General relativity states that clocks in an accelerated-reference frame run slower than stationary ones. This principle is used often in syncing clocks on Earth with those on satellites or planes, but the time difference has never been measured more accurately than five decimal places; more accurate measurements would help us better understand space-time curvature and develop a theory of quantum gravity. A group of scientists that includes Energy Secretary Steven Chu recognized that an atom in a quantum superposition simultaneously travels two paths at slightly different elevations, and therefore experience slightly different gravitational effects. This let them measure the relativistic effects out to nine decimal places using data they had apparently generated over a decade ago.

According to general relativity, an object in an accelerated frame experiences time more slowly than a stationary object. This effect is also generated by gravity, which is essentially an accelerated frame—being on Earth and in Earth’s gravitational pull of 9.8 meters/second/second is the same as being in a rocket in space traveling 9.8 meters/second/second. Time passes more slowly, or dilates, in these frames, an effect known as gravitational redshift.

Gravitational redshift can be measured at varying levels of Earth's own atmosphere, since the pull of gravity is less the farther away we are from the surface. For example, if we synchronize two clocks, take one of them to the top of a mountain for a while, and then bring it back to where the other clock is, the clock that sat still will be running behind the clock that was in the mountains—it was in a more accelerated frame, and time passed more slowly there.

While this effect is relatively easy to produce, it's hard to get exact measurements because there are so many confounding factors: the mountain clock spent a while in a variable amount of gravity as it was being carried up the mountain, the earth's orbit is elliptical, and so on. The math and integrals involved can get tricky when you have to transport clocks through unknown areas.

To solve this issue of carrying around different clocks to different places, the researchers revisited an experimental system that Chu's group had developed over a decade ago, which involved single atoms in a confined region. At the time, the team was using the atoms to get a precise measure of the acceleration due to gravity, but the same data could apparently be used to extract a measure of the gravitational redshift.

To get the necessary separation of "clocks," they launched the atoms into a vacuum, using laser pulses to put it in a superposition of two quantum states, each of which traveled a slightly different path. This provided a single test subject that would experience two gravitational potentials at the exact same time, allowing the experimenters to isolate the effects of redshift.

The two quantum states differed because one had received extra momentum from the laser, while the other did not. The two states would physically separate and, this being quantum mechanics, a single atom would travel both trajectories as it crossed the vacuum chamber. At the far side, a second pulse would alter the lower elevation path so that the paths would merge again. When the paths realigned, the atoms received a third laser pulse.

Aside from its gravity-influenced trajectory, the atoms also moved as waves that would interfere constructively or destructively, depending on the phase difference between the waves when the paths realigned. The phase difference was influenced by a number of factors, but the researchers found that the effects all canceled each other out—all except for the redshift from the slightly different gravitational effects of the two different trajectories. Plugging this into the right equations gave a new measure of the gravitational redshift parameter that is 10,000 times more accurate than previously obtained values.

The authors suggest that it is possible to obtain even more accurate measurements of the redshift. If the local gravity gradient is well-characterized, one to two additional decimal places can be squeezed out of the same set-up. For this work, they had to include some uncertainty in their gravitational variable because they didn't know the exact gravity gradient in their location in Stanford. However, the more accurate measurement of gravitational redshift provides more constraints on the curvature of space-time, which may influence the development of a theory of quantum gravity.

Nature, 2010. DOI: 10.1038/nature08776