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{{Use dmy dates|date=July 2013}}
{{Quantum field theory}}
In [[physics]], the '''fine-structure constant''', also known as '''Sommerfeld's constant''', commonly denoted by {{math|''α''}} (the [[Alpha|Greek letter ''alpha'']]), is a [[fundamental physical constant]] characterizing the strength of the [[electromagnetic interaction]] between elementary charged particles. It is a [[dimensionless quantity]] related to the [[elementary charge]] {{math|''e''}}, which characterizes the strength of the coupling of an elementary charged particle with the [[electromagnetic field]], by the formula {{math|1=4π''ε''<sub>0</sub>''ħcα'' = ''e''<sup>2</sup>}}.  As a [[dimensionless quantity]], it has the same [[numerical value]] whatever [[system of units]] is being used, which is nearly {{sfrac|137}}. <ref name="CODATA 2018 inverse">
{{cite web
|last1=Mohr |first1=P. J.
|last2=Taylor |first2=B. N.
|last3=Newell |first3=D. B.
|year=2019
|title=Inverse fine structure constant
|work=CODATA Internationally recommended 2018 values of the fundamental physical constants
|url=https://physics.nist.gov/cgi-bin/cuu/Value?alphinv
|publisher=[[National Institute of Standards and Technology]]
|access-date=2019-05-20
}}</ref>

While there are multiple [[Fine-structure_constant#Physical_interpretations|physical interpretations]] for {{math|''α''}}, it received its name from [[Arnold Sommerfeld]] introducing it (1916) in extending the [[Bohr model]] of the atom: {{math|''α''}} quantifies the gap in the [[fine structure]] of the [[spectral lines]] of the hydrogen atom, which had been precisely measured by [[Albert A. Michelson|Michelson]] and [[Edward W. Morley|Morley]].<ref>As {{math|''α''}} is the [[coupling constant]] for the electromagnetic force, there is an analogous constant  parameterizing the interaction strength of the [[nuclear strong force]], known as {{math|''α''}}<sub>s</sub> (≈1), and further the [[gravitational coupling constant]] {{math|''α''}}<sub>G</sub> (≈ {{val|1.75|e=-45}}, which is the square of the [[electron mass]], expressed in [[Planck units]]).  The much larger value of {{math|''α''}} and {{math|''α''}}<sub>s</sub> in comparison to {{math|''α''}}<sub>G</sub> indicates that gravity is by far the weakest of the forces.</ref>

==Definition==
Some equivalent definitions of {{math|''α''}} in terms of other fundamental [[physical constant]]s are:
:<math>\alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar} = \frac{k_\text{e} e^2}{\hbar c} = \frac{c \mu_0}{2 R_\text{K}} = \frac{e^2}{4 \pi}\frac{Z_0}{\hbar}</math>

where:
*{{math|''e''}} is the [[elementary charge]] (:= {{val|1.602176634|e=-19|u=C}});
*{{math|π}} is the mathematical constant [[pi]];
*{{math|''ħ'' {{=}} {{sfrac|''h''|2π}}}} is the reduced [[Planck constant]] (:= {{sfrac|{{val|6.62607015|e=-34|u=J.s}}|2π}});
*{{math|''c''}} is the [[speed of light in vacuum]] (:= {{val|299792458|u=m/s}});
*{{math|''ε''<sub>0</sub>}} is the [[electric constant]] or permittivity of free space;
*{{math|''µ''<sub>0</sub>}} is the [[magnetic constant]] or permeability of free space;
*{{math|''k''<sub>e</sub>}} is the [[Coulomb constant]];
*{{math|''R''<sub>K</sub>}} is the [[von Klitzing constant]];
*{{math|''Z''<sub>0</sub>}} is the [[vacuum impedance]] or impedance of free space.

The definition reflects the relationship between {{math|''α''}} and the permeability of free space {{math|''µ''<sub>0</sub>}}, which equals {{math|1=''µ''<sub>0</sub> = {{sfrac|2''h&alpha;''|''ce''<sup>2</sup>}}}}.
In the [[2019 redefinition of SI base units]], 4{{pi}}&nbsp;×&nbsp;{{val|1.00000000082|(20)|e=-7|u=H.m-1}} is the value for {{math|''µ''<sub>0</sub>}} based upon more accurate measurements of the fine structure constant.<ref>{{Cite web|url=https://www.bipm.org/utils/en/pdf/CGPM/Convocation-2018.pdf#page=30|title=Convocationde la Conférence générale des poids et mesures (26e réunion)}}</ref><ref>{{Cite journal|last=Parker|first=Richard H.|last2=Yu|first2=Chenghui|last3=Zhong|first3=Weicheng|last4=Estey|first4=Brian|last5=Müller|first5=Holger|date=2018-04-13|title=Measurement of the fine-structure constant as a test of the Standard Model|journal=Science|language=en|volume=360|issue=6385|pages=191–195|doi=10.1126/science.aap7706|issn=0036-8075|pmid=29650669|bibcode=2018Sci...360..191P|arxiv=1812.04130}}</ref><ref>{{Cite journal|last=Davis|first=Richard S.|date=2017|title=Determining the value of the fine-structure constant from a current balance: Getting acquainted with some upcoming changes to the SI|journal=American Journal of Physics|language=en|volume=85|issue=5|pages=364–368|doi=10.1119/1.4976701|issn=0002-9505|bibcode=2017AmJPh..85..364D|arxiv=1610.02910}}</ref>

