Editing Gravitational redshift (section)

=== Terrestrial tests ===
{{For|experiments measuring the slowing of clocks|Gravitational time dilation#Experimental confirmation}}
Between 1925 and 1955, very few attempts were made to measure the gravitational redshift.<ref name=Hentschel-1996>{{Cite journal |last=Hentschel |first=Klaus |date=May 1996 |title=Measurements of gravitational redshift between 1959 and 1971 |url=https://www.tandfonline.com/doi/full/10.1080/00033799600200211 |journal=Annals of Science |language=en |volume=53 |issue=3 |pages=269–295 |doi=10.1080/00033799600200211 |issn=0003-3790}}</ref>
The effect is now considered to have been definitively verified by the experiments of [[Robert Pound|Pound]], Rebka and Snider between 1959 and 1965. The [[Pound–Rebka experiment]] of 1959 measured the gravitational redshift in spectral lines using a terrestrial [[Iron-57|<sup>57</sup>Fe]] [[gamma rays|gamma]] source over a vertical height of 22.5 metres.<ref name="Pound–Rebka">{{cite journal | doi = 10.1103/PhysRevLett.4.337 | title = Apparent Weight of Photons | date = 1960 | last1 = Pound | first1 = R. | last2 = Rebka | first2 = G. | journal = Physical Review Letters | volume = 4 | issue = 7 | pages = 337–341 | bibcode=1960PhRvL...4..337P| doi-access = free }}</ref> This paper was the first determination of the gravitational redshift which used measurements of the change in wavelength of gamma-ray photons generated with the [[Mössbauer effect]], which generates radiation with a very narrow line width. The accuracy of the gamma-ray measurements was typically 1%.

An improved experiment was done by Pound and Snider in 1965, with an accuracy better than the 1% level.<ref>{{cite journal|last=Pound| first=R. V.|author2=Snider J. L. | date= November 2, 1964| title=Effect of Gravity on Nuclear Resonance| journal=[[Physical Review Letters]]| volume = 13 | issue = 18 | pages=539–540 | doi = 10.1103/PhysRevLett.13.539 | bibcode=1964PhRvL..13..539P| doi-access=free}}</ref>

A very accurate gravitational redshift experiment was performed in 1976,<ref>{{cite journal | display-authors=8 | last=Vessot | first= R. F. C.| date= December 29, 1980| title=Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser | journal=Physical Review Letters | volume = 45 | issue = 26 | pages=2081–2084 | doi = 10.1103/PhysRevLett.45.2081 | author2 = M. W. Levine | author3 = E. M. Mattison | author4 = E. L. Blomberg| author5 = T. E. Hoffman | author6 = G. U. Nystrom| author7 = B. F. Farrel | author8 = R. Decher| author9 = P. B. Eby | author10 = C. R. Baugher| author11 = J. W. Watts | author12 = D. L. Teuber | author13 = F. D. Wills | name-list-style = amp | bibcode=1980PhRvL..45.2081V}}</ref> where a [[hydrogen]] [[maser]] clock on a rocket was launched to a height of {{val|10,000|u=km}}, and its rate compared with an identical clock on the ground. It tested the gravitational redshift to 0.007%.

Later tests can be done with the [[Global Positioning System]] (GPS), which must account for the gravitational redshift in its timing system, and physicists have analyzed timing data from the GPS to confirm other tests. When the first satellite was launched, it showed the predicted shift of 38 microseconds per day. This rate of the discrepancy is sufficient to substantially impair the function of GPS within hours if not accounted for. An excellent account of the role played by general relativity in the design of GPS can be found in Ashby 2003.<ref>{{cite journal|title=Relativity in the Global Positioning System|journal=Living Reviews in Relativity|volume=6|issue=1|pages=1|doi=10.12942/lrr-2003-1|pmid=28163638|pmc=5253894|year = 2003|last1 = Ashby|first1 = Neil|doi-access=free |bibcode=2003LRR.....6....1A}}</ref>

In 2010, an experiment placed two aluminum-ion quantum clocks close to each other, but with the second elevated 33&nbsp;cm compared to the first, making the gravitational red shift effect visible in everyday lab scales.<ref>{{cite journal|last1=Chou|first1=C.W.|last2=Hume|first2=D.B.|last3=Rosenband|first3=T.|last4=Wineland|first4=D.J.|title=Optical Clocks and Relativity|journal=Science|year=2010|volume=329|issue=5999|pages=1630–1633|doi=10.1126/science.1192720|pmid=20929843 |bibcode=2010Sci...329.1630C |s2cid=125987464 |url=https://zenodo.org/record/1230910 }}</ref><ref>
{{cite press release
 |url=https://arstechnica.com/science/2010/09/einsteins-relativity-measured-in-newtons-domain/
 |title=Einstein's time dilation apparent when obeying the speed limit
 |publisher=[[Ars Technica]] 
 |date=24 September 2010
 |access-date=2015-04-10
}}</ref>

