Editing Hafele–Keating experiment (section)

==Overview==
===Kinematic time dilation===
According to [[special relativity]], 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 more slowly, as expressed by the [[Lorentz factor]]. This effect, called [[time dilation]], has been confirmed in many [[tests of special relativity]], such as the [[Ives–Stilwell experiment]] and [[experimental testing of time dilation|others]].<ref>{{cite book |title=Astrophysical Formulae: Space, Time, Matter and Cosmology |edition=3rd, illustrated |first1=Kenneth |last1=Lang |publisher=Springer |year=2013 |isbn=978-3-662-21639-2 |page=152 |url=https://books.google.com/books?id=Nq_1CAAAQBAJ}} [https://books.google.com/books?id=Nq_1CAAAQBAJ&pg=PA152 Extract of page 152]</ref> Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the Earth (because this is an inertial frame<ref>{{cite book |title=Relativity in Rotating Frames: Relativistic Physics in Rotating Reference Frames |edition=illustrated |first1=Guido |last1=Rizzi |first2=Matteo Luca |last2=Ruggiero |publisher=Springer Science & Business Media |year=2003 |isbn=978-1-4020-1805-3 |page=25 |url=https://books.google.com/books?id=DH7jEf48KjgC}} [https://books.google.com/books?id=DH7jEf48KjgC&pg=PA25 Extract of page 25]</ref>), a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground.<ref name="donkoks">{{cite book |title=Explorations in Mathematical Physics: The Concepts Behind an Elegant Language |edition=illustrated |first1=Don |last1=Koks |publisher=Springer Science & Business Media |year=2006 |isbn=978-0-387-30943-9 |page=500 |url=https://books.google.com/books?id=ytTFazXPy6oC}} [https://books.google.com/books?id=ytTFazXPy6oC&pg=PA500 Extract of page 500]</ref>

===Gravitational time dilation===
{{main|Gravitational time dilation}}
[[General relativity]] predicts an additional effect, in which an increase in gravitational potential due to altitude speeds the clocks up. That is, clocks at higher altitude tick faster than clocks on Earth's surface. This effect has been confirmed in many [[tests of general relativity]], such as the [[Pound–Rebka experiment]] and [[Gravity Probe A]]. In the Hafele–Keating experiment, there was a slight increase in gravitational potential due to altitude that tended to speed the clocks back up. Since the aircraft flew at roughly the same altitude in both directions, this effect was approximately the same for the two planes, but nevertheless it caused a difference in comparison to the clocks on the ground.<ref name="donkoks" />

===Results===
The results were published in ''[[Science (journal)|Science]]'' in 1972:<ref name=paper1>{{Cite journal | last1 = Hafele | first1 = J. C. | author-link1 = Joseph C. Hafele | last2 = Keating | first2 = R. E. | author-link2 = Richard E. Keating | doi = 10.1126/science.177.4044.166 | title = Around-the-World Atomic Clocks: Predicted Relativistic Time Gains | journal = [[Science (journal)|Science]] | volume = 177 | issue = 4044 | pages = 166–168 | date = July 14, 1972 | pmid = 17779917 | bibcode = 1972Sci...177..166H | s2cid = 10067969 | ref = {{harvid|Hafele|Keating|1972a}} | url = http://www.personal.psu.edu/rq9/HOW/Atomic_Clocks_Predictions.pdf | access-date = March 30, 2017 | archive-date = March 31, 2017 | archive-url = https://web.archive.org/web/20170331121014/http://www.personal.psu.edu/rq9/HOW/Atomic_Clocks_Predictions.pdf | url-status = dead }}</ref><ref name=paper2>{{Cite journal | last1 = Hafele | first1 = J. C. | author-link1 = Joseph C. Hafele | last2 = Keating | first2 = R. E. | author-link2 = Richard E. Keating | doi = 10.1126/science.177.4044.168 | title = Around-the-World Atomic Clocks: Observed Relativistic Time Gains | journal = Science | volume = 177 | issue = 4044 | pages = 168–170 | date = July 14, 1972 | pmid = 17779918 | bibcode = 1972Sci...177..168H | s2cid = 37376002 | ref = {{harvid|Hafele|Keating|1972b}} | url = http://www.personal.psu.edu/rq9/HOW/Atomic_Clocks_Experiment.pdf | access-date = March 30, 2017 | archive-date = March 31, 2017 | archive-url = https://web.archive.org/web/20170331121107/http://www.personal.psu.edu/rq9/HOW/Atomic_Clocks_Experiment.pdf | url-status = dead }}</ref>

{| class="wikitable" style="text-align: center"
| rowspan=2 | 
! colspan=3 | [[nanoseconds]] gained, predicted
! rowspan=2 | nanoseconds<br/>gained,<br />measured 
! rowspan=2 | difference
|- 
! gravitational
([[general relativity]])
! kinematic
([[special relativity]])
! total 
|- 
! eastward
| +144 ±14
| −184 ±18
| −40 ±23
| −59 ±10
| {{#expr:(-40 - -59)/sqrt(23*23 + 10*10) round 2}} σ
|- 
! westward
| +179 ±18
| +96 ±10
| +275 ±21
| +273 ±7
| {{#expr:(275 - 273)/sqrt(21*21 + 7*7) round 2}} σ
|}

The published outcome of the experiment was consistent with both special and general relativity. The observed time gains and losses were in agreement with relativistic predictions to within the ~10% precision expected of the experiment.<ref>{{cite book |title=Fundamentals of Physics, Part 4 |edition=7th, illustrated |first1=David |last1=Halliday |first2=Robert |last2=Resnick |first3=JearlWalker |last3=Walker |publisher=Wiley |year=2004 |isbn=978-0-471-42964-7 |page=1030 |url=https://archive.org/details/fundamentalsofph0000hall|url-access=registration }}</ref>