===In non-SI units===
In electrostatic [[cgs]] units, the unit of [[electric charge]], the [[statcoulomb]], is defined so that the [[Coulomb's law|Coulomb constant]], {{math|''k''<sub>e</sub>}}, or the [[electric constant|permittivity factor]], {{math|4π''ε''<sub>0</sub>}}, is 1 and [[dimensionless]]. Then the expression of the fine-structure constant, as commonly found in older physics literature, becomes
:<math>\alpha = \frac{e^2}{\hbar c}. </math>

In [[natural units]], commonly used in high energy physics, where {{math|1=''ε''<sub>0</sub> = ''c'' = ''ħ'' = 1}}, the value of the fine-structure constant is<ref>
{{cite book
|last=Peskin |first=M.
|last2=Schroeder |first2=D.
|year=1995
|title=An Introduction to Quantum Field Theory
|page=125
|publisher=[[Westview Press]]
|isbn=978-0-201-50397-5
}}</ref>
:<math> \alpha = \frac{e^2}{4 \pi}. </math>
As such, the fine-structure constant is just another, albeit dimensionless, quantity determining (or determined by) the [[elementary charge]]: {{math|1=''e'' = {{radic|4π''α''}} ≈ {{val|0.30282212}}}} in terms of such a natural unit of charge.

In [[atomic units]] ({{math|1=''e'' = ''m''<sub>e</sub> = ''ħ'' = 1}} and {{math|''ε''<sub>0</sub> {{=}} {{sfrac|1|4π}}}}), the fine structure constant is
:<math>\alpha = \frac{1}{c}. </math>

==Measurement==
[[File:EighthOrderMagMoment.svg|frame|right|Two example eighth-[[Perturbation theory|order]] [[Feynman diagrams]] that contribute to the electron self-interaction. The horizontal line with an arrow represents the electron while the wavy lines are virtual photons, and the circles represent virtual [[electron]]–[[positron]] pairs.]]
The 2018 [[CODATA]] recommended value of {{math|''α''}} is<ref name="CODATA 2018">
{{cite web
|last1=Mohr |first1=P. J.
|last2=Taylor |first2=B. N.
|last3=Newell |first3=D. B.
|year=2019
|title=Fine structure constant
|work=CODATA Internationally recommended 2018 values of the fundamental physical constants
|url=https://physics.nist.gov/cgi-bin/cuu/Value?alph
|publisher=[[National Institute of Standards and Technology]]
}}</ref>
:{{math|''α'' {{=}} {{sfrac|''e''<sup>2</sup>|4π''ε''<sub>0</sub>''ħc''}} {{=}} {{val|0.0072973525693|(11)}}.}}
This has a relative standard uncertainty of 0.15&nbsp;[[parts per billion]].<ref name="CODATA 2018"/>

For reasons of convenience, historically the value of the [[multiplicative inverse|reciprocal]] of the fine-structure constant is often specified. The 2018 CODATA recommended value is given by<ref name="CODATA 2018 inverse"/>
:{{math|''α''<sup>−1</sup> {{=}} {{val|137.035999084|(21)}}.}}

While the value of {{math|''α''}} can be ''estimated'' from the values of the constants appearing in any of its definitions, the theory of [[quantum electrodynamics]] (QED) provides a way to measure {{math|''α''}} directly using the [[quantum Hall effect]] or the [[anomalous magnetic moment]] of the [[electron]]. The theory of QED predicts a relationship between the [[g-factor (physics)|dimensionless magnetic moment]] of the [[electron]] and the fine-structure constant {{math|''α''}} (the magnetic moment of the electron is also referred to as "[[Landé g-factor|Landé {{math|''g''}}-factor]]" and symbolized as {{math|''g''}}). The most precise value of {{math|''α''}} obtained experimentally (as of 2012) is based on a measurement of {{math|''g''}} using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved {{val|12672}} tenth-order [[Feynman diagrams]]:<ref>
{{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 ''g''&nbsp;-&minus;&nbsp;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
}}</ref>
:{{math|''α''<sup>−1</sup> {{=}} {{val|137.035999174|(35)}}.}}