In 2020, a group at the [[University of Tokyo]] measured the gravitational redshift of two strontium-87 [[optical lattice]] clocks.<ref>{{cite journal |author=Takamoto, M. |author2=Ushijima, I. |author3=Ohmae, N. |display-authors=etal |date=6 April 2020|title=Test of general relativity by a pair of transportable optical lattice clocks|doi=10.1038/s41566-020-0619-8|journal=Nat. Photonics|volume=14|issue=7 |pages=411–415|bibcode=2020NaPho..14..411T |s2cid=216309660 }}</ref> The measurement took place at [[Tokyo Skytree]] where the clocks were separated by approximately 450&nbsp;m and connected by telecom fibers. The gravitational redshift can be expressed as
: <math> z = \frac{\Delta\nu}{\nu_{1}} = (1+\alpha)\frac{\Delta U}{c^2} </math>,
where <math>\Delta\nu=\nu_{2}-\nu_{1}</math> is the gravitational redshift, <math>\nu_{1}</math> is the optical clock transition frequency, <math>\Delta U= U_{2}- U_{1}</math> is the difference in gravitational potential, and <math>\alpha</math> denotes the violation from general relativity. By [[Ramsey interferometry|Ramsey spectroscopy]] of the strontium-87 optical clock transition (429&nbsp;THz, 698&nbsp;nm) the group determined the gravitational redshift between the two optical clocks to be 21.18&nbsp;Hz, corresponding to a ''z''-value of approximately 5 × 10<sup>−14</sup>. Their measured value of <math>\alpha</math>, <math>(1.4 \pm 9.1)\times 10^{-5} </math>, is an agreement with recent measurements made with hydrogen masers in elliptical orbits.<ref>{{cite journal |author=Sven Herrmann |author2=Felix Finke |author3=Martin Lülf |author4=Olga Kichakova |author5=Dirk Puetzfeld |author6=Daniela Knickmann |author7=Meike List |author8=Benny Rievers |author9=Gabriele Giorgi |author10=Christoph Günther |author11=Hansjörg Dittus |author12=Roberto Prieto-Cerdeira |author13=Florian Dilssner |author14=Francisco Gonzalez |author15=Erik Schönemann |author16=Javier Ventura-Traveset |author17=Claus Lämmerzahl|title=Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit |journal=Physical Review Letters |volume=121 |issue=23 |date=December 2018 |page=231102 |doi=10.1103/PhysRevLett.121.231102|pmid=30576165 |arxiv=1812.09161 |bibcode=2018PhRvL.121w1102H |s2cid=58537350 }}</ref><ref>{{cite journal |author=P. Delva |author2=N. Puchades |author3=E. Schönemann |author4=F. Dilssner |author5=C. Courde |author6=S. Bertone |author7=F. Gonzalez |author8=A. Hees |author9=Ch. Le Poncin-Lafitte |author10=F. Meynadier |author11=R. Prieto-Cerdeira |author12=B. Sohet |author13=J. Ventura-Traveset |author14=P. Wolf|title=Gravitational Redshift Test Using Eccentric Galileo Satellites |journal=Physical Review Letters |volume=121 |issue=23 |date=December 2018 |page=231101 |doi=10.1103/PhysRevLett.121.231101|pmid=30576203 |arxiv=1812.03711 |bibcode=2018PhRvL.121w1101D |s2cid=58666075 }}</ref>

In October 2021, a group at [[JILA]] led by physicist [[Jun Ye]] reported a measurement of gravitational redshift in the submillimeter scale. The measurement is done on the <sup>87</sup>Sr clock transition between the top and the bottom of a millimeter-tall ultracold cloud of 100,000 [[strontium]] atoms in an [[optical lattice]].<ref>{{cite journal |last1=Bothwell |first1=Tobias |last2=Kennedy |first2=Colin J. |last3=Aeppli |first3=Alexander |last4=Kedar |first4=Dhruv |last5=Robinson |first5=John M. |last6=Oelker |first6=Eric |last7=Staron |first7=Alexander |last8=Ye |first8=Jun |year=2022 |title=Resolving the gravitational redshift across a millimetre-scale atomic sample |url=https://jila.colorado.edu/sites/default/files/2022-02/Redshift%201%20mm_Nature%202022.pdf |journal=Nature |volume=602 |issue=7897 |pages=420–424 |arxiv=2109.12238 |bibcode=2022Natur.602..420B |doi=10.1038/s41586-021-04349-7 |pmid=35173346 |s2cid=237940816}}</ref><ref>{{Cite web|last=McCormick|first=Katie|date=2021-10-25|title=An Ultra-Precise Clock Shows How to Link the Quantum World With Gravity|url=https://www.quantamagazine.org/an-atomic-clock-promises-link-between-quantum-world-and-gravity-20211025/|access-date=2021-10-29|website=Quanta Magazine|language=en}}</ref>