Editing Fine-structure constant (section)

=== Past rate of change ===
The first experimenters to test whether the fine-structure constant might actually vary examined the [[spectral line]]s of distant astronomical objects and the products of [[radioactive decay]] in the [[Oklo]] [[natural nuclear fission reactor]]. Their findings were consistent with no variation in the fine-structure constant between these two vastly separated locations and times.<ref>
{{cite journal
 |last=Uzan |first=J.-P.
 |year=2003
 |title=The fundamental constants and their variation: Observational status and theoretical motivations
 |journal=[[Reviews of Modern Physics]]
 |volume=75 |issue=2 |pages=403–455
 |arxiv=hep-ph/0205340 |bibcode=2003RvMP...75..403U
 |doi=10.1103/RevModPhys.75.403 |s2cid=118684485
}}</ref><ref>
{{cite journal
 |last=Uzan |first=J.-P.
 |year=2004
 |title=Variation of the constants in the late and early universe
 |journal=[[AIP Conference Proceedings]]
 |volume=736  |pages=3–20
 |arxiv=astro-ph/0409424 |bibcode=2004AIPC..736....3U
 |doi=10.1063/1.1835171 |s2cid=15435796
}}</ref><ref>
{{cite magazine
 |last1=Olive |first1=K.
 |last2=Qian |first2=Y.-Z.
 |year=2003
 |title=Were fundamental constants different in the past?
 |magazine=[[Physics Today]]
 |volume=57 |issue=10 |pages=40–45
 |bibcode=2004PhT....57j..40O
 |doi=10.1063/1.1825267
}}</ref><ref>
{{cite book
 |last=Barrow |first=J.D.
 |year=2002
 |title=The Constants of Nature: From Alpha to Omega – the Numbers That Encode the Deepest Secrets of the Universe
 |publisher=[[Random House|Vintage]]
 |isbn=978-0-09-928647-9
}}</ref><ref>
{{cite book
 |last1=Uzan     |first1=J.-P.
 |last2=Leclercq |first2=B.
 |year=2008
 |title=The Natural Laws of the Universe: Understanding fundamental constants
 |series=Springer-Praxis Books in Popular Astronomy
 |publisher=[[Springer Science+Business Media|Springer Praxis]]
 |isbn=978-0-387-73454-5
 |bibcode=2008nlu..book.....U
}}</ref><ref>
{{cite book
 |last=Fujii  |first=Yasunori
 |year=2004
 |chapter=Oklo constraint on the time-variability of the fine-structure constant
 |title=Astrophysics, Clocks, and Fundamental Constants
 |series=Lecture Notes in Physics
 |volume=648 |pages=167–185
 |isbn=978-3-540-21967-5
 |doi=10.1007/978-3-540-40991-5_11
}}</ref>

Improved technology at the dawn of the 21st century made it possible to probe the value of {{mvar|α}} at much larger distances and to a much greater accuracy. In 1999, a team led by John K. Webb of the [[University of New South Wales]] claimed the first detection of a variation in {{mvar|α}}.<ref>
{{cite journal
 |last1=Webb      |first1=John K.           |last2=Flambaum   |first2=Victor V.
 |last3=Churchill |first3=Christopher W.    |last4=Drinkwater |first4=Michael J.
 |last5=Barrow    |first5=John D.
 |date=February 1999
 |title=Search for time variation of the fine structure constant
 |journal=[[Physical Review Letters]]
 |volume=82 |issue=5 |pages=884–887
 |doi=10.1103/PhysRevLett.82.884 |arxiv=astro-ph/9803165
 |bibcode=1999PhRvL..82..884W |s2cid=55638644
}}</ref><ref>
{{cite journal
 |last1=Murphy    |first1=M.T.       |last2=Webb      |first2=J.K.
 |last3=Flambaum  |first3=V.V.       |last4=Dzuba     |first4=V.A.
 |last5=Churchill |first5=C.W.       |last6=Prochaska |first6=J.X.
 |last7=Barrow    |first7=J.D.       |last8=Wolfe     |first8=A.M.
 |display-authors=6
 |date=11 November 2001
 |title=Possible evidence for a variable fine-structure constant from QSO absorption lines: motivations, analysis and results
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=327 |issue=4 |pages=1208–1222
 |doi=10.1046/j.1365-8711.2001.04840.x |doi-access=free |arxiv=astro-ph/0012419
 |bibcode=2001MNRAS.327.1208M |s2cid=14294586
}}</ref><ref>
{{cite journal
 |last1=Webb      |first1=J.K.       |last2=Murphy    |first2=M.T.
 |last3=Flambaum  |first3=V.V.       |last4=Dzuba     |first4=V.A.
 |last5=Barrow    |first5=J.D.       |last6=Churchill |first6=C.W.
 |last7=Prochaska |first7=J.X.       |last8=Wolfe     |first8=A.M.
 |display-authors=6
 |date=9 August 2001
 |title=Further evidence for cosmological evolution of the fine structure constant
 |journal=[[Physical Review Letters]]
 |volume=87 |issue=9 |page=091301
 |doi=10.1103/PhysRevLett.87.091301 |pmid=11531558
 |arxiv=astro-ph/0012539 |bibcode=2001PhRvL..87i1301W
 |s2cid=40461557
}}</ref><ref>
{{cite journal
 |last1=Murphy   |first1=M.T.
 |last2=Webb     |first2=J.K.
 |last3=Flambaum |first3=V.V.
 |date=October 2003
 |title=Further evidence for a variable fine-structure constant from Keck/HIRES QSO absorption spectra
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=345 |issue=2 |pages=609–638
 |doi=10.1046/j.1365-8711.2003.06970.x |doi-access=free
 |arxiv=astro-ph/0306483
 |bibcode=2003MNRAS.345..609M |s2cid=13182756
}}</ref>
Using the [[Keck telescopes]] and a data set of 128 [[quasar]]s at [[redshift]]s {{math|0.5 < ''z'' < 3}}, Webb ''et al.'' found that their spectra were consistent with a slight increase in {{mvar|α}} over the last 10–12&nbsp;billion years. Specifically, they found that
<math display="block">\frac{\ \Delta \alpha\ }{\alpha} ~~ \overset{\underset{\mathsf{~def~}}{}}{=} ~~ \frac{\ \alpha _\mathrm{prev}-\alpha _\mathrm{now}\ }{\alpha_\mathrm{now}} ~~=~~  \left(-5.7\pm 1.0 \right) \times 10^{-6} ~.</math>