This measurement of {{math|''α''}} has a relative standard uncertainty of {{val|2.5|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 |pages=080801
|arxiv=1012.3627
|bibcode=2011PhRvL.106h0801B
|doi=10.1103/PhysRevLett.106.080801
|pmid=21405559
|url=https://hal.archives-ouvertes.fr/hal-00547525/file/MesureAlpha2010.pdf
|type=Submitted manuscript
}}</ref>

==Physical interpretations==
The fine-structure constant, {{math|''α''}}, has several physical interpretations. {{math|''α''}} is:
*The square of the ratio of the [[elementary charge]] to the [[Planck charge]]
:<math>\alpha = \left( \frac{e}{q_\text{P}} \right)^2.</math>
*The ratio of two energies: (i) the energy needed to overcome the [[electrostatic repulsion]] between two electrons a distance of {{math|''d''}} apart, and (ii) the energy of a single [[photon]] of wavelength {{math|''λ'' {{=}} 2π''d''}} (or of [[wavelength#Angular wavelength|angular wavelength]] {{math|''d''}}; see [[Planck relation]]):
:<math>\alpha = \left. \frac{e^2}{4 \pi \varepsilon_0 d} \right/ \frac{h c}{\lambda} = \frac{e^2}{4 \pi \varepsilon_0 d} \times {\frac{2 \pi d}{h c}} = \frac{e^2}{4 \pi \varepsilon_0 d} \times {\frac{d}{\hbar c}} = \frac{e^2}{4 \pi \varepsilon_0 \hbar c}.</math>
*The ratio of the velocity of the electron in the first circular orbit of the [[Bohr model of the atom]], which is {{math|{{sfrac|1|4π''ε''<sub>0</sub>}} {{sfrac|''e''<sup>2</sup>|''ħ''}}}} to the [[speed of light]] in vacuum, {{math|''c''}}.<ref>[[NIST]] [http://physics.nist.gov/cuu/ Reference on Constants, Units, and Uncertainty] [http://physics.nist.gov/cuu/Constants/alpha.html Current advances: The fine-structure constant and quantum Hall effect]</ref> This is [[Arnold Sommerfeld|Sommerfeld]]'s original physical interpretation. Then the square of {{math|''α''}} is the ratio between the [[Hartree energy]] ({{nowrap|27.2 eV {{=}} twice the [[Rydberg constant|Rydberg energy]]}} {{=}} approximately twice its ionization energy) and the [[electron]] [[rest energy]] (511&nbsp;keV).
*The two ratios of three characteristic lengths: the [[classical electron radius]] {{math|''r''<sub>e</sub>}}, the [[Compton wavelength]] of the electron {{math|''λ''<sub>e</sub>}}, and the [[Bohr radius]] {{math|''a''<sub>0</sub>}}:
:<math>r_\text{e} = \frac{\alpha \lambda_\text{e}}{2\pi} = \alpha^2 a_0</math>
*In [[quantum electrodynamics]], {{math|''α''}} is directly related to the [[coupling constant]] determining the strength of the interaction between [[electron]]s and [[photon]]s.<ref>{{cite book|last1=Riazuddin|first1=Fayyazuddin|title=A Modern Introduction to Particle Physics|publisher=World Scientific|pages=4|edition=Third|url=https://books.google.com/?id=dbysnBTHF4QC&printsec=frontcover#v=onepage&q&f=false|accessdate=20 April 2017|isbn=9789814338837|year=2012}}</ref> The theory does not predict its value. Therefore, {{math|''α''}} must be determined experimentally. In fact, {{math|''α''}} is one of about 20 empirical [[Standard Model#Theoretical aspects|parameters in the Standard Model]] of [[particle physics]], whose value is not determined within the Standard Model.
*In the [[electroweak theory]] unifying the [[weak interaction]] with [[electromagnetism]], {{math|''α''}} is absorbed into two other [[coupling constant]]s associated with the electroweak [[gauge theory|gauge fields]]. In this theory, the [[electromagnetic interaction]] is treated as a mixture of interactions associated with the electroweak fields. The strength of the [[electromagnetic interaction]] varies with the strength of the [[energy]] field.
*Given two hypothetical point particles each of [[Planck mass]] and elementary charge, separated by any distance, {{math|''α''}} is the ratio of their electrostatic repulsive force to their gravitational attractive force.
