Clocks low in the gravity well run slower than those higher up. That’s just a relativistic fact of life—one that we take advantage of every time we use the Global Positioning System. (I remember how cool I thought it was when I first learned that clocks in orbiting GPS satellites have to be programmed to correct for relativistic time dilation.) Within the past year, experimentalists comparing the speeds of widely separated atomic clocks (connected via fiber optic cable) have shown that current chronometers, with uncertainties around 10-16, are sensitive enough to detect the change in time’s flow that accompanies a shift of a meter or less in relative elevation.
The geoid is the Earth-swaddling surface of equal gravitational potential that more or less coincides with global mean sea level. Or, from the chronometric viewpoint, the surface on which all clocks tick at the same rate. The geoid isn’t smooth. As we have known for years (and continue to prove with increasing detail), the geoid undulates. Its rise and fall betray details of objects and events far below the surface.
Writing in Geophysical Journal International (the paper is also available on arXiv.org), a team of researchers from Switzerland, the United States, and Romania shows that clocks accurate to within 10-18 could map the geoid to within about a centimeter and show the sizes and locations of mass variations far below the surface. Since the accuracy of standard reference clocks has increased at a steady order-of-magnitude-per-decade since the 1950s—and since newly built optical atomic clocks and proposed designs for highly charged ion and nuclear clocks promise to increase that rate substantially—it is clearly time prepare for an age in which we can map the crust and mantle by watching time slip by.
Imagine a bubble of magma 20 percent denser than the surrounding rock. University of Zurich physicist Ruxandra Bondarescu and her co-workers show that a clock with 10-18 accuracy can easily detect and locate a 1.5-kilometer-radius, high-density sphere centered 2 km below the surface. It could also unmask a 4 km-radius sphere 45 km below our feet. Time changes can reveal subtler differences, too—such as a 1 percent density anomaly 10 km in radius centered 37 km underground.
Established methods (like those used in a recently published report linking variations in the Earth’s magnetic field to mass flows deep under the Atlantic and Indian Oceans) use satellites to detect variations in gravitational force. Bondarescu, et al maintain that chronometric mapping of the geoid presents some distinct advantages. Clock readings measure the potential surface directly. The researchers point out that force (the first derivative of the potential) must be integrated (over a path) to yield figures for potential, reducing resolution. Though acceleration is a vector, moreover, many instruments record only its magnitude, and not its precise direction. This also, say the chronometrists, compromises accuracy of the geoid measurement, and potentially degrades resolution of subterranean features.
Image: European Space Agency ESA, D. Ducros