Editing Fine-structure constant (section)

== History ==
[[File:Sommerfeld-Muenchen.jpg|thumb|right|upright|Sommerfeld memorial at [[Ludwig Maximilian University of Munich|University of Munich]] ]]
Based on the precise measurement of the hydrogen atom spectrum by [[Albert A. Michelson|Michelson]] and [[Edward W. Morley|Morley]] in 1887,{{efn|
"Among other substances [that were] tried in the preliminary experiments, were thallium, lithium, and hydrogen. ... It may be noted, that in [the] case of the red hydrogen line, the interference phenomena disappeared at about 15,000&nbsp;wave-lengths, and again at about 45,000&nbsp;wave-lengths: So that the red hydrogen line must be a double line with the components about one-sixtieth as distant as the sodium lines."{{refn|
 {{cite journal
  |last1=Michelson |first1=Albert A.  |author1-link=Albert A. Michelson
  |last2=Morley    |first2=Edward W.  |author2-link=Edward W. Morley 
  |year=1887
  |title=Method of making the wave-length of sodium light the actual and practical standard of length
  |journal=[[The American Journal of Science]]
  |volume=34 |issue=204 |pages=427–430
  |url=https://babel.hathitrust.org/cgi/pt?id=coo.31924084352636&view=1up&seq=461
  |series=3rd series
 }} — Article reprinted same year in ''[[the Philosophical Magazine]]''.<ref>
  {{cite journal
   |last1=Michelson |first1=Albert A.  |author1-link=Albert A. Michelson
   |last2=Morley    |first2=Edward W.  |author2-link=Edward W. Morley 
   |year=1887
   |title=Method of making the wave-length of sodium light the actual and practical standard of length
   |journal=[[The Philosophical Magazine]]
   |volume=24 |issue=151 |pages=463–466
   |url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015024088174&view=1up&seq=493
   |series=5th series
   |type=reprint
  }}</ref>
 }}{{rp|style=ama|p=430}}
}} 
[[Arnold Sommerfeld]] extended the [[Bohr model]] to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916.{{efn|
''"Wir fügen den Bohrschen Gleichungen (46) und (47) die charakteristische Konstante unserer Feinstrukturen'' {{nowrap|1=(49) ''&alpha;'' = {{sfrac|2''&pi;e''<sup>2</sup>|''ch''}}}} ''hinzu, die zugleich mit der Kenntnis des Wasserstoffdubletts oder des Heliumtripletts in §10 oder irgend einer analogen Struktur bekannt ist."''<br/>
{{---}}<br/>
(We add, to Bohr's equations (46) and (47), the characteristic constant of our fine structures {{nowrap|1=(49) ''&alpha;'' = {{sfrac|2''&pi;e''<sup>2</sup>|''ch''}}}} which is known at once from knowledge of the hydrogen doublet or the helium triplet in §10 or any analogous structure.)<ref>
 {{cite journal
  |last=Sommerfeld |first=A. |author-link=Arnold Sommerfeld
  |date=1916
  |title=Zur Quantentheorie der Spektrallinien |language=de
  |trans-title=On the quantum theory of spectral lines
  |journal=Annalen der Physik
  |volume=51 |issue=17 |pages=1–94
  |series=4th series
  |doi=10.1002/andp.19163561702
  |bibcode=1916AnP...356....1S
  |url=https://zenodo.org/records/1424309/files/article.pdf
 }}</ref>{{rp|style=ama|p=[https://babel.hathitrust.org/cgi/pt?id=nyp.33433090771183&view=1up&seq=107  91]}}
}}
The first physical interpretation of the fine-structure constant {{mvar|α}} was as the ratio of the velocity of the electron in the first circular orbit of the relativistic [[Bohr atom]] to the [[speed of light]] in the vacuum.<ref>
{{cite web
 |title=Current advances: The fine-structure constant and quantum Hall effect
 |series=Introduction to the Constants for Nonexperts
 |website=The NIST Reference on Constants, Units, and Uncertainty
 |publisher=[[National Institute for Standards and Technology]]
 |url=http://physics.nist.gov/cuu/Constants/alpha.html
 |access-date=11 April 2009
}}</ref>
Equivalently, it was the quotient between the minimum [[angular momentum]] allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfeld's analysis, and determines the size of the splitting or [[fine structure|fine-structure]] of the hydrogenic [[Lyman series|spectral lines]]. This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.<ref name=Kragh-2003/>{{rp|407}}

With the development of [[quantum electrodynamics]] (QED) the significance of {{math|''α''}} has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term {{math|{{sfrac|''α''|2''π''}}}} is engraved on the tombstone of one of the pioneers of QED, [[Julian Schwinger]], referring to his calculation of the [[anomalous magnetic dipole moment]].

