Editing Gravitational redshift (section)

{{Short description|Physical effect in general relativity}}
{{About-distinguish|redshift caused by gravitation|Gravitational wave#Redshifting{{!}}Redshifting of gravitational waves}}
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[[File:Gravitational red-shifting2.png|thumb|200px|The gravitational [[redshift]] of a light wave as it moves upwards against a gravitational field (produced by the yellow star below). The effect is greatly exaggerated in this diagram.]]

In [[physics]] and [[general relativity]], '''gravitational redshift''' (known as '''Einstein shift''' in older literature)<ref>{{cite web|title=Einstein shift definition and meaning {{!}} Collins English Dictionary|url=https://www.collinsdictionary.com/dictionary/english/einstein-shift|access-date=2021-01-21|website=www.collinsdictionary.com|language=en}}</ref><ref name=":4">{{Cite journal|last=Eddington|first=A. S.|date=1926|title=Einstein Shift and Doppler Shift|journal=Nature|language=en|volume=117|issue=2933|pages=86|doi=10.1038/117086a0|bibcode=1926Natur.117...86E|s2cid=4092843|issn=1476-4687|doi-access=free}}</ref> is the phenomenon that [[Electromagnetic radiation|electromagnetic waves]] or [[photon]]s travelling out of a [[gravity well|gravitational well]] lose [[energy]]. This loss of energy corresponds to a decrease in the wave [[frequency]] and increase in the [[wavelength]], known more generally as a ''[[redshift]]''. The opposite effect, in which photons gain energy when travelling into a gravitational well, is known as a '''gravitational blueshift''' (a type of ''[[blueshift]]''). The effect was first described by [[Albert Einstein|Einstein]] in 1907,<ref>{{Cite journal |last=Einstein |first=Albert |date=1907 |title=Relativitätsprinzip und die aus demselben gezogenen Folgerungen |trans-title=On the Relativity Principle and the Conclusions Drawn from It |url=http://www.soso.ch/wissen/hist/SRT/E-1907.pdf |journal=Jahrbuch der Radioaktivität |issue=4 |pages=411–462}}</ref><ref>{{Cite journal|last=Valente|first=Mário Bacelar|date=2018-12-06|title=Einstein's redshift derivations: its history from 1907 to 1921|url=https://revistas.pucsp.br/index.php/circumhc/article/view/36437|journal=Circumscribere: International Journal for the History of Science|language=en|volume=22|pages=1–16|doi=10.23925/1980-7651.2018v22;1-16|s2cid=239568887 |issn=1980-7651|doi-access=free}}</ref> eight years before his publication of [[General relativity|the full theory of relativity]].

Gravitational redshift can be interpreted as a consequence of the [[equivalence principle]] (that gravitational effects are locally equivalent to inertial effects and the redshift is caused by the [[Relativistic Doppler effect|Doppler effect]])<ref name=":1">{{Cite web|last=Florides|first=Petros S.|date=|title=Einstein's Equivalence Principle and the Gravitational Red Shift|url=https://www.maths.tcd.ie/report_series/tcdmath/tcdm1111.pdf|access-date=|website=School of Mathematics, Trinity College, Ireland}}</ref> or as a consequence of the [[mass–energy equivalence]] and conservation of energy ('falling' photons gain energy),<ref>{{Cite journal |last=Chang |first=Donald C. |date=2018 |title=A quantum mechanical interpretation of gravitational redshift of electromagnetic wave |url=https://linkinghub.elsevier.com/retrieve/pii/S0030402618312774 |journal=Optik |language=en |volume=174 |pages=636–641 |doi=10.1016/j.ijleo.2018.08.127|bibcode= |s2cid=126341445 |url-access=subscription }}</ref><ref>{{cite arXiv|last1=Evans|first1=R. F.|last2=Dunning-Davies|first2=J.|date=2004|title=The Gravitational Red-Shift|eprint=gr-qc/0403082}}</ref> though there are numerous subtleties that complicate a rigorous derivation.<ref name=":1" /><ref name=":2">{{Cite conference|last=Scott|first=Robert B|date=2015|title=Teaching the gravitational redshift: lessons from the history and philosophy of physics|journal=Journal of Physics: Conference Series |conference=Spanish Relativity Meeting (ERE 2014)|language=en|volume=600|issue=1|page=012055|doi=10.1088/1742-6596/600/1/012055|bibcode=2015JPhCS.600a2055S|doi-access=free}}</ref> A gravitational redshift can also equivalently be interpreted as [[gravitational time dilation]] at the source of the radiation:<ref name=":2" /><ref name=":4" /> if two [[electronic oscillator|oscillator]]s (attached to [[transmitter]]s producing electromagnetic radiation) are operating at different [[gravitational potential]]s, the oscillator at the higher gravitational potential (farther from the attracting body) will tick faster; that is, when observed from the same location, it will have a higher measured frequency than the oscillator at the lower gravitational potential (closer to the attracting body).