*In the fields of [[electrical engineering]] and [[solid-state physics]], the fine-structure constant is one fourth the product of the characteristic [[impedance of free space]], {{math|1=''Z''<sub>0</sub> = ''μ''<sub>0</sub>''c''}}, and the [[conductance quantum]], {{math|1=''G''<sub>0</sub> = {{sfrac|2''e''<sup>2</sup>|''h''}}}}:
:<math>\alpha = \tfrac{1}{4} Z_0 G_0</math>.
:The [[optical conductivity]] of [[graphene]] for visible frequencies is theoretically given by {{math|{{sfrac|π''G''<sub>0</sub>|4}}}}, and as a result its light absorption and transmission properties can be expressed in terms of the fine structure constant alone.<ref name="NairBlake2008">{{cite journal |last1=Nair |first1=R. R. |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. |year=2008 |title=Fine Structure Constant Defines Visual Transparency of Graphene |journal=[[Science (journal)|Science]] |volume=320 |issue=5881 |pages=1308 |bibcode=2008Sci...320.1308N |doi=10.1126/science.1156965 |pmid=18388259|arxiv=0803.3718 }}</ref> The absorption value for normal-incident light on graphene in vacuum would then be given by {{math|{{sfrac|''πα''|(1 + ''πα''/2)<sup>2</sup>}}}} or 2.24%, and the transmission by {{math|{{sfrac|1|(1 + ''πα''/2)<sup>2</sup>}}}} or 97.75% (experimentally observed to be between 97.6% and 97.8%).
*The fine-structure constant gives the maximum positive charge of an atomic nucleus that will allow a stable electron-orbit around it within the Bohr model (element [[feynmanium]]).<ref>{{cite web |title=On Stars, Their Evolution and Their Stability |date=8 December 1983 |author=Subrahmanyan Chandrasekhar |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1983/chandrasekhar-lecture.pdf}}</ref> For an electron orbiting an atomic nucleus with atomic number {{math|''Z''}}, {{math|{{sfrac|''mv''<sup>2</sup>|''r''}} {{=}} {{sfrac|1|4''πε''<sub>0</sub>}} {{sfrac|''Ze''<sup>2</sup>|''r''<sup>2</sup>}}}}. The Heisenberg [[uncertainty principle]] momentum/position uncertainty relationship of such an electron is just {{math|''mvr'' {{=}} ''ħ''}}. The relativistic limiting value for {{math|''v''}} is {{math|''c''}}, and so the limiting value for {{math|''Z''}} is the reciprocal of the fine-structure constant, 137.<ref>{{cite journal |last1=Bedford |first1=D. |last2=Krumm |first2=P. |title=Heisenberg indeterminacy and the fine structure constant |journal=[[American Journal of Physics]] |date=2004 |volume=72 |issue=7 |pages=969 |doi=10.1119/1.1646135|bibcode=2004AmJPh..72..969B}}</ref>
*The magnetic moment of the electron indicates that the charge is circulating at a radius {{math|''r<sub>Q</sub>''}} with the velocity of light.<ref>{{cite arXiv |last=Poelz |first=G. |date=5 Oct 2016 |title=An Electron Model with Synchrotron Radiation |eprint=1206.0620v24|class=physics.class-ph}}</ref> It generates the radiation energy {{math|''m''<sub>e</sub>''c''<sup>2</sup>}} and has an angular momentum {{math|1=''L'' = 1 ħ = ''r<sub>Q</sub>m''<sub>e</sub>''c''}}. The field energy of the stationary Coulomb field is {{math|''m''<sub>e</sub>''c''<sup>2</sup> {{=}} {{sfrac|''e''<sup>2</sup>|4π''ε''<sub>0</sub>''r''<sub>e</sub>}}}} and defines the classical electron radius {{math|''r''<sub>e</sub>}}. These values inserted into the definition of alpha yields {{math|''α'' {{=}} {{sfrac|''r''<sub>e</sub>|''r<sub>Q</sub>''}}}}. It compares the dynamic structure of the electron with the classical static assumption.
*Alpha is related to the probability that an electron will emit or absorb a photon.<ref>[[Leon M. Lederman|Lederman, Leon]], ''The God Particle: If the Universe is the Answer, What is the Question?'' (1993), [[Houghton Mifflin Harcourt]], pp. 28-29.</ref>