=== History of measurements ===
{| class="wikitable"
|+ Successive values determined for the fine-structure constant<ref name="The number 137.035... at MROB">
 {{cite web
  |title = The number 137.035...
  |website=MROB
  |url=https://mrob.com/pub/num/n-b137_035.html
 }}</ref>{{efn|Numbers in parentheses (e.g. the "(11)" appearing at the end of the value "137.035999206(11)") give its [[standard uncertainty]] referred to the least significant preceding digit.}}
! Date
! {{math|''α''}}
! {{math|1/''α''}}
! Sources
|-
| 1969 Jul
| 0.007297351(11)
| 137.03602(21)
| CODATA 1969
|-
| 1973
| 0.0072973461(81)
| 137.03612(15)
| CODATA 1973
|-
| 1987 Jan
| 0.00729735308(33)
| 137.0359895(61)
| CODATA 1986
|-
| 1998
| 0.007297352582(27)
| 137.03599883(51)
| Kinoshita
|-
| 2000 Apr
| 0.007297352533(27)
| 137.03599976(50)
| CODATA 1998
|-
| 2002
| 0.007297352568(24)
| 137.03599911(46)
| CODATA 2002
|-
| 2007 Jul
| 0.0072973525700(52)
| 137.035999070(98)
| Gabrielse (2007)
|-
| 2008 Jun
| 0.0072973525376(50)
| 137.035999679(94)
| CODATA 2006
|-
| 2008 Jul
| 0.0072973525692(27)
| 137.035999084(51)
| Gabrielse (2008), Hanneke (2008)
|-
| 2010 Dec
| 0.0072973525717(48)
| 137.035999037(91)
| Bouchendira (2010)
|-
| 2011 Jun
| 0.0072973525698(24)
| 137.035999074(44)
| CODATA 2010
|-
| 2015 Jun
| 0.0072973525664(17)
| 137.035999139(31)
| CODATA 2014
|-
| 2017 Jul
| 0.0072973525657(18)
| 137.035999150(33)
| Aoyama ''et al''. (2017)<ref name=Aoyama-2018>
 {{cite journal
  |first1=Tatsumi  |last1=Aoyama
  |first2=Toichiro |last2=Kinoshita
  |first3=Makiko   |last3=Nio
  |date=8 February 2018
  |title=Revised and improved value of the QED tenth-order electron anomalous magnetic moment
  |journal=[[Physical Review D]]
  |volume=97 |issue=3 |page=036001
  |doi=10.1103/PhysRevD.97.036001 |arxiv=1712.06060
  |bibcode=2018PhRvD..97c6001A |s2cid=118922814
 }}</ref>
|-
| 2018 Dec
| 0.0072973525713(14)
| 137.035999046(27)
| Parker, Yu, ''et al''. (2018)<ref name="Parker">
 {{cite journal
  |first1=Richard H. |last1=Parker       |first2=Chenghui |last2=Yu
  |first3=Weicheng   |last3=Zhong        |first4=Brian    |last4=Estey
  |first5=Holger     |last5=Müller
  |year=2018
  |title=Measurement of the fine-structure constant as a test of the Standard Model
  |journal=[[Science (journal)|Science]]
  |volume=360 |issue=6385 |pages=191–195
  |doi=10.1126/science.aap7706
  |pmid=29650669 |arxiv=1812.04130 |bibcode=2018Sci...360..191P |s2cid=4875011
 }}</ref>
|-
| 2019 May
| 0.0072973525693(11)
| 137.035999084(21)
| CODATA 2018
|-
| 2020 Dec
| 0.0072973525628(6)<!--Reciprocals of published max/avg/min are ...622014/...627871/...633729, rounded to ...622/628/634-->
| 137.035999206(11)
| Morel ''et al''. (2020)<ref name="morel2020"/>
|-
| 2022 Dec
| 0.0072973525643(11)
| 137.035999206(21) 
| CODATA 2022
|-
| 2023 Feb
| 0.0072973525649(8)
| 137.035999166(15)
| Fan ''et al''. (2023)<ref name=":0" />{{efn|This is not an experimentally measured value; instead it is a value determined ''by the current theory'' from an experimentally determined value of the [[electron magnetic moment]].}}
|}

The CODATA values in the above table are computed by averaging other measurements; they are not independent experiments.