Hafele–Keating experiment

The Hafele–Keating experiment was a test of the theory of relativity. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. In October of 1971, J. Year 1971 ( MCMLXXI) was a Common year starting on Friday (link will display full calendar of the 1971 Gregorian calendar. C. Hafele and Richard E. Keating took four caesium-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. An atomic clock is a type of Clock that uses an Atomic resonance Frequency standard as its timekeeping element The United States Naval Observatory ( USNO) is one of the oldest Scientific agencies in the United States.

1 Overview
2 Equations
3 References
4 See also

Overview

According to special relativity, the speed of a clock is greatest according to an observer who is not in motion with respect to the clock. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial 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, is moving faster than a clock that remains on the ground, while the clock aboard the plane moving westward, against the earth's rotation, is moving slower.

According to general relativity, another effect comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 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:^[1]^[2]

	predicted			measured
	nanoseconds gained
	gravitational (general relativity)	kinematic (special relativity)	total	measured
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 relativity, and the observed time gains and losses were reportedly different from zero to a high degree of confidence. Year 1972 ( MCMLXXII) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. A nanosecond ( ns) is one billionth of a second See also times of other orders of magnitude. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial

That result was contested by Dr. A. G. Kelly who examined the raw data: according to him, the final published outcome had to be averaged in a biased way in order to claim such a high precision. ^[3] Also, Louis Essen, the inventor of the atomic clock, published an article in which he discussed the (in his opinion) inadequate accuracy of the experiment. Louis Essen ( September 6, 1908 &ndash August 24, 1997) was an English Physicist whose most notable achievements were in ^[4]; however, neither of these publications are in peer-reviewed sources.

One notable approximate repetition of the original experiment took place on the 25th anniversary of the original experiment, using more precise atomic clocks, and the results were verified to a higher degree of accuracy. ^[5]. Nowadays such relativistic effects have been incorporated into the calculations used for the GPS system^[6]. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth

Equations

The equations and effects involved in the experiment are:

Total time dilation

Τ = Δτ v + Δτ g + Δτ s

Velocity

$\Delta\tau_v = - \frac{1}{2c^2} \sum_{i=1}^{k}v_i^2 \Delta\tau_i$

Gravitation

$\Delta\tau_g = \frac{g}{c^2} \sum_{i=1}^{k} (h_i - h_0) \Delta\tau_i$

Sagnac effect

$\Delta\tau_s = - \frac{\omega}{c^2} \sum_{i=1}^{k} R_i^2 \cos^2 \phi_i \Delta\lambda_i$

Where h = height, v = velocity, $ω$ = Earth's rotation and τ represents the duration/distance of a section of the flight. This article discusses a concept in physics For the concept in sociology see Time displacement. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 The Sagnac effect (also called Sagnac Interference) named after French physicist Georges Sagnac, is a phenomenon encountered in Interferometry that is The effects are summed over the entire flight, since the parameters will change with time.

References

^ Hafele, J. ; Keating, R. (July 14, 1972). Events 1223 - Louis VIII becomes King of France upon the death of his father Philip II of France. Year 1972 ( MCMLXXII) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. "Around the world atomic clocks:predicted relativistic time gains". Science 177 (4044): 166-168. doi:10.1126/science.177.4044.166. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
^ Hafele, J. ; Keating, R. (July 14 1972). "Around the world atomic clocks:observed relativistic time gains". Science 177 (4044): 168-170. doi:10.1126/science.177.4044.168. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
^ A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No. 3 Feb. 1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9
^ Louis Essen, Electron. Louis Essen ( September 6, 1908 &ndash August 24, 1997) was an English Physicist whose most notable achievements were in Wireless World 94 (1988) 238.
^ Page not found : Feedback : National Physical Laboratory
^ Deines, "Uncompensated relativity effects for a ground-based GPSA receiver", Position Location and Navigation Symposium, 1992. Record. '500 Years After Columbus - Navigation Challenges of Tomorrow'. IEEE PLANS '92.

Contents

Overview

Equations

References

See also