When [[perturbation theory (quantum mechanics)|perturbation theory]] is applied to [[quantum electrodynamics]], the resulting [[perturbative]] expansions for physical results are expressed as sets of [[power series]] in {{math|''α''}}. Because {{math|''α''}} is much less than one, higher powers of {{math|''α''}} are soon unimportant, making the perturbation theory practical in this case. On the other hand, the large value of the corresponding factors in [[quantum chromodynamics]] makes calculations involving the [[strong nuclear force]] extremely difficult.

==Variation with energy scale==
In [[quantum electrodynamics]], the more thorough quantum field theory underlying the electromagnetic coupling,  the [[renormalization group]]  dictates how the strength of the electromagnetic interaction grows [[logarithm]]ically as the relevant [[energy scale]] increases. The value of the fine-structure constant  {{math|''α''}} is linked to the observed value  of this coupling associated with the energy scale of the [[electron mass]]: the electron is a lower bound for this energy scale, because it (and the [[positron]]) is the lightest charged object whose [[Quantum_electrodynamics#Renormalizability|quantum loops]] can contribute to the running. Therefore, {{sfrac|1|137.036}} is the asymptotic value of the fine-structure constant at zero energy. 
At higher energies, such as the scale of the [[Z boson]], about 90&nbsp;[[GeV]], one measures an ''effective'' {{nowrap|''α'' ≈ 1/127}}, [[Coupling_constant#QED_and_the_Landau_pole |instead]].

As the energy scale increases, the strength of the electromagnetic interaction  in the [[Standard Model]] approaches that of the other two [[fundamental interaction]]s, a feature important for [[grand unification]] theories. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the [[Landau pole]]—this fact  undermines the consistency of quantum electrodynamics  beyond  [[perturbative]] expansions.

==History==
[[File:Sommerfeld-Muenchen.jpg|thumb|right|upright|[[Arnold Sommerfeld|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]],<ref>AA. Michelson and E. W. Morley, Amer. J. Sci.34, 427 (1887); Phil Mag. 24, 463 (1887)</ref> [[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.<ref>Sommerfeld, Arnold (1919). "Atombau und Spektrallinien". Braunschweig: Friedrich Vieweg und Sohn. {{ISBN|3-87144-484-7}}.</ref> The first physical interpretation of the fine-structure constant {{math|''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=Introduction to the Constants for Nonexperts – Current Advances: The Fine-Structure Constant and Quantum Hall Effect
|url=http://physics.nist.gov/cuu/Constants/alpha.html
|work=The NIST Reference on Constants, Units, and Uncertainty
|publisher=[[NIST]]
|accessdate=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]].

With the development of [[quantum electrodynamics]] (QED) the significance of 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''|2π}}}} is engraved on the tombstone of one of the pioneers of QED, [[Julian Schwinger]], referring to his calculation of the [[anomalous magnetic dipole moment]].

==Is the fine-structure constant actually constant?==
{{Further|Time-variation of physical constants}}
Physicists have pondered whether the fine-structure constant is in fact constant, or whether its value differs by location and over time. A varying {{math|''α''}} has been proposed as a way of solving problems in [[physical cosmology|cosmology]] and [[astrophysics]].<ref>
{{cite book
|last=Milne |first=E. A.
|year=1935
|title=Relativity, Gravitation and World Structure
|publisher=[[Clarendon Press]]
|pages=
|isbn=
|lccn=
|oclc=
}}</ref><ref>
{{cite journal
|last=Dirac |first=P. A. M.
|year=1937
|title=The Cosmological Constants
|journal=[[Nature (journal)|Nature]]
|volume=139 |issue=3512 |page=323
|bibcode=1937Natur.139..323D
|doi=10.1038/139323a0
}}</ref><ref>
{{cite journal
|last=Gamow |first=G.
|year=1967
|title=Electricity, Gravity, and Cosmology
|journal=[[Physical Review Letters]]
|volume=19 |issue=13 |pages=759–761
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|doi=10.1103/PhysRevLett.19.759
}}</ref><ref>
{{cite journal
|last=Gamow |first=G.
|year=1967
|title=Variability of Elementary Charge and Quasistellar Objects
|journal=[[Physical Review Letters]]
|volume=19 |issue=16 |pages=913–914
|bibcode=1967PhRvL..19..913G
|doi=10.1103/PhysRevLett.19.913
}}</ref> [[String theory]] and other proposals for going beyond the [[Standard Model]] of particle physics have led to theoretical interest in whether the accepted [[physical constant]]s (not just {{math|''α''}}) actually vary.

In the experiments below, {{math|Δ''α''}} represents the change in {{math|''α''}} over time, which can be computed by {{math|''α''<sub>prev</sub> − ''α''<sub>now</sub>}}. If the fine-structure constant really is a constant, then any experiment should show that
:<math>\frac{\Delta \alpha}{\alpha} \ \stackrel{\mathrm{def}}{=}\ \frac{\alpha _\mathrm{prev}-\alpha _\mathrm{now}}{\alpha_\mathrm{now}}=0,</math>
or as close to zero as experiment can measure. Any value far away from zero would indicate that {{math|''α''}} does change over time. So far, most experimental data is consistent with {{math|''α''}} being constant.

