Joseph Hafele and Richard Keating with their atomic clock.
It is a well-known prediction of the special theory of relativity that a clock moving past an observer will be seen to run slow compared with the observer’s clocks – time dilation. It is a less well-known prediction of the general theory of relativity that a clock in a gravitational field will be seen to run slow compared with the clocks of an observer in a weaker gravitational field. This is linked to an observed change in the wavelength of light coming from a source in a gravitational field, which is known as the gravitational redshift. These predictions were tested in 1971 by an experiment that involved flying clocks around the world in ordinary commercial aircraft.
The experiment was carried out by two American physicists, Joseph Hafele and Richard Keating. The idea was to see how the time recorded on moving clocks at high altitude (combining the effects of both the special theory and the general theory) compared with the time recorded by clocks that stayed at rest on the ground. It would have been a lot easier for them if they could have chartered a private plane, but because of a limited budget they had to fly economy class on ordinary scheduled flights. The ultra-precise atomic clocks that they used were strapped to the front wall of the passenger cabin and connected to the power supply of the aircraft; an identical set of clocks stayed at the US Naval Observatory in Washington, DC, ready to be compared with the travelling clocks when they returned home.
Between 4 and 7 October 1971, the clocks were flown completely around the world from west to east. After making allowances for the various stopovers, changes of altitude and changes of speed made by the aircraft, the team calculated that the clocks should have gained between 254 and 296 nanoseconds (billionths of a second), with two-thirds of this attributable to the gravitational effect of being at altitude (the clocks ran faster, because gravity is weaker at altitude). The rest of the calculated difference was due to the effect predicted by the special theory, which added to the gravitational effect because of complications caused by the Earth’s rotation. The simplest way to picture this is to think in terms of a ‘frame of reference’ stationary relative to the centre of the Earth. A clock in an aircraft moving eastward, in the direction of the Earth’s rotation, moves faster than one on the ground, but a clock aboard an aircraft moving westward moves slower than one on the ground. The measured difference was 273 nanoseconds, smack in the middle of the predicted range.
The same clocks were then flown westward around the world, between 13 and 17 October 1971. The results from this leg of the experiment were slightly less impressive. This time, the time-dilation effect from the motion of the clocks was expected to cause the clocks to lose more than they would gain from the gravitational effect, producing a time difference of 40 ± 23 nanoseconds compared with the clocks on the ground. Because of some problems with the data measurements, this time the team could say only that the measured difference was between 49 and 69 nanoseconds, which just about matched the prediction. But together the two legs of the experiment confirmed, if anyone had doubted it, that the time-dilation effects predicted by Einstein’s two great theories were real.
A more accurate test along the same lines was carried out in June 1976, involving the Smithsonian Astrophysical Observatory and NASA. A rocket-borne experiment known as Gravity Probe A reached an altitude of 10,000 kilometres (far higher than any aircraft) on a flight going almost straight up and down that lasted just under two hours. This meant that effects due to the Earth’s rotation could be ignored. At the top of its flight, the payload felt a gravitational influence only 10 per cent as strong as the influence we feel on the surface of the Earth.
During the flight, the time recorded on a clock in the payload of the rocket, incorporating a maser, was monitored over a radio link and compared with the timekeeping of an identical clock on the ground while the flight was still in progress. The changing speed of the rocket and its payload was also monitored, by the Doppler effect (see here), using a second signal transmitted from the Earth and received and retransmitted by the probe back to Earth. The observations were then compared with the predictions calculated using the equations of relativity theory. This time, the measurements matched the predictions to a precision of 70 parts per million, or seven thousandths of 1 per cent. Nobody was surprised, but a lot of physicists were very pleased; this is still the most complete and accurate measurement of the gravitational redshift yet carried out.