of spinning
and precession of each gyroscope, is the same for the two
rotations. An oscillator capable of switching polarities
and a voltage amplifier are used to change the frequency
of rotation of the rotor and to supply the driving power
to the gyroscope. The directions of the left and right ro-
tations are determined by the polarity. A phototachome-
ter is used to measure the frequency of rotation of the ro-
tor. The chemical balance is made of nonmagnetic ma-
terials, and the measurable range is 0 to 500 g with an
accuracy ± 0 . 3 mg. To exclude fluid eff'ects of air on the
rotating gyroscope, a vacuum container made of glass is
used. An overview of the experimental apparatus is
shown in Fig. 1.
The first experiment was carried out in the environ-
ment magnetic field of 0.35 G that is nearly totally due
to the geomagnetism. The degree of vacuum in the con-
tainer containing the gyroscope is kept between 1.3
xlO~^ and 1.3x10^ Pa. The electric power is supplied
to the gyroscope through superfine wires. The rotational
frequency of the rotor is brought to the desired value by
increasing the supply voltage and the frequency of the
oscillator under the same driving condition for all the
measurements. After the desired value of the rotational
frequency is attained, the electrical circuit is opened.
Then the weight of the rotating gyroscope is measured
under inertial rotation. The weight measurements are
repeatedly carried out, 10 times, for a given frequency of
rotation.
As shown in Fig. 2, the right rotations of each gyro-
scope always cause weight decreases of the order of mil-
ligrams, proportional to the frequency of rotation. The
weight reduction occurs for both normal and reverse atti-
tudes. Here, reverse attitude of a gyroscope means
merely its upside-down attitude without change of the
states of the other equipment and the environment con-
sidered. Right rotation means the spin vector pointing
downward for both the normal and the upside-down atti-
tudes. On the other hand, the left rotations of each
gyroscope yield zero weight change for all frequencies of
rotation and both attitudes, within the accuracy of the
chemical balance. The weight changes for both rotations
vaccum container
FIG. 1. Overview of the experimental apparatus including
the chemical balance.
© 1989 The American Physical Society 2701

VOLUME 63, NUMBER 25 PHYSICAL REVIEW LETTERS 18 DECEMBER 1989
- I 4
- I 3
- I 2
- I I
- I O
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
• M = I 7 5 . 5 0 4 g
X M = I 3 9 . 8 6 3 g
n M = 175. 504g
A M = I 3 9 . 8 6 3 g
j normal aft.
reverse aft.
right rotation
left rotation
frequency of rotatonsdo^ rpm)
FIG. 2. Weight changes of gyroscopes for both left and
right rotations around the vertical axis in the natural-
environment magnetic field.
are independent of the placement of the balance's lever
arm along the N-S or the E-W direction. Furthermore,
the weight changes for both rotations are independent of
the various ways of performing the experiment: The
weight measurements are carried out after opening the
electrical circuit while the rotation is speeding up, kept
at constant speed, or slowing down, under the conditions
of putting a polyurethane foam pad under the gyro to
partially absorb the mechanical vibrations and of ex-
changing the positions of the gyro and the reference
weights on the balance's pans. The experimental results
do not change under these variations.
In Fig. 2, the data on the M = 174.882-g rotor are om-
itted because the weight changes are nearly the same as
those for A / = 175.504 g. The vertical error bars denote
the fluctuation of weight changes, and the horizontal er-
ror bars denote the decreasing range of the frequency of
rotation in one period of the movement of the direction
needle of the chemical balance.
The experimental results show that the weight changes
for rotations around the vertical axis are completely
asymmetrical. Meanwhile, based on the conventional
theory, the weight changes of a gyroscope under rotation
should by symmetrical. Therefore, we have studied
whether such an extraordinary phenomenon is due to
systematic errors in our experimental equipment and
method. Most dynamical problems can be solved in the
framework of Newtonian mechanics, which is symmetri-
cal under a mirror reflection, as concretely discussed
later.
There might be a question of weak magnetic coupling
between the environment magnetic field of 0.35 G and
the weak residual magnetism of the gyroscope after the
opening of the electrical circuit. However, the anoma-
lous weight reductions for the right rotations are not due
to magnetic coupling. First of all, this is supported by
the experiments with an upside-down attitude for each
gyroscope as follows: Let us suppose that magnetic cou-
plings during the gyroscope's right rotations cause the
weight reductions in the normal attitude. This assump-
tion means that the coupling serves the upward force
during the right rotation. Next, let only the attitude of
the gyroscope reverse without changing the states of the
other equipment and the environment magnetic field. If
the above assumption is correct, the weight of the gyro-
scope will increase for the left rotation in the reverse at-
titude, because the force by magnetic coupling will
operate down the gyroscope. However, the experimental
results for the reverse attitude shown in Fig. 2 refute the
correctness of the assumption.
Since the problem of magnetic coupling is important,
this problem has been checked further by means of the
following two methods, (i) It has been checked whether
there is a diff'erence between the residual magnetism of
the left rotation and that of the right one in each gyro-
scope. The residual magnetisms for both rotations are
measured in a magnetically shielded cylinder where the
strength of the magnetic field is w times the strength of
the environment magnetic field. The residual magne-
tisms for the left and right rotations are identical at the
same frequency of rotation, after cutting the same power
supplies. For instance, the residual magnetism associat-
ed with both the left and right rotations of the 175.504-g
rotor is 0.06 G at 15 000 rpm. Of course, these results
are independent of attitude, (ii) The weight changes for
both rotations in each attitude of the 175.504-g rotor
have been measured in a magnetically shielded room
(200x200x210 cm^) where the field strength is
3X 10 ""^ to 3X 10 "^ G; that is, T W to i k times the en-
vironment magnetic field mentioned previously. The
weight changes for both rotations of the gyroscope in
each attitude in this shielded room are entirely identical
with those obtained in the environment magnetic field.
The experimental results of these two methods definitely
show that the anomalous weight reduction is independent
of magnetic coupling.
Summarizing all the data obtained in the experiments,
the weight decrease for right rotations around the verti-
cal axis, AWR(CO), is approximately formulated, in units
2702