===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
}}</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
}}</ref><ref>
{{cite journal
|last1=Olive |first1=K.
|last2=Qian |first2=Y.-Z.
|year=2003
|title=Were Fundamental Constants Different in the Past?
|journal=[[Physics Today]]
|volume=57 |issue=10 |pages=40–45
|bibcode=2004PhT....57j..40O
|doi=10.1063/1.1825267
}}</ref><ref>
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{{cite book
|last=Yasunori |first=F.
|year=2004
|chapter=Oklo Constraint on the Time-Variability of the Fine-Structure Constant
|chapterurl=http://www.springerlink.com/content/20dt5p8t8ene319q/
|title=Astrophysics, Clocks and Fundamental Constants
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|volume=648
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|pages=167–185
|series=[[Lecture Notes in Physics]]
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|doi=10.1007/b13178
|arxiv=astro-ph/0309817
}}</ref>

Improved technology at the dawn of the 21st century made it possible to probe the value of {{math|''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 {{math|''α''}}.<ref>
{{cite journal
|last=Webb |first=J. K.
|display-authors=etal
|year=1999
|title=Search for Time Variation of the Fine Structure Constant
|journal=[[Physical Review Letters]]
|volume=82 |issue=5 |pages=884–887
|arxiv=astro-ph/9803165
|bibcode=1999PhRvL..82..884W
|doi=10.1103/PhysRevLett.82.884
|url=http://cds.cern.ch/record/349066
|type=Submitted manuscript
}}</ref><ref>
{{cite journal
|last=Murphy |first=M. T.
|display-authors=etal
|year=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
|arxiv=astro-ph/0012419
|bibcode=2001MNRAS.327.1208M
|doi=10.1046/j.1365-8711.2001.04840.x
}}</ref><ref>
{{cite journal
|last=Murphy |first=M. T.
|display-authors=etal
|year=2001
|title=Further Evidence for Cosmological Evolution of the Fine Structure Constant
|journal=[[Physical Review Letters]]
|volume=87 |issue=9 |page=091301
|arxiv=astro-ph/0012539
|bibcode=2001PhRvL..87i1301W
|doi=10.1103/PhysRevLett.87.091301
|pmid=11531558
}}</ref><ref>
{{cite journal
|last1=Murphy |first1=M. T.
|last2=Webb |first2=J .K.
|last3=Flambaum |first3=V. V.
|year=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
|arxiv=astro-ph/0306483
|bibcode=2003MNRAS.345..609M
|doi=10.1046/j.1365-8711.2003.06970.x
}}</ref> Using the [[Keck telescopes]] and a data set of 128 [[quasars]] at [[redshift]]s {{math|0.5 < ''z'' < 3}}, Webb ''et al.'' found that their spectra were consistent with a slight increase in {{math|''α''}} over the last 10–12&nbsp;billion years. Specifically, they found that
:<math>\frac{\Delta \alpha}{\alpha} \ \stackrel{\mathrm{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, nearly zero, but their error bars do not actually include zero. This result either indicates that ''α'' is not constant or that there is experimental error that the experimenters did not know how to measure.

In 2004, a smaller study of 23 absorption systems by Chand ''et al.'', using the [[Very Large Telescope]], found no measurable variation:<ref>
{{cite journal
|last=Chand |first=H.
|display-authors=etal
|year=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
|arxiv=astro-ph/0401094
|bibcode=2004A&A...417..853C
|doi=10.1051/0004-6361:20035701
}}</ref><ref>
{{cite journal
|author=R. Srianand
|author-link=Raghunathan Srianand
|display-authors=etal
|year=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 |page=121302
|doi=10.1103/PhysRevLett.92.121302
|pmid=15089663
|bibcode=2004PhRvL..92l1302S
|arxiv=astro-ph/0402177}}</ref>
:<math> \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
|author1=M. T. Murphy |author2=J.K. Webb |author3=V. V. Flambaum |year=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 |page=239001
|doi=10.1103/PhysRevLett.99.239001
|bibcode=2007PhRvL..99w9001M
|issue=23
|arxiv=0708.3677 |pmid=18233422}}</ref><ref>{{cite journal
|author1=M. T. Murphy |author2=J.K. Webb |author3=V. V. Flambaum |year=2008
|title=Revision of VLT/UVES Constraints on a Varying Fine-Structure Constant
|journal=[[Monthly Notices of the Royal Astronomical Society]]
|volume=384 |pages=1053–1062
|doi=10.1111/j.1365-2966.2007.12695.x
|bibcode=2008MNRAS.384.1053M
|arxiv=astro-ph/0612407
|issue=3}}</ref>

