The Hafele–Keating Experiment: Clocks Around the World

Einstein's relativity says that moving clocks run slow and that clocks higher in a gravitational field run fast. In 1971 the physicist Joseph Hafele and the astronomer Richard Keating tested both ideas with an experiment that sounds almost like a stunt. They took four cesium-beam atomic clocks aboard commercial airliners, flew twice around the world, first eastward and then westward, and compared them with stationary clocks at the United States Naval Observatory Hafele–Keating experiment, Wikipedia^[1]. When reunited, the three sets of clocks disagreed with one another, and the differences were consistent with special and general relativity Hafele–Keating experiment, Wikipedia^[1]. The trip is celebrated on our Jetlagga “Clocks Around the World 1971” tee.

Why fly atomic clocks around the world?

The idea is old. In his 1905 paper on special relativity, Einstein suggested that “a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles” Hafele–Keating experiment, Wikipedia^[1]. (We now know that all clocks at sea level tick at the same rate regardless of latitude, because the kinematic and gravitational effects cancel, assuming Earth's surface is an equipotential Hafele–Keating experiment, Wikipedia^[1].) Testing such tiny effects needs extraordinarily stable clocks. The clocks used were HP 5061A cesium-beam units Hafele–Keating experiment, Wikipedia^[1], and cesium is the atom that defines time itself: since 1968 the SI second has been 9 192 631 770 periods of the ground-state hyperfine transition of cesium-133 Caesium standard, Wikipedia^[2].

Hafele spent a year in fruitless attempts to get funding, until Keating, an astronomer at the Naval Observatory who worked with atomic clocks, approached him after a talk Hafele–Keating experiment, Wikipedia^[1]. They obtained $8000 from the Office of Naval Research, one of the most inexpensive tests of general relativity ever conducted. Of that, $7600 went on eight round-the-world plane tickets, including two seats on each flight for “Mr. Clock” Hafele–Keating experiment, Wikipedia^[1]. The flights were completed on October 7, 1971 Hafele–Keating experiment, Wikipedia^[1].

How does flying change the time on a clock?

Two effects compete Hafele–Keating experiment, Wikipedia^[1].

Speed: kinematic time dilation

Special relativity says a moving clock runs slow, by the Lorentz factor Time dilation, Wikipedia^[3]. The key is to measure speeds in a frame at rest with respect to the centre of the Earth, which is effectively inertial Hafele–Keating experiment, Wikipedia^[1]. In that frame, a clock flying eastward, in the direction of the Earth's rotation, moves faster than a clock on the ground and loses time, while a clock flying westward, against the rotation, moves slower than the ground clock Hafele–Keating experiment, Wikipedia^[1]. That is why direction matters, as our post on muon time dilation shows for particles moving much faster.

Height: gravitational time dilation

General relativity adds a second effect: clocks at higher altitude tick faster than clocks on Earth's surface Hafele–Keating experiment, Wikipedia^[1]. To first order in small quantities, the standard result for the fractional rate of a flying clock compared with a ground clock is

Δτ/τ ≈ gh/c² − (v² − v₀²)/(2c²)

where h is the height, g the gravitational acceleration, v the plane's speed and v₀ the ground clock's speed, both measured in the Earth-centred frame. For a cruising altitude of 10 km, our arithmetic gives

gh/c² ≈ 1.09 × 10⁻¹² (h = 10 km)

which adds up to roughly 94 ns per day. With an illustrative airspeed of 250 m/s over the equator, where the ground moves at about 465 m/s, our arithmetic gives a kinematic loss of about 142 ns per day flying east and a gain of about 82 ns per day flying west. The real flights followed real routes and altitudes, so Hafele and Keating calculated their predictions from the flight data the crews supplied Hafele–Keating experiment, Wikipedia^[1] Hafele and Keating 1972a^[4].

What did Hafele and Keating measure?

The results, published in two 1972 papers in Science Hafele and Keating 1972a^[4] Hafele and Keating 1972b^[5], are summarised below Hafele–Keating experiment, Wikipedia^[1]. Values are nanoseconds gained by the flying clocks relative to the Naval Observatory.

Direction	Gravitational (predicted)	Kinematic (predicted)	Total predicted	Measured
Eastward	+144 ± 14	−184 ± 18	−40 ± 23	−59 ± 10
Westward	+179 ± 18	+96 ± 10	+275 ± 21	+273 ± 7

east: −59 ± 10 ns · west: +273 ± 7 ns

The observed gains and losses agreed with relativistic predictions to within the roughly 10% precision expected of the experiment Hafele–Keating experiment, Wikipedia^[1]. The eastbound difference was 0.76σ and the westbound 0.09σ Hafele–Keating experiment, Wikipedia^[1].

Was the Hafele–Keating result controversial?

It drew criticism, but those criticisms did not address the later confirmation of the result by more accurate methods, and they have been shown to be in error Hafele–Keating experiment, Wikipedia^[1]. Between September 1975 and January 1976 a University of Maryland group flew three atomic clocks to 10 km over Chesapeake Bay in a turboprop at only 500 km/h, to minimise the velocity effect, with five flights of 15 hours each Hafele–Keating experiment, Wikipedia^[1].

Today the same physics fits on a lab bench. In 2010 Chou, Hume, Rosenband and Wineland used optical clocks to confirm velocity time dilation at the 10⁻¹⁶ level at speeds below 36 km/h, and measured gravitational time dilation from a height difference of just 33 cm Hafele–Keating experiment, Wikipedia^[1] Chou et al. 2010^[6]. Both effects are now routinely built into the Global Positioning System Hafele–Keating experiment, Wikipedia^[1], as our post on how GPS corrects for relativity explains.

Quick FAQ

Did the flying clocks really age differently, or did they just malfunction?

A common misconception holds that time dilation applies only to light-based clocks and not to atomic or mechanical ones, and it leads to wrong conclusions about the Hafele–Keating result Time dilation, Wikipedia^[3]. The flown clocks were compared directly with stationary ones Hafele–Keating experiment, Wikipedia^[1].

Where else can I see these effects?

Satellite clocks are corrected for exactly these two effects, the subject of our Orbitick GPS clock-correction sticker, and fast cosmic-ray muons show the kinematic one, as on our Muonaut muon time dilation sticker. More are in the Relativity and Cosmos collection.

References

1. Wikipedia, “Hafele–Keating experiment”. https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
2. Wikipedia, “Caesium standard”. https://en.wikipedia.org/wiki/Caesium_standard
3. Wikipedia, “Time dilation”. https://en.wikipedia.org/wiki/Time_dilation
4. J. C. Hafele and Richard E. Keating (1972), “Around-the-World Atomic Clocks: Predicted Relativistic Time Gains,” Science 177, 166–168 (DOI 10.1126/science.177.4044.166; metadata verified via Crossref). https://doi.org/10.1126/science.177.4044.166
5. J. C. Hafele and Richard E. Keating (1972), “Around-the-World Atomic Clocks: Observed Relativistic Time Gains,” Science 177, 168–170 (DOI 10.1126/science.177.4044.168; metadata verified via Crossref). https://doi.org/10.1126/science.177.4044.168
6. C. W. Chou et al. (2010), “Optical Clocks and Relativity,” Science 329, 1630–1633 (DOI 10.1126/science.1192720; metadata verified via Crossref). https://doi.org/10.1126/science.1192720

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.