Editing Fine-structure constant (section)

== Measurement ==
[[File:EighthOrderMagMoment.svg|frame|right|Eighth-[[Perturbation theory|order]] [[Feynman diagrams]] on electron self-interaction. The arrowed horizontal line represents the electron, the wavy lines are virtual photons, and the circles are virtual [[electron]]–[[positron]] pairs.]]
The [[CODATA]] recommended value of {{math|''α''}} is{{physconst|alpha|ref=only}}
{{block indent|{{math|1=''α'' = {{sfrac|''e''{{sup|2}}| 4''πε''{{sub|0}}''ħc''}}}} {{=}} {{physconst|alpha|ref=no}}.}} This has a relative standard uncertainty of {{physconst|alpha|runc=yes|after=.}}

This value for {{math|''α''}} gives {{nowrap|1={{mvar|µ}}{{sub|0}} = 4''π'' × {{val|0.99999999987|(16)|e=-7|u=H.m-1}}}}, 0.8 times the standard uncertainty away from its old defined value, with the mean differing from the old value by only 0.13&nbsp;[[parts per billion]].

Historically the value of the [[multiplicative inverse|reciprocal]] of the fine-structure constant is often given. The [[CODATA]] recommended value is {{physconst|alphainv|ref=only}}
{{block indent|{{math|{{sfrac|1|''α''}}}} {{=}} {{physconst|alphainv|ref=no}}.}}

While the value of {{mvar|α}} can be determined from estimates of the constants that appear in any of its definitions, the theory of [[quantum electrodynamics]] (QED) provides a way to measure {{mvar|α}} directly using the [[quantum Hall effect]] or the [[anomalous magnetic moment]] of the [[electron]].<ref name=":0">
{{cite journal |last1=Fan |first1=X. |last2=Myers |first2=T. G. |last3=Sukra |first3=B. A. D. |last4=Gabrielse |first4=G. |date=2023-02-13 |title=Measurement of the Electron Magnetic Moment |url=https://link.aps.org/doi/10.1103/PhysRevLett.130.071801 |journal=Physical Review Letters |volume=130 |issue=7 |pages=071801 |doi=10.1103/PhysRevLett.130.071801|pmid=36867820 |arxiv=2209.13084
|bibcode=2023PhRvL.130g1801F }}</ref> Other methods include the A.C. Josephson effect and photon recoil in atom interferometry.<ref name=Yu2019>
{{cite journal
 |last1=Yu     |first1=C.         |last2=Zhong  |first2=W.
 |last3=Estey  |first3=B.         |last4=Kwan   |first4=J.
 |last5=Parker |first5=R.H.       |last6=Müller |first6=H.
 |year=2019
 |title=Atom-interferometry measurement of the fine structure constant
 |journal=Annalen der Physik
 |volume=531  |issue=5  |page=1800346
 |doi=10.1002/andp.201800346 |doi-access=free 
 |bibcode=2019AnP...53100346Y
}}</ref>
There is general agreement for the value of {{mvar|α}}, as measured by these different methods. The preferred methods in 2019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry.<ref name=Yu2019/> The theory of QED predicts a relationship between the [[g-factor (physics)|dimensionless magnetic moment]] of the [[electron]] and the fine-structure constant {{mvar|α}} (the magnetic moment of the electron is also referred to as the [[g-factor (physics)|electron {{mvar|g}}-factor]] {{math|''g''<sub>e</sub>}}). One of the most precise values of {{mvar|α}} obtained experimentally (as of 2023) is based on a measurement of {{math|''g''<sub>e</sub>}} using a one-electron so-called "quantum cyclotron" apparatus,<ref name=":0" /> together with a calculation via the theory of QED that involved {{val|12672}} tenth-order [[Feynman diagrams]]:<ref name=Aoyama12>
{{cite journal
 |last1=Aoyama |first1=T. |last2=Hayakawa |first2=M.
 |last3=Kinoshita |first3=T. |last4=Nio |first4=M.
 |year=2012
 |title=Tenth-order QED contribution to the electron {{nowrap|''g'' − 2}} and an improved value of the fine structure constant
 |journal=[[Physical Review Letters]]
 |volume=109 |issue=11 |page=111807
 |arxiv=1205.5368 |bibcode=2012PhRvL.109k1807A
 |doi=10.1103/PhysRevLett.109.111807 |pmid=23005618
 |s2cid=14712017
}}
</ref>
{{block indent|{{math|{{sfrac|1|''α''}}}} {{=}} {{val|137.035999166|(15)}}.}}

This measurement of {{mvar|α}} has a relative standard uncertainty of {{val|1.1|e=-10}}. This value and uncertainty are about the same as the latest experimental results.<ref>
{{cite journal
 |last1=Bouchendira |first1=Rym          |last2=Cladé |first2=Pierre
 |last3=Guellati-Khélifa |first3=Saïda   |last4=Nez   |first4=François
 |last5=Biraben     |first5=François
 |year=2011
 |title=New determination of the fine-structure constant and test of the quantum electrodynamics
 |journal=[[Physical Review Letters]]
 |volume=106  |issue=8  |page=080801
 |arxiv=1012.3627  |bibcode=2011PhRvL.106h0801B
 |doi=10.1103/PhysRevLett.106.080801 |pmid=21405559
 |s2cid=47470092
 |type=Submitted manuscript
 |url=https://hal.archives-ouvertes.fr/hal-00547525/file/MesureAlpha2010.pdf |archive-url=https://web.archive.org/web/20181104125931/https://hal.archives-ouvertes.fr/hal-00547525/file/MesureAlpha2010.pdf |archive-date=2018-11-04 |url-status=live
}}</ref>

Further refinement of the experimental value was published by the end of 2020, giving the value
{{block indent|{{math|{{sfrac|1|''α''}}}} {{=}} {{val|137.035999206|(11)}},}}
with a relative accuracy of {{val|8.1|e=-11}}, which has a significant discrepancy from the previous experimental value.<ref name="morel2020">
{{cite journal
 |author1=Morel, Léo     |author2=Yao, Zhibin 
 |author3=Cladé, Pierre  |author4=Guellati-Khélifa, Saïda 
 |title=Determination of the fine-structure constant with an accuracy of 81&nbsp;parts per trillion
 |journal=[[Nature (journal)|Nature]]
 |volume=588 |pages=61–65
 |year=2020
 |issue=7836 
 |doi=10.1038/s41586-020-2964-7
 |pmid=33268866 
 |bibcode=2020Natur.588...61M 
 |s2cid=227259475 
 |url=https://hal.archives-ouvertes.fr/hal-03107990/file/main.pdf 
}}</ref>