Hafele–Keating experiment

The Hafele - Keating experiment was a test of the following from the theory of relativity time dilation. Joseph C. Hafele and Richard E. Keating 1971 brought four cesium atomic clocks on board a commercial airliner, and flew twice around the world, first eastward, then westward, and compared the clocks with those of the United States Naval Observatory.

According to the special theory of relativity, a clock is the quickest way for an observer who is at rest with respect to the clock. In a movable relative to the system clock runs slower ( time dilation ), and this effect is proportional to the square of the velocity. The existence of this effect has now been demonstrated in numerous tests of special relativity, see Ives - Stilwell experiment and time dilation of moving particles.

According to the general theory of relativity clocks go into greater heights with increasing gravitational potential faster than clocks to a lesser gravitational potential near the surface. Also, this effect has been confirmed in numerous tests of general relativity, such as the pound- Rebka experiment.

In contrast, both effects are simultaneously detected at Hafele - Keating experiment. Analogous experiments have now been repeated several times with increased precision, such as in the Maryland experiment, as well as part of the operation of the GPS.

Hafele - Keating experiment

In the reference system is at rest with respect to the Erdzentrums, the clock moves eastward in the direction of the earth's rotation, and has a greater speed than one located at the surface clock. According to the special theory of relativity, the clock runs slower than the Floorclocs, and thus losing time. However, the clock and thus the moves westward opposite to the Earth's rotation, has a lower speed than the Floorclocs, and thus gaining time. In addition, the slight increase of the gravitational potential both clocks According to the general theory of relativity comes into play at higher altitudes, which due to the gravitational time dilation to the same extent go faster than the ground clocks.

The results, published in 1972 the observed time gains or losses were consistent with the relativistic predictions agree within an accuracy of ~ 10 %.

Repetitions

Repetitions of the original experiment were carried out by the National Physical Laboratory ( NPL) in 1996 with a higher degree of accuracy, and that during a flight from London to Washington, DC and back again. Was measured action by the clocks of 39 ± 2 ns, in good agreement with the relativistic value of 39.8 ns. In June 2010, NPL undertook the experiment again, this time around the entire globe ( London - Los Angeles - Auckland - Hong Kong - London). The relativistic value was 246 ± 3 ns, measured 230 ± 20 ns, again in good agreement.

Maryland experiment

A more complex experiment of a similar nature was of 1975-1976 by ​​researchers from the University of Maryland, USA, carried out. Three atomic clocks were transported by air to about 10,000 m above the Chesapeake Bay in Maryland, and three atomic clocks were on the ground. Special containers protected the watch from external influences such as vibrations, magnetic fields, temperature and air pressure fluctuations. You turboprop aircraft used, the barely 500 km / h reached in order to keep the speed effect is small. The planes were on defining a fixed course and were constantly monitored by radar. First, we completed several test flights and finally five main flights of 15 hours of flight time. Per second determined to position and velocity.

On the one measured the time difference before by direct comparison of clocks on the ground and after the flight for about 20 hours. On the other was ns duration of the time difference read during the flight by laser light pulses of 0.1 by sending a signal to the aircraft, which was reflected by it and collected on the ground station again. The difference already took during the flight to an ongoing basis. Due to the gravitational effect, the aircraft clocks are running faster during the flight. It was observed a deviation of 47.1 ± 1.5 ns, consisting of -5.7 ns slowdown caused by the velocity effect and 52.8 ns due to gravity. This is consistent with the predicted by the theory of relativity value of 47.1 ± 0.25 ns very good. The error analysis yielded an accuracy of 1.6%.

Further experiments

Iijima & Fujiwara led by 1975-1977 measurements of gravitational time dilation by alternately from the National Astronomical Observatory of Japan in Mitaka to 58m above sea level, Mount Norikura at 2876m above sea level, transported a commercial cesium clock. The corresponding difference in height was so 2818m. During the periods of residence in Mitaka the clock was compared with another there stationary cesium clock. The calculated blue shift of the transported clock due to gravity amounted to 30.7 × 10-14, which was measured ( 29 ± 1.5 ) × 10-14 in agreement with the theoretical value. The ratio between the two values ​​was 0.94 ± 0.05.

1976 compared Briatore & Leschiutta the passage of two cesium clocks, with a clock in Turin at 250m, and the second was at the Plateau Rosa at 3500m above sea level. The comparison was carried out by evaluation of the times of arrival of VHF television synchronization pulses and LORAN-C chains. The predicted difference was 30.6 ns per day. By means of two operational criteria were ns / T measured differences of 33.8 ± 6.8 ns / T and 36.5 ± 5.8, in agreement with the predicted value.

2010 led Chou et al. Tests, which both gravitational and velocity -related effects at much lower distances and speeds were measured. This aluminum ions were used as highly accurate clocks. The time dilation due to the speed was measured with an accuracy of about 10-16 at speeds of about 36 km / hr. The gravitational time dilation was also confirmed by raising the clocks to only 33cm.

Other precise confirmations of gravitational time dilation are the pound- Rebka experiment, or Gravity Probe A. Today, both relativistic effects must be taken into account, for example, in the calculations of the GPS. Because of these and a number of other high- precision experiments, the existence of relativistic time dilation in the professional world is undisputed. See tests of special relativity theory and tests of general relativity.

Equations

The equations relevant to the Hafele - Keating experiment effects have the following form:

Time dilation is the sum of three contributions:

Contribution of the speed according to the SRT:

Contribution of gravity according to the ART:

Contribution from the Sagnac effect:

Where c = speed of light, h = height, g = gravitational acceleration, v = velocity = angular velocity of the Earth's rotation, τ = duration / length of a flight section. The effects have been integrated throughout the entire flight, since the parameters change with time.