In other words, they measured the value to be somewhere between {{val|−0.0000047}} and {{val|−0.0000067}}. This is a very small value, but the error bars do not actually include zero. This result either indicates that {{mvar|α}} is not constant or that there is experimental error unaccounted for.

In 2004, a smaller study of 23&nbsp;absorption systems by Chand ''et al.'', using the [[Very Large Telescope]], found no measurable variation:<ref>
{{cite journal
 |last1=Chand     |first1=H.       |last2=Srianand |first2=R.
 |last3=Petitjean |first3=P.       |last4=Aracil   |first4=B.
 |date=April 2004
 |title=Probing the cosmological variation of the fine-structure constant: Results based on VLT-UVES sample
 |journal=[[Astronomy & Astrophysics]]
 |volume=417 |issue=3 |pages=853–871
 |doi=10.1051/0004-6361:20035701 |arxiv=astro-ph/0401094
 |bibcode=2004A&A...417..853C |s2cid=17863903
}}</ref><ref>
{{cite journal
 |last1=Srianand |first1=R. |last2=Chand |first2=H.
 |last3=Petitjean |first3=P. |last4=Aracil |first4=B.
 |date=26 March 2004
 |title=Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars
 |journal=[[Physical Review Letters]]
 |volume=92 |issue=12 |pages=121302
 |doi=10.1103/PhysRevLett.92.121302 |pmid=15089663
 |arxiv=astro-ph/0402177 |bibcode=2004PhRvL..92l1302S
 |s2cid=29581666
}}</ref>
<math display="block"> \frac{\Delta \alpha}{\alpha_\mathrm{em}}\ =\ \left(-0.6\pm 0.6\right) \times 10^{-6}~.</math>

However, in 2007 simple flaws were identified in the analysis method of Chand ''et al.'', discrediting those results.<ref>
{{cite journal
 |last1=Murphy   |first1=M.T.
 |last2=Webb     |first2=J.K.
 |last3=Flambaum |first3=V.V.
 |date=6 December 2007
 |title=Comment on 'Limits on the time Variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars'
 |journal=[[Physical Review Letters]]
 |volume=99 |issue=23 |pages=239001
 |doi=10.1103/PhysRevLett.99.239001 |pmid=18233422
 |arxiv=0708.3677 |bibcode=2007PhRvL..99w9001M
 |s2cid=29266168
}}</ref><ref>
{{cite journal
 |last1=Murphy   |first1=M.T.
 |last2=Webb     |first2=J.K.
 |last3=Flambaum |first3=V.V.
 |date=March 2008
 |title=Revision of VLT/UVES constraints on a varying fine-structure constant
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=384 |issue=3 |pages=1053–1062
 |doi=10.1111/j.1365-2966.2007.12695.x |doi-access=free
 |arxiv=astro-ph/0612407
 |bibcode=2008MNRAS.384.1053M |s2cid=10476451
}}</ref>