To first approximation, gravitational redshift is proportional to the difference in [[gravitational potential]] divided by the [[speed of light]] squared, <math>z = \Delta U / c^2</math>, thus resulting in a very small effect. Light escaping from the surface of the Sun was predicted by Einstein in 1911 to be redshifted by roughly 2 [[Parts per million|ppm]] or 2 × 10<sup>−6</sup>.<ref name=":0">{{Cite news|last=Gräfe|first=Franziska|date=23 October 2020|title=New study verifies prediction from Einstein's General Theory of Relativity — English|language=en|work=Leibniz Institute for Astrophysics Potsdam|url=https://www.aip.de/en/news/science/new-study-verifies-prediction-from-einsteins-general-theory-of-relativity#:~:text=In%201911,%20Einstein%20predicted%20a,spectrum%20reflected%20by%20the%20moon|access-date=2021-01-14}}</ref> Navigational signals from [[Global Positioning System|GPS satellites]] orbiting at {{val|20,000|u=km}} altitude are perceived blueshifted by approximately 0.5 [[part per billion|ppb]] or 5 × 10<sup>−10</sup>,<ref>{{Cite web|last=Ashby|first=Neil|date=July 20–21, 2006|title=Relativity in the Global Positioning System|url=https://www.aapt.org/doorway/tgrutalks/ashby/AshbyTalk3of6.htm#gravitational%20redshift|access-date=2021-01-14|website=American Association of Physics Teachers}}</ref> corresponding to a (negligible) increase of less than 1&nbsp;Hz in the frequency of a 1.5&nbsp;GHz GPS radio signal (however, the accompanying [[gravitational time dilation]] affecting the atomic clock in the satellite ''is'' crucially important for accurate navigation<ref>{{Cite journal |last=Ashby |first=Neil |date=2003 |title=Relativity in the Global Positioning System |journal=Living Reviews in Relativity |volume=6 |issue=1 |pages=1 |doi=10.12942/lrr-2003-1 |doi-access=free |issn=1433-8351 |pmc=5253894 |pmid=28163638|bibcode=2003LRR.....6....1A }}</ref>). On the surface of the Earth the gravitational potential is proportional to height, <math>\Delta U = g \Delta h</math>, and the corresponding redshift is roughly 10<sup>−16</sup> (0.1 [[parts per quadrillion]]) per meter of change in [[elevation]] and/or [[altitude]].

In [[astronomy]], the magnitude of a gravitational redshift is often expressed as the velocity that would create an equivalent shift through the [[relativistic Doppler effect]]. In such units, the 2 ppm sunlight redshift corresponds to a 633&nbsp;m/s receding velocity, roughly of the same magnitude as convective motions in the Sun, thus complicating the measurement.<ref name=":0" /> The GPS satellite gravitational blueshift velocity equivalent is less than 0.2&nbsp;m/s, which is negligible compared to the actual Doppler shift resulting from its orbital velocity. In astronomical objects with strong gravitational fields the redshift can be much greater; for example, light from the surface of a [[white dwarf]] is gravitationally redshifted on average by around (50&nbsp;km/s)/''c'' (around 170&nbsp;ppm).<ref>{{cite web|last1=Trimble|first1=Virginia|last2=Barstow|first2=Martin|date=November 2020|title=Gravitational redshift and White Dwarf stars|url=https://www.einstein-online.info/en/spotlight/redshift_white_dwarfs/|access-date=2021-01-16|website=[[Einstein Online]]|publisher=[[Max Planck Institute for Gravitational Physics]]|language=en}}</ref>

Observing the gravitational redshift in the [[Solar System]] is one of the [[classical tests of general relativity]].<ref>{{Cite web|last=Alley|first=Carrol Overton|date=|title=GPS Setup Showed General Relativistic Effects on Light Operate at Emission and Reception, Not In-Flight as Required by Big Bang's Friedman-Lemaitre Spacetime Expansion Paradigm|url=http://www.theorionfoundation.com/Proof/gps.pdf|access-date=|website=The Orion Foundation}}</ref> Measuring the gravitational redshift to high precision with [[atomic clock]]s can serve as a test of [[Lorentz covariance|Lorentz symmetry]] and guide searches for [[dark matter]].