From PHYSICAL REVIEW LETTERS  -- 18-Dec-1989, p 2701 - 2704 
 
 
"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) 
 
Abstract: 
 
        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) case weight decreases 
of the order of milligrams (weight), proportional to the 
frequency of rotation at 3000 - 13000 rpm.  However, the left 
rotations do not cause any change in weight. 
 
Text: 
 
        To confirm the reflection symmetry relating to the 
rotational 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 downward) inertial rotations around 
the vertical axis by means of a chemical balance.  The 
experimental apparatus 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 gyroscope 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 rotations are determined by the 
polarity.  A phototachometer is used to measure the frequency of 
rotation of the rotor.  The chemical balance is made of 
nonmagnetic materials, and the measurable range is 0 to 500 g 
with an accuracy of +/- 0.3 mg.  To exclude fluid effects 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. 
 
[ Fig. 1, my (FP) description -- Balance beam -- two pans.  Pan 
on right has standard weights, pan on left hold gyro, enclosed in 
vacuum container.  Voltage is fed to gyro via "super-fine wires", 
passing through vacuum container. Phototach is pointed at gyro's 
rotor.  Diagram is schematic, and quite simple and clear.] 
 
        The first experiment was carried out in the environment 
magnetic field of 0.35 G that is nearly totally due to the 
geomagnetism.  The degree of vacuum in the container containing 
the gyroscope is kept between 1.3x10e-2 and 1.3x10e1 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 repeated carried out, 10 
times, for a given frequency of rotation. 
 
        As shown in Fig. 2, [ Fig. 2, my (FP) description: a simple 
two axis graph, y-axis is titled "Weight Reduction (mg-weight)", 
runs from +1,0,-1,-2, 
up through -14. X-axis is titled "Frequency of rotations (10e3 
rpm), runs from origin, 3,4,5, up through 13.  There are three 
lines plotted through points on the chart -- the points represent 
the experiment carried out with the three different gyro's, each 
undergoing right and left rotation. The right rotations have a 
positive slope: for all gyro's, weight reduction appears to 
increase linearly with rotation frequency.  For left rotation, 
the line is perfectly flat: under left rotation, no gyro shows 
any change in weight.]  the right rotations of each gyroscope 
always cause weight decreases of the order of milligrams, 
proportional to the frequency of rotation.  The weight reduction 
occurs for both normal and reverse attitudes.  Here, reverse 
attitude of a gyroscope means merely its upside-down attitude 
with change of the states of other equipment and environment 
considered.  Right rotation means the spin vector pointing 
downward for both the normal and the upside-down attitudes.  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 are independent of the placement of the 
balance's lever arm along the N-S or 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 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 exchanging 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 omitted 
because the weight changes are nearly the same as those for 
M=175.504 g.  The vertical error bars denote the fluctuation of 
weight changes, and the horizontal error 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 be 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 symmetrical 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 anomalous 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 
couplings during the gyroscope's right rotations cause the weight 
reductions in the normal attitude.  This assumption 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 gyroscope will increase for the left rotation in the 
reverse attitude, 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 difference 
between the residual magnetism of the left rotation and that of 
the right one in each gyroscope.  The residual magnetisms for 
both rotations are measured in a magnetically shielded cylinder 
where the strength of the magnetic field is 1/100 times the 
strength of the environment magnetic field.  The residual 
magnetisms 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 associated with 
both left and right rotations of the 175.504-g rotor is 0.06 G at 
15000 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 has been measured in a magnetically shielded 
room (200x200x210 cm 3) where the field strength is 3 x 10 e-4 to 
3 x 10 e-3 G; that is, 1/1000 to 1/100 times the environment 
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 vertical axis 
dWr(w) [ (FP) I mean to express "Delta Weight sub Reduction at 
omega" ], is approximately formulated, in units of dynes, as 
follows: 
 
        dWr(w)= -2 x 10 e-5 Mreq W g cm s -2.  
 
[ (FP) I mean to express "Delta W  sub r at Omega = minus 2 x 10 
to the minus fifth M sub r equivalent Omega grams centimeter 
second to the minus 2"  These terms are explained further in the 
text ] 
 
where M is the mass of rotor (in g), w is the angular frequency 
of rotation (in rad/s), and req is the equivalent radius (in cm), 
defined as follows.  A rotor is composed of various materials and 
domains, and hence req is given by 
 
        Mreq = SS p(r,z)2pi r2 dr dz, 
 
[ (FP) The S's are supposed to be integral signs ] 
 
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 chemical balance. 
 
        Here, it should be especially noted that the weight changes 
during inertial rotations of the three rotors repeatedly 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 trough system caused by a weight is compensated by 
electromagnetic 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 fine- 
control valve.  The latter pump and valve are set near the 
vessel. The weight measurements 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 the 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 rotor, 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 3x10e3, 4x10e3,...,13x10e3 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 rotations 
around the vertical axis.  In a common-sense view, anyone might 
consider that such a phenomenon is induced 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 
gyroscope for the two rotations. (2) The different 
electromagnetic couplings of the gyroscope for the two rotations. 
(3) The different fluid effects of air on the gyroscope for the 
two rotations. (4) The difference between the respective torques 
induced by the friction between ball bearings and the shaft of 
the gyroscope for the two rotations. (5) The different 
environmental conditions 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 previously, the dynamic 
characteristic of each mechanical gyroscope is the same for the 
two rotations.  As one example, the overall effective values of 
the accelerations of mechanical vibrations (bandwidth, 0-2 kHz) 
for the two rotations of the 140-g rotor are 0.0995 G and 0.0965 
G at 13000 rpm in the normal attitude, where G is 980 cm/s2.  The 
values in the reverse attitude are nearly the same.  From the 
above, we conclude that there are no differences between the 
dynamic characteristics of each gyroscope for the two rotations 
or the two attitudes.  For (2): The problem of magnetic couplings 
has been perfectly 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 magnetic 
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 container.  The reasons are 
as follows: Under the standard atmosphere (1x10e5 Pa), both 
rotations of the 175-g rotor 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 1.3x10e-2 and 1.3x10e1 Pa.  Further, the gyroscope and 
air are in a closed system.  From the above, we find that the 
weight decrease for the right rotation is independent 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 system.  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 frequency 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, although there are uniform 
temperature increases of less than 1 degree C over the whole 
surface of the container due to the friction at the supports of 
the rotor's axis for both rotations.  Further, there is 
repoducibility of the data obtained on different days.  Hence, 
changes of the environmental 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 frequency.  In the 
view of Newtonian mechanics, generally there is an inertial force 
M(wxr), where M is the mass of a rotor, W is the vector of the 
rate of change of the angular frequency w, and r is the vector in 
the radial direction.  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 inertial force.  For (7):  First, the 
weight reduction is not due to the Lense-Thirring precession (ref 
1), or the geodetic or mass-current precessions (ref 2).  Second, 
in the framework of Einstein-Cartan theory, there might exist the 
possibility of a gravitational repulsive force caused by the 
parallel spin-spin interaction of the angular momenta of the 
Earth and the gyroscope, as discussed by Kopczynski (ref 3) and 
Trautman (ref 4) for spinning ducts.  If these theories are 
applied to our experiment, 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 [sic] for his support in the use of 
the magnetically shielded room. 
 
[References] 
1       J. Lense and J. Thirring, Phys. Z. 19, 156(1918). 
2.      L.I. Schiff, Phys. Rev. Lett. 4, 215(1960). 
3.      W. Kopczynski, Phys Lett. 43A, 63(1973). 
4.      A. Trautman, Nature(London),Phys. Sci. 242, 7(1973)