Science or fiction, sometimes it is hard to tell. In 1997, a group of Chinese scientists hooked up a sensitive gravimeter, to automatically record the earth’s gravitational field (or more accurately, the local acceleration of the earth’s crust) in the obscure northeast China town of Mohe, Heilongjiang (Black Dragon River) province. They chose this town because it was near the center of the 1997 solar eclipse, achieving totality for about 2 minutes. They chose the most accurate unit available, it can detect the reduction in gravitation when it is raised 1cm.
After the eclipse they examined their data. They found the usual tidal effects and slow drifts but they also found an interesting signal at the beginning and end of the eclipse, a signal that indicated that the earth’s gravitation field weakened slightly, or that the location was lifted into the air a few cm, or, perhaps, the gravitational field of the sun or moon had increased slightly. Their data, published in Phys Rev D 62, 041101, in units of looked like this:
Let’s look at the data. Our first step will be to look at the elevation of the sun.
Elevation of the Sun
If the Mohe anomaly is due to gravitons emitted from the sun and or moon, then we need to adjust for how far off the horizon these bodies are. The eclipse was observed at latitude 53°29’20″ N and longitude 122°20’30″ E, on March 9, 1997. Sunrise was at 06:20:00 local time, with first contact at 08:03:29, totality from 09:08:18 to 09:11:04, and fourth (last) contact at 10:19:50. The first anomaly peaked at around at around 7:30 while the second anomaly goes to at 10:20.
To see how far off the horizon the sun was at 7:30 and 10:20, we go to John Walker’s convenient applet Your Sky, and find the sky map for that spot on the earth at that time. Whoops, he doesn’t quite manage to get the numbers exactly right. Here’s his picture for the center of totality, showing the sun erroneously peeking out underneath the moon:
Okay, so let’s go to Chris Obyrne’s Javacript eclipse calculator and select the 1997 data at the given longitude and latitude. We find that first contact has the sun 14 degrees of the horizon while fourth contact is 28 degrees. This is compatible with Walker’s program having the sun 21 degrees over the horizon at the center of totality.
Now, if the Mohe measurements are to be interpreted as modifications of the total gravity strength due to (a change in) the sun and moon, then, since the earth’s gravity dominates, we need to divide by the sine of the elevation of the sun. At first contact, this is a factor of 4.13, and at fourth contact 2.13; adjusting the anomaly peaks, this gives the first contact peak at around and the fourth contact goes to . These numbers are somewhat closer to symmetric than the originals.
Tides and Gravimeters
But we can’t interpret the data as measurements of the force of gravity. It is impossible, in a certain sense, to measure the force of gravity at a single point in space. What a gravimeter actually measures, at best, is an acceleration. Installed properly, this acceleration is the force applied to the base of the gravimeter. Consistent with Einstein’s Equivalence principle, a gravimeter in free-fall will measure no gravitational force.
Consequently, interpreting the anomaly peaks as corresponding to changes in the flux of gravitons is simplistic and wrong. But before we discuss what gravimeters actually do measure, let’s discuss the timing of the anomalies.
A significant difference between Einstein’s theory of gravity and Newton’s is that in Newton’s theory, the force is instantaneous at a distance. For theories based on superluminal gravitons, the timing of the pulses needs to be adjusted.
It takes light from the sun about 8.3 minutes to reach the earth. Consequently, while we detect the center of the total eclipse at 09:09:41, the sun actually emitted that light at 09:01:23. This was the time at which the bodies were in alignment.
Thus, if gravitons travel at very high rates, we would expect that the eclipse’s modification of gravity would be symmetric not around the time of deepest eclipse, 09:09:41, but instead around the actual time of alignment, 09:01:23. Thus those who believe in faster than light gravitons expect the gravitonal eclipse effects to appear around 8 minutes before the photon eclipse effects.
Returning to the Mohe gravity data, we see that the first pulse is almost entirely over by the time of first contact, but that the second pulse is close to coincident with fourth contact. To make these two pulses symmetric with respect to the photon measurements of the time of the eclipse, we have to shift the gravity measurements later by around 7 or 8 minutes.
The Acceleration of the Sun and Moon
In preparation for discussing tides and gravimeters, it’s useful to calculate the acceleration, on the earth, of the sun and moon. Since I am a (hopefully soon to be published) general relativity theorist, I will make these calculations in the professional way, using units of centimeters only. To convert from cm to those ugly pedestrian units involving grams and seconds, we will be setting to unity, the gravitational constant G, and the speed of light c:
Looking in wikipedia’s collection of Solar System values, the masses of the sun and moon, and their distances from the earth, are:
Mass Sun: ,
Mass Moon: ,
In theoretical general relativity, the formula for (Newtonian) acceleration is very simple; A = M/r^2. Applying this formula to the above, we get the force that the sun and moon apply to the earth, in units of 1/cm. We can convert these into cm/s^2 by multiplying by c^2. We find:
Sun accel: .
Moon accel: .
Sailors know that the moon makes stronger tides than the sun; so it is a little surprising that the gravitational acceleration of the sun is stronger in its effect on the earth. The tidal effects of the moon are stronger because the moon is so close.
Tidal forces are caused not by gravitational accelerations, but instead by differences in gravitational accelerations. The strong tides of the moon are caused by the difference in gravitational acceleration between the side of the earth closest to the moon and the side farthest away. As far as tides go, gravity is a 1/r^3 force, not a 1/r^2.
Gravimeters show tidal forces rather handily. They cannot measure actual gravitational forces. Consequently, when we use a gravimeter to look for gravitational anomalies, we need to interpret what we measure not as a gravitational force, but instead as a tidal force.
Since eclipses last several hours, the data for these sorts of experiments has to be corrected for the usual tidal forces. This means that there are lots of opportunities for getting the wrong answer. Later experiments, particularly with the European eclipse of 2003,
Like I said, I don’t know if this is significant. At least it is interesting. For a recent review of conventional explanations for these sorts of observations, see A review of conventional explanations of anomalous observations during solar eclipses by Chris P. Duif, and Review on Possible Gravitational Anomalies by Xavier E. Amador.
Corpuscular Gravity Shielding
The corpuscular graviton shielding theory is that gravity is a shielding effect; two masses are attracted to each other by their shielding of each other from the effect of an isotropic and universal sea of gravitons. This sort of theory expects to see a reduction in the effect of the combined sun and moon gravitational attraction during an eclipse.
Such a reduction would mean that the earth’s gravity field would become stronger. This is the opposite of the observation above, but there is evidence for a decrease in other gravimeter measurements. See Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French). These are difficult measurements and difficult interpretation.
For how corpuscular theories of the graviton fit with these observations, see Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French).