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SPECIAL RELATIVITY

HAFELE-KEATING EXPERIMENT WITH ATOMIC CLOCKS

Experimental evidence for the time dilation effect

SUMMARY

Inertial frames of reference You must always identify the frames of reference

station frame (S)

moving frame (M)

relativity factor

Time dilation effect

proper time interval

dilated time interval

Length contraction

proper length

contracted length

The Hafele-Keating experiment provided experimental evidence to support the time dilation effects of special and general relativity.

HAFELE-KEATING EXPERIMENT WITH ATOMIC CLOCKS

Video: Hafele-Keating Experiment

An extremely accurate measurement of time can be made using a well-defined electronic transition in the ¹³³Cs₅₅ atom that has a frequency of 9 192 961 770 Hz.

"During October 1971, four caesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40 23 nanoseconds during the eastward trip and should have gained 275 21 nanoseconds during the westward trip ... relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 5910 nanoseconds during the eastward trip and gained 2737 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)

In this experiment, both gravitational time dilation and kinematic time dilation are significant and are in fact of comparable magnitude. Their predicted and measured time dilation effects were as follows.

	East – West [ns]	West -East [ns]
Gravitational	144 14	179 18
Kinematic	-184 18	96 10
Net effect	-40 23	275 21
Observed	-59 10	273 7

(1 ns = 1x10^-9 s)

A negative time indicates that the time on the moving clock is less than the reference clock. The moving clocks lost time (ran slow) on the eastward trip but gained time (ran faster) during the westward trip. This occurs because of the rotation of the Earth, indicating that the flying clocks ticked faster or slower than the reference clocks on Earth. The special theory of relativity is verified with the experimental uncertainties.

Fig. 2. Two planes take off from Washington D.C. where two atomic clocks are located at the U.S. Naval Observatory. One plane travels around the world in an easterly direction carrying a caesium atomic clock, while another caseium atomic clock is flown in a plane around the world in a westerly direction as the Earth rotates. At the end of the flights the clocks are compared. The results show that the effects of time dilation are correct.