From The Economist print edition

An unexplained effect during solar eclipses casts doubt on General Relativity

"ASSUME nothing" is a good motto in science. Even the humble pendulum may spring a surprise on you. In 1954 Maurice Allais, a French economist who would go on to win, in 1988, the Nobel prize in his subject, decided to observe and record the movements of a pendulum over a period of 30 days. Coincidentally, one of his observations took place during a solar eclipse. When the moon passed in front of the sun, the pendulum unexpectedly started moving a bit faster than it should have done.

Since that first observation, the "Allais effect", as it is now called, has confounded physicists. If the effect is real, it could indicate a hitherto unperceived flaw in General Relativity--the current explanation of how gravity works.

Space

That would be a bombshell--and an ironic one, since it was observations taken during a solar eclipse (of the way that light is bent when it passes close to the sun) which established General Relativity in the first place. So attempts to duplicate Dr Allais's observation are important. However, they have had mixed success, leading sceptics to question whether there was anything to be explained. Now Chris Duif, a researcher at the Delft University of Technology, in the Netherlands, has reviewed the evidence. According to a paper he has just posted on arXiv.org, an online publication archive, the effect is real, unexplained, and could be linked to another anomaly involving a pair of American spacecraft.

Three different types of instrument have been used to detect the Allais effect. The first are conventional pendulums, such as the one Dr Allais used originally. The second are torsion pendulums, which work by hanging a bar that has weights at each end from a wire. As the wire twists back and forth, the bar rotates in pendulum-like motion. The third are gravimeters, which are, in essence, very precise scales. All of these instruments measure the acceleration due to gravity at the Earth's surface, a quantity known as g. The Allais effect is a small additional acceleration, so tiny that it would take an apple about a day to fall from a tree branch if it were the only gravitational effect around.

Allez, Allais

Dr Duif has examined various conventional explanations for the Allais effect. He finds the most obvious suggestion--that it is a mere measuring error--unlikely, because similar results have been found by many different groups, operating independently and, in at least one case, without knowledge of Dr Allais's results.

He also discounts several explanations that rely on conventional physical changes that might take place during an eclipse. One of these is that the anomaly is caused by the seismic disturbance induced as crowds of sightseers move into and out of a place where an eclipse is visible. That seems unlikely, given that one of the experiments with a positive result was conducted in a remote area of China while another that had a negative result took place in Belgium, one of the most crowded parts of the planet. Dr Duif also considered the possibility that, because the moon's shadow cools the air during an eclipse, this cooler, and thus denser, air might exert a different gravitational pull on the instruments. This change could, he reckons, affect a gravimeter, but it cannot account for the results from the pendulums.

Dr Duif rules out a third explanation, too: that cooling of the Earth's crust due to the eclipse shadow causes the ground to tilt slightly, and thus distorts the results. He notes that although a detectable tilt is caused when the temperature drops by a few degrees, that tilt is too small to explain the anomalies and, in any case, it would lag roughly 30 minutes behind the shadow (because it takes time for the ground to cool) while the experimental measurements show a change in g instantaneously during an eclipse.

Although Dr Duif discounts each of the conventional explanations on its own, he admits that they might, in combination, account for the Allais effect. But the possibility also remains that General Relativity--Einstein's sacred child--is wrong.

This suggestion would fit in with another odd phenomenon: the fact that the Pioneer 10 and 11 space-probes, launched by NASA, America's space agency, in the early 1970s, are receding from the sun slightly more slowly than they should be.

According to a painstakingly detailed study by the Jet Propulsion Laboratory, the part of NASA responsible for the craft, there is no conventional explanation for this. There may, of course, be no relationship with the Allais effect. But Dr Duif points out that the anomalous force felt by both Pioneer probes (which are travelling in opposite directions from the sun) is about the same size as that measured by some gravimeters during solar eclipses.

So what are the alternatives? One possibility (though it could not account for the Pioneer observations) is known as Majorana shielding. This eponymous theory is that large masses (such as the moon) partially block the gravitational force from more distant objects (such as the sun). Another idea is "MOND", or Modified Newtonian Dynamics, a theory put forward in 1983 by Moti Milgrom of the Weizmann Institute in Israel. MOND suggests that at very low accelerations gravity gets a bit stronger. An even stranger suggestion, made in 2002 by Mikhail Gershteyn, then at the Massachusetts Institute of Technology, is that the force of gravity is different in different directions. Most physicists do not like that one at all. It requires that the conceptual "frames of reference" against which movement, acceleration and so on are measured, are not uniform in all directions. But it was a similarly radical idea--that there is no absolute frame of reference in the universe, only local frames that can be measured relative to one another, which put the "relativity" into relativity theory in the first place...