Holzwarth, and Theodor
Max-Planck-Institut für Quantenoptik (MPQ) , Laser Spectroscopy Division
Hahn, and Jens
Deutsches Zentrum für Luft und Raumfahrt (DLR), Institut für Hochfrequenztechnik
Previous reports on detected influences of solar eclipses on atomic clocks and the movement of pendulums have brought up speculations that some yet undetected gravitational shielding effect exists. We have compared the relative pace of three types of atomic clocks, based on the ground state hyperfine transitions of hydrogen, rubidium and cesium during the total solar eclipse on 11th of August 1999 over central Europe. In our experiment, no anomalous changes in the relative clock rates correlated with the eclipse were found, at a level much smaller than previously reported.
A change in the relative rate of rubidium and cesium atomic clocks during four partial solar eclipses between 1987 and 1992 has been reported by S.W.Zhou et al. . An accumulated time difference of two cesium clocks of 468 ns and 65 µs for two rubidium clocks located in the same laboratory was observed. In these experiments, the change in the clock rates not only occurred during the eclipse, but also up to one day before and after the maximum of the eclipse. Most of the clocks contributing to this comparison returned to their original rate after this time interval.
In 1954 and in 1959 Maurice Allais reported on peculiar movements of a Foucault pendulum at the time of the onset of a solar eclipse . In related experiments performed with torsion pendulums, a variation in the oscillation period during the onset of the eclipse  was observed, while other groups did not confirm this behaviour [4,5,6].
It has been speculated that all these phenomena are related to unknown features of gravity, even though neither the Foucault effect nor the period of a torsion pendulum depends on the gravitational acceleration (gravity is just needed to suspend the pendulums). To follow these speculations, it might be important to take into account the height of the sun during the eclipse as the angle between the earth-moon-sun line and the local gravitation vector may matter. No such dependence is apparent from the observations made so far. In the case of a Foucault pendulum the plane of oscillation might also make a difference, but was never specified.
General relativity predicts that gravity does have an influence on clock rates, but it is not expected that clocks located at the same place in the frame should change their relative pace unless gravity has an influence on the value of the fine structure constant . Some yet undetected gravitational shielding effects  or unknown radiation may explain why these effects are observed as the sun is eclipsed by the moon and not just every new moon when the the sun and the moon are almost aligned. In this case the question remains why this does not result in a daily variation of clock rates, as the sun is shielded by the earth once per revolution .
Besides the above mentioned effects that should, according to the current theory of gravity, not be connected with a change in the gravitational acceleration, a direct observation with a gravimeter has been reported by D.C.Mishra and M.B.S.Rao . These authors observed a highly significant variation of the gravity field which occurred with the onset of a solar eclipse.
To settle this issue, David Noever and Ron Koczor of NASA's Marshall Space Flight Center initiated a campaign with about 20 laboratories participating around the world to perform time coordinated measurements with Foucault and torsion pendulums, gravimeters, seismometers, magnetometers and barometers at the solar eclipse on 11 August 1999 .
As the shadow of totality of this eclipse passed over the DLR laboratory in Weßling/Germany (N 48:05:03, E 11:16:40, 620 m above sea level) we decided to take the chance to repeat the experiments of S.W.Zhou et al. by comparing four atomic clocks. The clocks were based on ground state hyperfine splittings of different species of atoms: one hydrogen maser (Kvarz, model CH1-76), one rubidium clock (Rohde & Schwarz, model XSRM) and two cesium clocks (Hewlett Packard, model 5071A and Frequency and Time Systems, model FTS4010). Theory shows that their frequency depends differently on the value of the fine structure constant . The advantage of using three different types of clocks is that the relative changes in clock rates are known, if the solar eclipse has an effect on the value of the fine structure constant . Therefore the relative changes of clock rates between the three possible pairs can be compared with the theory.
