Hafele-Keating experiment
Encyclopedia
The Hafele–Keating experiment was a test of the theory of relativity
. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory
.
, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs slower, and the effect is proportional to the square of the velocity. In a frame of reference at rest with respect to the center of the earth, the clock aboard the plane moving eastward, in the direction of the Earth's rotation, has a greater velocity (resulting in a relative time loss) than a clock that remains on the ground, while the clock aboard the plane moving westward, against the Earth's rotation, has a lower velocity than the one on the ground, resulting in a relative time gain.
According to general relativity
, another effect comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. Since the aircraft are flying at roughly the same altitude in both directions, this effect is more "constant" between the two clocks, but nevertheless it causes a difference in comparison to the clock on the ground.
The results were published in Science in 1972:
The published outcome of the experiment was consistent with special and general relativity. The observed time gains and losses were different from zero to a high degree of confidence, and were in agreement with relativistic predictions to within the ~10% precision of the experiment.
A reenactment of the original experiment by the NPL took place in 1996 on the 25th anniversary of the original experiment, using more precise atomic clocks during a flight from London
to Washington, D.C.
and back again. The results were verified to a higher degree of accuracy. A time gain of 39 ± 2 ns was observed, compared to a relativistic prediction of 39,8 ns. In June 2010, NPL again repeated the experiment, this time around the globe (London - Los Angeles
- Auckland
- Hongkong - London). The relativistic value was 246 ± 3 ns, the measured value was 230 ± 20 ns.
Nowadays such relativistic effects are, for example, routinely incorporated into the calculations used for the Global Positioning System.
Because the experiment was reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified. Criticisms of the experiment did not address the subsequent verification of the result by more accurate methods, and have been shown to be in error.
Total time dilation
Velocity
Gravitation
Sagnac effect
Where c = speed of light, h = height, g=acceleration of gravity, v = velocity,
= angular velocity of Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time.
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory
United States Naval Observatory
The United States Naval Observatory is one of the oldest scientific agencies in the United States, with a primary mission to produce Positioning, Navigation, and Timing for the U.S. Navy and the U.S. Department of Defense...
.
Overview
According to special relativitySpecial relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs slower, and the effect is proportional to the square of the velocity. In a frame of reference at rest with respect to the center of the earth, the clock aboard the plane moving eastward, in the direction of the Earth's rotation, has a greater velocity (resulting in a relative time loss) than a clock that remains on the ground, while the clock aboard the plane moving westward, against the Earth's rotation, has a lower velocity than the one on the ground, resulting in a relative time gain.
According to general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, another effect comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. Since the aircraft are flying at roughly the same altitude in both directions, this effect is more "constant" between the two clocks, but nevertheless it causes a difference in comparison to the clock on the ground.
The results were published in Science in 1972:
| nanosecond Nanosecond A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns.... s gained | ||||
|---|---|---|---|---|
| predicted | measured | |||
| gravitational (general relativity General relativity General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics... ) | kinematic (special relativity Special relativity Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's... ) | total | ||
| eastward | 144±14 | −184 ± 18 | −40 ± 23 | −59 ± 10 |
| westward | 179±18 | 96±10 | 275±21 | 273±7 |
The published outcome of the experiment was consistent with special and general relativity. The observed time gains and losses were different from zero to a high degree of confidence, and were in agreement with relativistic predictions to within the ~10% precision of the experiment.
Repetitions
The results were verified in an improved experiment in 1976 by the University of Maryland, this time verifying the relativistic predictions to a precision of about 1%.A reenactment of the original experiment by the NPL took place in 1996 on the 25th anniversary of the original experiment, using more precise atomic clocks during a flight from London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
to Washington, D.C.
Washington, D.C.
Washington, D.C., formally the District of Columbia and commonly referred to as Washington, "the District", or simply D.C., is the capital of the United States. On July 16, 1790, the United States Congress approved the creation of a permanent national capital as permitted by the U.S. Constitution....
and back again. The results were verified to a higher degree of accuracy. A time gain of 39 ± 2 ns was observed, compared to a relativistic prediction of 39,8 ns. In June 2010, NPL again repeated the experiment, this time around the globe (London - Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...
- Auckland
Auckland
The Auckland metropolitan area , in the North Island of New Zealand, is the largest and most populous urban area in the country with residents, percent of the country's population. Auckland also has the largest Polynesian population of any city in the world...
- Hongkong - London). The relativistic value was 246 ± 3 ns, the measured value was 230 ± 20 ns.
Nowadays such relativistic effects are, for example, routinely incorporated into the calculations used for the Global Positioning System.
Because the experiment was reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified. Criticisms of the experiment did not address the subsequent verification of the result by more accurate methods, and have been shown to be in error.
Equations
The equations and effects involved in the experiment are:Total time dilation
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
Velocity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
Gravitation
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
Sagnac effect
Sagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
Where c = speed of light, h = height, g=acceleration of gravity, v = velocity,
= angular velocity of Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time.See also
- Tests of general relativityTests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...
- Twin paradoxTwin paradoxIn physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth...
- Time dilationTime dilationIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
- GPS Time Dilation