VOLUME 63, N U M B E R 25 P H Y S I C A L R E V I E W L E T T E R S 18 DECEMBER 1989
of dynes, as follows:
AWR(CO) = - 2 X 10 ~^Mreqft) gems "^ ,
where M is the mass of rotor (in g), co is the angular fre-
quency of rotation (in rad/s), and /-gq is the equivalent
radius (in cm), defined as follows. A rotor is composed
of various materials and domains, and hence Teq is given
by
M r e q = J J p{r,z)2Kr'^drdz ,
where p(r,z) is the density of any material constituting
the rotor, and r and z denote cylindrical coordinates.
The values of req for the three rotors of 139.863,
174.882, and 175.504 g are 1.85, 2.26, and 2.26 cm. On
the other hand, the weight changes for left rotations in
each attitude are zero within the accuracy of the chemi-
cal balance.
Here, it should be especially noted that the weight
changes during inertial rotations of three rotors repeat-
edly measured using an electronic balance are nearly the
same as those obtained with the chemical balance. The
mechanism of the balance, the experimental method, and
the results are as follows: The deviation of the vertical
component in the bending of a horizontal metal trough
system caused by a weight is compensated by elec-
tromagnetic force. The balance has no standard weight
inside, and the measurable range is 0 to 300 g with an
accuracy of ± 1 mg. The system of the balance and
gyro closed in a vessel is rigorously held at a vacuum
state using a rotary pump and a coarse control valve, and
also a sorption pump and a fine-control valve. The latter
pump and valve are set near the vessel. The weight mea-
surements are carried out during the inertial rotations
after opening the electric circuit of the gyroscope. The
strength of the magnetic field is of the order of 1.7 G at
the balance's pan. As examples, the mean values of
weight reductions for right rotations of two rotors of
139.863 and 175.504 g at 1.33 Pa are 1.8, 2.4, 3.0, 3.6,
4.1, 4.6, 5.3, 5.8, 6.5, 7.1, and 7.7 mg for the former ro-
tor, and 2.6, 3.6, 4.4, 5.3, 6.3, 7.2, 8.1, 9.1, 10.0, 10.9,
and 11.9 mg for the latter, at 3 x l 0 4 x l 0 ^ . . . , 1 3
xlO^ rpm. Meanwhile, the left rotations do not cause
weight changes. The results are independent of attitude.
As shown in Fig. 2, the weight change of each rotating
gyroscope is completely asymmetrical for inertial rota-
tions around the vertical axis. In a common-sense view,
anyone might consider that such a phenomenon is in-
duced by systematic errors. However, the phenomenon
is free from systematic errors; our reasoning is given
below. The causes of systematic errors are as follows:
(1) The different dynamic characteristics of the gyro-
scope for the two rotations. (2) The different electro-
magnetic couplings of the gyroscope for the two rota-
tions. (3) The different fluid effects of air on the gyro-
scope for the two rotations. (4) The difference between
the respective torques induced by the friction between
the ball bearings and the shaft of the gyroscope for the
two rotations. (5) The different environmental condi-
tions for the repetitive experiments. (6) The difference
in the forces of inertia for the two inertial rotations. (7)
The difference between the two spin-spin couplings of the
angular momenta of the Earth and the gyroscope for the
two rotations.
For (1): The dynamic characteristic includes the
effect of mechanical vibrations and, as mentioned previ-
ously, the dynamic characteristic of each mechanical
gyroscope is the same for the two rotations. As one ex-
ample, the overall effective values of the accelerations of
mechanical vibrations (bandwidth, 0-2 kHz) for the two
rotations of the 140-g rotor are 0.0995G and 0.0965G at
13000 rpm in the normal attitude, where G is 980 cm/s^.
The values in the reverse attitude are nearly the same.
From the above, we conclude that there are no dif-
ferences between the dynamic characteristics of each
gyroscope for the two rotations or the two attitudes. For
(2): The problem of magnetic couplings has been per-
fectly solved by the three kinds of experiments already
mentioned. Further, as each weight measurement was
carried out after opening the electric circuit, there is no
electrical-current effect. Therefore, the gigantic weight
reduction for the right rotation is independent of mag-
netic coupling and electrical-current effect. For (3):
The weight reduction for the right rotation is not due to
lift from the fluid effect of air within the vacuum con-
tainer. The reasons are as follows: Under the standard
atmosphere (1 x 10^ Pa), both rotations of the 175-g ro-
tor cause the same lift of about 260 mg at 12000 rpm.
The lift power is proportional to the density of gas. As
described previously, the gas pressure in the container is
between 1.3x10"^ and 1.3x10' Pa. Further, the gyro-
scope and air are in a closed system. From the above, we
find that the weight decrease for the right rotation is in-
dependent of the lift of air. For (4): Since the friction
in a gyroscope is originally within the gyroscope system,
this friction does not influence anything outside the sys-
tem. Hence, the weight reduction is not due to the
torque induced by the friction. For (5): A pair of
weight measurements for both rotations at the same fre-
quency of rotation are always completed within about
30 min under a constant temperature. It has been
confirmed that there are no convection effects of the air
surrounding the glass container for either rotation, al-
though there are uniform temperature increases of less
than 1 °C over the whole surface of the container due to
the friction at the supports of the rotor's axis for both ro-
tations. Further, there is reproducibility of the data ob-
tained on different days. Hence, the changes of the envi-
ronmental conditions of the Earth's tide, the fluctuations
of the Earth's spinning, temperature, and magnetic fields
can be neglected. For (6): The weight measurements
have always been made for decreasing rotational fre-
quency. In the view of Newtonian mechanics, generally
2703

