Hafele–Keating experiment: Difference between revisions
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Nevertheless, similar experiments have been done a number of times. One notable approximate repetition 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. [http://www.npl.co.uk/publications/metromnia/issue18/]. Nowadays such relativistic effects have been incorporated into the calculations used for the [[GPS]] system. |
Nevertheless, similar experiments have been done a number of times. One notable approximate repetition 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. [http://www.npl.co.uk/publications/metromnia/issue18/]. Nowadays such relativistic effects have been incorporated into the calculations used for the [[GPS]] system. |
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==GPS== |
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It is often mistakenly reported that SR and GR theories are critical in operating the NAVSTAR GPS navigation system. However, GPS was never designed to utilize or test either of the two theories. Upon insisting by some relativity physicists in the late 1990-ies, GPS navigation and control messages were included immeasurably small corrections in addition to the originally pre-programmed position corrections (as due to the atmospheric, signal-multipath and other effects). Without explanation however, and in a manner that is not entirely transparent, the relativity physics community has recently started using this correction as a proof for the two relativity theories. |
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The equations and effects involved in the experiment are: |
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In fact, the so-called "GPS relativistic correction" is too small to be measured on Earth using even the most precise (geodetic) GPS techniques so-called differential positioning (DGPS), also called the relative or geodetic GPS positioning. Thus in his classical book [http://www.amazon.com/gp/product/0471059307/sr=1-2/qid=1156085902/ref=sr_1_2/102-7705539-2972104?ie=UTF8&s=books GPS Satellite Surveying], Alfred Leick writes (p.170): "In relative (mm) positioning, most of the relativistic effects cancel or become negligible." This is because the relativity-predicted values, if real, would amount to less than one half of the normal environmental (insurmountable) geophysical noise. Therefore, geometrical differencing in precise positioning cancels out most of the so-called "relativistic effects"; the GPS system can perform equally superb without SR or GR theories. Hence no known (scientific or commercial) GPS receiver seems to utilize the so-called "GPS relativistic correction". |
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Total [[time dilation]] |
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:<math>\Tau = \Delta\tau_v + \Delta\tau_g + \Delta\tau_s</math> |
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The above-cited Leick's book is considered by some to be one of the most authoritative sources on GPS geodesy nowadays. It also lists numerous references that show in greater detail why the so-called "relativistic effects" turn out to be irrelevant for achieving the highest (millimetre-level) obtainable accuracy in precision positioning. Similarly, non-geodetic (navigation) accuracy would not suffer to a noticeable degree either, since, if real, the so-called "relativistic effects" would amount to a centimetre level, which is less than [http://gge.unb.ca/Research/GRL/GeodesyGroup/tutorial/precision_navigation.htm any other single error-source in modern navigation]. For instance, the most reliable utilization of GPS in global navigation, the [[WAAS]] system, requires no so-called "relativistic corrections" to achieve its metre-level accuracy. |
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[[Special relativity|Velocity]] |
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Hence, there is no evidence at the present that either of the Einstein's relativity theories is critical for the operation of the GPS system as used in local (precision) positioning or global navigation. |
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:<math>\Delta\tau_v = \frac{1}{2c^2} \sum_{i=1}^{k}v_i^2 \Delta\tau_i</math> |
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[[General relativity|Gravitation]] |
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:<math>\Delta\tau_g = \frac{g}{c^2} \sum_{i=1}^{k} (h_i - h_0) \Delta\tau_i</math> |
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[[Sagnac effect]] |
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:<math>\Delta\tau_s = - \frac{\omega}{c^2} \sum_{i=1}^{k} R_i^2 cos^2 \phi \Delta\lambda_i</math> |
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Where h = height, v = velocity, <math>\omega</math> = 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. |
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==References== |
==References== |
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Revision as of 20:30, 26 September 2006
The Hafele-Keating experiment was a test of the theory of relativity. In October of 1971, J. C. Hafele and Richard E. Keating 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.
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. 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. 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:
| nanoseconds gained | ||||
|---|---|---|---|---|
| predicted | measured | |||
| gravitational (general relativity) | kinematic (special relativity) | 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 relativity, and the observed time gains and losses were reportedly different from zero to a high degree of confidence.
That result was contested by Dr. Kelly who examined the raw data: he found that the final published outcome had to be averaged in a biased way in order to claim such a high precision. [citation needed] 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.
Nevertheless, similar experiments have been done a number of times. One notable approximate repetition 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. [1]. Nowadays such relativistic effects have been incorporated into the calculations used for the GPS system.
GPS
It is often mistakenly reported that SR and GR theories are critical in operating the NAVSTAR GPS navigation system. However, GPS was never designed to utilize or test either of the two theories. Upon insisting by some relativity physicists in the late 1990-ies, GPS navigation and control messages were included immeasurably small corrections in addition to the originally pre-programmed position corrections (as due to the atmospheric, signal-multipath and other effects). Without explanation however, and in a manner that is not entirely transparent, the relativity physics community has recently started using this correction as a proof for the two relativity theories.
In fact, the so-called "GPS relativistic correction" is too small to be measured on Earth using even the most precise (geodetic) GPS techniques so-called differential positioning (DGPS), also called the relative or geodetic GPS positioning. Thus in his classical book GPS Satellite Surveying, Alfred Leick writes (p.170): "In relative (mm) positioning, most of the relativistic effects cancel or become negligible." This is because the relativity-predicted values, if real, would amount to less than one half of the normal environmental (insurmountable) geophysical noise. Therefore, geometrical differencing in precise positioning cancels out most of the so-called "relativistic effects"; the GPS system can perform equally superb without SR or GR theories. Hence no known (scientific or commercial) GPS receiver seems to utilize the so-called "GPS relativistic correction".
The above-cited Leick's book is considered by some to be one of the most authoritative sources on GPS geodesy nowadays. It also lists numerous references that show in greater detail why the so-called "relativistic effects" turn out to be irrelevant for achieving the highest (millimetre-level) obtainable accuracy in precision positioning. Similarly, non-geodetic (navigation) accuracy would not suffer to a noticeable degree either, since, if real, the so-called "relativistic effects" would amount to a centimetre level, which is less than any other single error-source in modern navigation. For instance, the most reliable utilization of GPS in global navigation, the WAAS system, requires no so-called "relativistic corrections" to achieve its metre-level accuracy.
Hence, there is no evidence at the present that either of the Einstein's relativity theories is critical for the operation of the GPS system as used in local (precision) positioning or global navigation.
References
- J.C. Hafele and R. Keating, Science 14 July 1972 177: 166-168
- J.C. Hafele and R. Keating, Science 14 July 1972 177: 168-170
- L Essen, Electron. Wireless World 94 (1988) 238.
- M Omerbashich, J of Air Transportation 2002 7: 103-118, NASA-STI #20020041935