King ''et al.'' have used [[Markov chain Monte Carlo]] methods to investigate the algorithm used by the UNSW group to determine {{math|{{sfrac|Δ''α''|''α''}}}} from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for {{math|{{sfrac|Δ''α''|''α''}}}} for particular models.<ref>{{cite journal
|author1=J. King |author2=D. Mortlock |author3=J. Webb |author4=M. Murphy |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 |arxiv=0910.2699
|bibcode=2009MmSAI..80..864K }}</ref> This suggests that the statistical uncertainties and best estimate for {{math|{{sfrac|Δ''α''|''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 {{math|''α''}} has changed in the past 2&nbsp;billion years by 45 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 to be verified.<ref>{{cite book
|author=R. Kurzweil
|year=2005
|title=The Singularity Is Near
|publisher=[[Penguin Group|Viking Penguin]]
|pages=139–140
|isbn=978-0-670-03384-3
|title-link=The Singularity Is Near
}}</ref><ref>{{cite journal
|author1=S. K. Lamoreaux |author2=J.R. Torgerson |year=2004
|title=Neutron Moderation in the Oklo Natural Reactor and the Time Variation of Alpha
|journal=[[Physical Review D]]
|volume=69 |page=121701
|doi=10.1103/PhysRevD.69.121701
|arxiv=nucl-th/0309048
|bibcode=2004PhRvD..69l1701L
|issue=12}}</ref><ref>{{cite magazine
|author=E. S. Reich
|date=30 June 2004
|title=Speed of Light May Have Changed Recently
|url=https://www.newscientist.com/article/dn6092-speed-of-light-may-have-changed-recently.html
|magazine=[[New Scientist]]
|accessdate=30 January 2009
}}</ref><ref>{{cite web
|date=12 May 2005
|title=Scientists Discover One Of The Constants Of The Universe Might Not Be Constant
|url=https://www.sciencedaily.com/releases/2005/05/050512120842.htm
|website=[[ScienceDaily]]
|accessdate=30 January 2009
}}</ref>

In 2007, Khatri and 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
|author1=R. Khatri |author2=B. D. Wandelt |year=2007
|title=21-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
|arxiv=astro-ph/0701752
|pmid=17501040
|bibcode=2007PhRvL..98k1301K
}}</ref> They proposed using this effect to measure the value of {{math|''α''}} during the epoch before the formation of the first stars. In principle, this technique provides enough information to measure a variation of 1 part in {{val|e=9}} (4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on {{math|''α''}} is strongly dependent upon effective integration time, going as {{math|''t''<sup>−{{1/2}}</sup>}}. The European [[LOFAR]] [[radio telescope]] would only be able to constrain {{math|{{sfrac|Δ''α''|''α''}}}} to about 0.3%.<ref name=Khatri/> The collecting area required to constrain Δ''α''/''α'' to the current level of quasar constraints is on the order of 100&nbsp;square kilometers, which is economically impracticable at the present time.

===Present rate of change===
In 2008, Rosenband ''et al.''<ref>{{cite journal
|author=T. Rosenband
|display-authors=etal
|year=2008
|title=Frequency Ratio of Al<sup>+</sup> and Hg<sup>+</sup> Single-Ion Optical Clocks; Metrology at the 17th Decimal Place
|journal=[[Science (journal)|Science]]
|volume=319 |issue=5871 |pages=1808–12
|doi=10.1126/science.1154622
|pmid=18323415
|bibcode=2008Sci...319.1808R|url=https://zenodo.org/record/1230892
}}</ref> used the frequency ratio of {{Element|aluminium|charge=+}} and {{Element|mercury|charge=+}} in single-ion optical atomic clocks to place a very stringent constraint on the present-time temporal variation of {{math|''α''}}, namely {{math|1={{sfrac|''α̇''|''α''}} = {{val|-1.6|2.3|e=-17}}}} per year. Note that any present day null constraint on the time variation of alpha does not necessarily rule out time variation in the past. Indeed, some theories<ref>{{cite journal
|author1=J. D. Barrow |author2=H.B. Sandvik |author3=J. Magueijo |year=2002
|title=The Behaviour of Varying-Alpha Cosmologies
|journal=Phys. Rev. D
|arxiv=astro-ph/0109414 |bibcode=2002PhRvD..65f3504B |doi=10.1103/PhysRevD.65.063504
|volume=65
|issue=6 |pages=063504}}</ref> that predict a variable fine-structure constant also predict that the value of the fine-structure constant should become practically fixed in its value once the universe enters its current [[dark energy]]-dominated epoch.