VOLUME 63, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 18 DECEMBER 1989
there is an inertial force AfCcoxr), where M is the mass
of a rotor, fi> is the vector of the rate of change of the an-
gular frequency (o, and r is the vector in the radial direc-
tion. However, since the gyro-rotor rotates on the
horizontal plane in this experiment, the force does not
occur in the vertical direction. Therefore, the anomalous
weight reduction is not due to the inertial force. For (7):
First, the weight reduction is not due to the Lense-
Thirring precession, ^ or the geodetic or mass-current pre-
cessions.^ Second, in the framework of Einstein-Cartan
theory, there might exist the possibility of a gravitational
repulsive force caused by the parallel spin-spin interac-
tion of the angular momenta of the Earth and the gyro-
scope, as discussed by Kopczyriski^ and Trautman"^ for
spinning dusts. If these theories are applied to our ex-
periment, such an interaction causes only an extremely
small effect. Hence, the gigantic weight reduction for
the right rotation cannot be explained from the above
theories, and then the weight reduction is independent of
the Earth's spinning.
As discussed above, the experimental result cannot be
explained by the usual theories.
The authors acknowledge discussions with Professor T.
Nakamura of Tohoku University. They wish to thank
Dr. H. Tanaka for his help in the experiment, and also
Dr. Y. Higashino of Yokogawa Electric Cooperation for
his support in the use of the magnetically shielded room.
'J. Lense and J. Thirring, Phys. Z. 19, 156 (1918).
2L. I. Schiff, Phys. Rev. Lett. 4, 215 (1960).
^W. Kopczyiiski, Phys. Lett. 43A, 63 (1973).
'•A. Trautman, Nature (London), Phys. Sci. 242, 7 (1973).
2704

Anomalous weight reduction on a gyroscope’s right rotations around the vertical axis on the Earth

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