The clocks where placed in an air conditioned room in the basement. A computer recorded the relative phases Rb-Cs(FTS), Cs(FTS)-H, H-Cs(HP) and Cs(HP)-Rb using the 5 MHz output signals of the clocks. Data where taken approximately every 4 seconds from the 3rd to the 23rd of August, 1999 with four phase detectors (Hewlett Packard, model 53131A). To check possible limitations of the measuring apparatus, the sum of the four relative phases was calculated. During the experiment the total phase stayed within ±1.5 degrees (±0.83 ns) of some finite mean value caused by cable propagation times.
To exclude the influence of some spurious effects, like possible variations in the background magnetic field (due to changes in the ionosphere for example), temperature variations, power line fluctuations, barometric pressure changes we recorded these parameters. Increased magnetic field fluctuations of up to ±0.1 µT in the vertical direction due to human activity were observed at working hours from Monday through Friday. No significant changes that seemed to be connected with the eclipse were observed in all the parameters, except for the power line voltage. The mains voltage dropped by about 3.6 V (1.5%) 930 seconds before the maximum of the eclipse and recovered to the previous value 450 seconds after it (figure 1). This voltage drop might be connected with the switch of the outside light controlled street lightning. Several similar voltage jumps are visible in the total data set. There was no effect on the clock rates observable that could be identified with the mains voltage jumps. Small changes in the supply voltage are unlikely to cause any perturbations, as the clock have stabilized internal supplies.
The sun was fully eclipsed from 10:36:48 to 10:38:44 universal time UTC (local time = UTC+2h) when the sun was at an angle of 56° above the horizon. In figure 1 the relative time differences of the clocks are shown for a 800 second interval with the eclipse in the center. The beginning of the totality (second contact) and the end of the totality (third contact) are labeled by b and c respectively. The clocks are obviously not perfectly stable in their relativ rates. Linear phase drifts, like the one clearly visible in the Cs(HP)-Rb comparison, can be subtracted to obtain the residue shown in red so as to better reveal possible effects of the eclipse.
Figure 2 shows the recording of other parameters that might influence the clocks. The outside light intensity is recorded to verify the synchronization of the data with the eclipse. The time axis was constantly calibrated by a time signal that is broadcasted by the Physikalisch-Technische Bundesanstalt in Braunschweig and zeroed at 10:37:46 UTC, the maximum of the eclipse. The leading edge of the moon's shadow appeared sharper since it had the shape of an ellipse that was not exactly travelling along the shorter axis and the observation site was not located exactly in the center of the totality zone but 32 km away (south-west).
Figure 3 shows, with a longer period of time, the partial phase of the eclipse which lasted 2 hours and 45 min (from 9:15:53 to 12:00:59 UTC). The beginning of the partial eclipse (first contact) is marked with a and the end of the partial eclipse is marked with d. The red plots show the time differences where quadratic phase drifts (linear frequency drifts) have been removed. Figure 4 shows the recording of the other parameters recorded for this interval. To facilitate comparison with the results of S.W.Zhou et al.  who observed a changed clock rate for 8 hours in one case and for 3 days in another case, we plot our data for periods of 32 hours and 6 days in figure 5 and figure 6.
In conclusion we have shown that the effect of a total solar eclipse on the relative pace of atomic clocks based on the ground state hyperfine splittings of different types of atoms, is much smaller than previously reported. An upper limit of ±20 ns, independent of the type of clock, for a non-regular accumulated time difference was found. For observation times of 800 seconds this limit is even below ±6 ns. Previous reports of accumulated time differences of 468 ns and 65 µs for a pair of cesium clocks and a pair of rubidium clocks respectively, for an observation period of several days, are up to 3 orders of magnitude larger. Some readers may feel that some features might be suppressed in the way we plot the data, choose the time window or what type of relative drift is attributed to be a regular drift. Therefore the complete data set is available here.
We would like to thank K.Zioutas (CERN) for suggesting this experiment.