King ''et al.'' have used [[Markov chain Monte Carlo]] methods to investigate the algorithm used by the UNSW group to determine {{sfrac|{{math|Δ''α''}} | {{mvar|α}} }} from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for {{sfrac|{{math|Δ''α''}} | {{mvar|α}} }} for particular models.<ref>
{{cite journal
 |last1=King |first1=J. A.      |last2=Mortlock |first2=D. J.
 |last3=Webb |first3=J. K.      |last4=Murphy   |first4=M. T.
 |year=2009
 |title=Markov chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy
 |journal=Memorie della Societa Astronomica Italiana
 |volume=80 |pages=864
 |bibcode=2009MmSAI..80..864K
 |arxiv=0910.2699
}}</ref> This suggests that the statistical uncertainties and best estimate for {{sfrac|{{math|Δ''α''}} | {{mvar|α}} }} stated by Webb ''et al.'' and Murphy ''et al.'' are robust.

Lamoreaux and Torgerson analyzed data from the [[Oklo]] [[natural nuclear fission reactor]] in 2004, and concluded that {{mvar|α}} has changed in the past 2&nbsp;billion years by 45&nbsp;parts per billion. They claimed that this finding was "probably accurate to within 20%". Accuracy is dependent on estimates of impurities and temperature in the natural reactor. These conclusions have yet to be verified.<ref>
{{cite book
 |last=Kurzweil |first=R.
 |year=2005
 |title=The Singularity is Near
 |publisher=[[Penguin Group|Viking Penguin]]
 |pages=[https://archive.org/details/singularityisnea00kurz/page/139 139–140]
 |isbn=978-0-670-03384-3
 |title-link=The Singularity Is Near
}}</ref><ref>
{{cite journal
 |last1=Lamoreaux |first1=S. K.
 |last2=Torgerson |first2=J. R.
 |year=2004
 |title=Neutron moderation in the Oklo natural reactor and the time variation of alpha
 |journal=[[Physical Review D]]
 |volume=69 |issue=12 |page=121701
 |doi=10.1103/PhysRevD.69.121701 |arxiv=nucl-th/0309048
 |bibcode=2004PhRvD..69l1701L |s2cid=119337838
}}</ref><ref>
{{cite magazine
 |last=Reich |first=E. S.
 |date=30 June 2004
 |title=Speed of light may have changed recently
 |magazine=[[New Scientist]]
 |url=https://www.newscientist.com/article/dn6092-speed-of-light-may-have-changed-recently.html
 |access-date=30 January 2009
}}</ref><ref>
{{cite news
 |title=Scientists discover one of the constants of the universe might not be constant
 |date=12 May 2005
 |website=[[ScienceDaily]]
 |url=https://www.sciencedaily.com/releases/2005/05/050512120842.htm
 |access-date=30 January 2009
}}</ref>

In 2007, Khatri and [[Benjamin D. Wandelt|Wandelt]] of the University of Illinois at Urbana-Champaign realized that the [[hydrogen line|21&nbsp;cm hyperfine transition in neutral hydrogen]] of the early universe leaves a unique absorption line imprint in the [[cosmic microwave background]] radiation.<ref name=Khatri>
{{cite journal
 |last1=Khatri |first1=Rishi
 |last2=Wandelt |first2=Benjamin D.
 |date=14 March 2007
 |title=21&nbsp;cm radiation: A new probe of variation in the fine-structure constant
 |journal=[[Physical Review Letters]]
 |volume=98 |issue=11 |page=111301
 |doi=10.1103/PhysRevLett.98.111301 |pmid=17501040
 |arxiv=astro-ph/0701752 |bibcode=2007PhRvL..98k1301K
 |s2cid=43502450
}}</ref>
They proposed using this effect to measure the value of {{mvar|α}} during the epoch before the formation of the first stars. In principle, this technique provides enough information to measure a variation of 1&nbsp;part in {{val|e=9}} (4&nbsp;orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on {{mvar|α}} is strongly dependent upon effective integration time, going as {{frac|{{sqrt|{{mvar|t}} }} }}. The European [[Low-Frequency Array (LOFAR)|LOFAR]] [[radio telescope]] would only be able to constrain {{sfrac| {{math|Δ}}{{mvar|α}} | {{mvar|α}} }} to about 0.3%.<ref name=Khatri/> The collecting area required to constrain {{sfrac| {{math|Δ}}{{mvar|α}} | {{mvar|α}} }} to the current level of quasar constraints is on the order of 100&nbsp;square kilometers, which is economically impracticable at present.