Superaccurate Clocks Confirm Time is Slower for Your Feet

Out of sync. Because of the effects of gravity, a clock high on a wall should run ever so slightly faster than a watch just below it.

According to Einstein's theory of relativity, a clock on the floor ought to run very slightly slower than an identical one on top of a step stool because the lower clock nestles deeper into Earth's gravitational field. Now, physicists have demonstrated this effect using two super-accurate clocks and hoisting one several centimeters above the other. It's the first time scientists have used clocks to show that time flies faster for your nose than for your navel.

"The demonstration of the gravitational shift by elevating a clock about one foot is quite stunning," says Daniel Kleppner, a physicist at the Massachusetts Institute of Technology in Cambridge, who was not involved in the work. He adds, however, that the demonstration "does not change anyone's view on relativity."

Einstein realized that time passes at different rates depending on the circumstances. For example, suppose you stand on a train platform with a Rolex on your wrist while a friend wearing an identical watch zooms by in a train. Your friend's watch runs slower than yours simply because he is moving relative to you, Einstein predicted in his theory of special relativity. And according to his theory of general relativity, gravity comes about because massive things like Earth stretch the fabric of space and time. As a result, a clock at lower altitude and, hence, lower gravitational energy, should run slower than one at higher altitude—by about 3 microseconds per year per kilometer of elevation.

Such seemingly nonsensical predictions have long since been confirmed by comparing ultra-accurate atomic clocks on the ground with those in high-flying jets. And the satellite-based global position system takes them into account. Now Chin-wen Chou, Till Rosenband, and colleagues at the National Institute of Standard and Technology (NIST) in Boulder, Colorado, have detected changes in the passage of time caused by speeds of less than 10 meters per second and height changes of less than a meter, using a new type of atomic clock called an optical clock.

An atomic clock exploits the fact that the electrons in at atom occupy "states" with distinct energies and can hop between two states by emitting or absorbing electromagnetic waves of a set frequency. Researchers shine such waves on the atoms, and a feedback loop keeps their frequency tuned so that the atoms continually jump back and fourth between the two states. The oscillating waves then mark time just as a pendulum does, only very much faster and more evenly. The atomic clocks that now set the international time standard use microwaves with a frequency of 9.2 billion cycles per second to make cesium atoms flip between two states of nearly the same energy.

In contrast, the NIST researchers' clock uses laser light with a frequency of 1,120,000 billion cycles per second to drive a higher-energy jump called an optical transition in a single aluminum ion held in an elaborate trap. The cesium standard is accurate to three parts in 10 million billion; the new aluminum clock has an accuracy nearly 40 times better. That extra accuracy makes it possible to demonstrate the effect of relativity on a more human scale. The researchers built two aluminum clocks, and to test the velocity effect they set the ion in one jiggling back and forth in its trap with a speed as low as 4 meters per second. They were able to resolve the 2-parts-in-10-million-billion slowing that motion caused in the clock with the moving ion. To test the gravity effect, the physicists started with one clock 17 centimeters below the other and then raised the first clock by 33 centimeters. This time they detected a 4-parts-in-100-million-billion shift in the frequency of the raised clock, as predicted by the theory of general relativity, the researchers report in the 24 September issue of Science.

"What amazes me is the advancement of the optical clocks—10 or 20 years ago they were only a dream," say Nan Yu, a quantum physicist at NASA Jet Propulsion Laboratory in Pasadena, California. Only recent advances in laser techniques have made that dream a reality, says Yu, who expects that within a few years some type of optical clock may replace the cesium microwave standard. ...

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