===Spatial variation – Australian dipole===
In September 2010 researchers from Australia said they had identified a dipole-like structure in the variation of the fine-structure constant across the observable universe. They used data on [[quasar]]s obtained by the [[Very Large Telescope]], combined with the previous data obtained by Webb at the [[Keck telescopes]]. The fine-structure constant appears to have been larger by one part in 100,000 in the direction of the southern hemisphere constellation [[Ara (constellation)|Ara]], 10&nbsp;billion years ago. Similarly, the constant appeared to have been smaller by a similar fraction in the northern direction, 10 billion years ago.<ref>{{cite web
|author=H. Johnston
|date=2 September 2010
|url=https://physicsworld.com/a/changes-spotted-in-fundamental-constant/
|title=Changes spotted in fundamental constant
|work=[[Physics World]]
|accessdate=11 September 2010
}}</ref><ref>{{cite journal
|author=J. K. Webb
|date=23 August 2010
|arxiv=1008.3907
|title=Evidence for spatial variation of the fine-structure constant
|journal=Physical Review Letters
|bibcode=2011PhRvL.107s1101W
|author2=King, J. A.
|author3=Murphy, M. T.
|author4=Flambaum, V. V.
|author5=Carswell, R. F.
|author6=Bainbridge, M. B.
|doi=10.1103/PhysRevLett.107.191101
|pmid=22181590
|volume=107
|issue=19 |pages=191101
}}</ref><ref>{{cite thesis
|degree=PhD
|title=Searching for variations in the fine-structure constant and the proton-to-electron mass ratio using quasar absorption lines
|author=J. A. King
|year=2010
|publisher=University of New South Wales
|url=http://handle.unsw.edu.au/1959.4/50886
}}</ref>

In September and October 2010, after Webb's released research, physicists [[Chad Orzel]] and [[Sean M. Carroll]] suggested various approaches of how Webb's observations may be wrong. Orzel argues<ref>{{cite web |title=Why I'm Skeptical About the Changing Fine-Structure Constant |url=http://scienceblogs.com/principles/2010/09/14/httpksjtrackermitedu20100907e/ |first=Chad |last=Orzel |authorlink=Chad Orzel |date=14 October 2010 |publisher=ScienceBlogs}}</ref> that the study may contain wrong data due to subtle differences in the two telescopes, in which one of the telescopes the data set was slightly high and on the other slightly low, so that they cancel each other out when they overlapped. He finds it suspicious that the sources showing the greatest changes are all observed by one telescope, with the region observed by both telescopes aligning so well with the sources where no effect is observed. Carroll suggested<ref>{{cite web |title=The Fine Structure Constant is Probably Constant |url=http://www.preposterousuniverse.com/blog/2010/10/18/the-fine-structure-constant-is-probably-constant/ |first=Sean M. |last=Carroll |authorlink=Sean M. Carroll |date=18 October 2010}}</ref> a totally different approach; he looks at the fine-structure constant as a scalar field and claims that if the telescopes are correct and the fine-structure constant varies smoothly over the universe, then the scalar field must have a very small mass. However, previous research has shown that the mass is not likely to be extremely small. Both of these scientists' early criticisms point to the fact that different techniques are needed to confirm or contradict the results, as Webb, et al., also concluded in their study.

In October 2011, Webb ''et al.'' reported<ref>{{cite journal
|author1=J. K. Webb |author2=J. A. King |author3=M. T. Murphy |author4=V. V. Flambaum |author5=R. F. Carswell |author6=M. B. Bainbridge
|title=Indications of a Spatial Variation of the Fine Structure Constant
|url=http://www.nat.vu.nl/~wimu/Varying-Constants-Papers/Spatial-Var-PhysRevLett.107.191101.pdf
|journal=[[Physical Review Letters]]
|volume=107 |issue=19 |date=4 November 2011
|pages=191101 |doi=10.1103/PhysRevLett.107.191101
|bibcode=2011PhRvL.107s1101W
|arxiv=1008.3907 |pmid=22181590}}</ref>
a variation in {{math|''α''}} dependent on both redshift and spatial direction. They report "the combined data set fits a spatial dipole" with an increase in ''α'' with redshift in one direction and a decrease in the other. "Independent VLT and Keck samples give consistent dipole directions and amplitudes...."{{Clarify|date=December 2017|reason=Is this a complete sentence? Answer: It is a part of sentence from abstract of 1008.3907, though am not sure what is a proper way to cite it here.}}

== Anthropic explanation ==
The [[anthropic principle]] is a controversial argument of why the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were much different. For instance, were {{math|''α''}} to change by 4%, stellar [[nuclear fusion|fusion]] would not produce [[carbon]], so that carbon-based life would be impossible. If {{math|''α''}} were greater than 0.1, stellar fusion would be impossible, and no place in the universe would be warm enough for life as we know it.<ref>{{cite journal
|author = J. D. Barrow
|year = 2001
|title = Cosmology, Life, and the Anthropic Principle
|journal = [[Annals of the New York Academy of Sciences]]
|volume = 950 | issue = 1 | pages = 139–153
|doi = 10.1111/j.1749-6632.2001.tb02133.x
|pmid = 11797744
|bibcode = 2001NYASA.950..139B}}</ref>

==Numerological explanations and multiverse theory==
As a dimensionless constant which does not seem to be directly related to any [[mathematical constant]], the fine-structure constant has long fascinated physicists.

[[Arthur Eddington]] argued that the value could be "obtained by pure deduction" and he related it to the [[Eddington number]], his estimate of the number of protons in the universe.<ref>{{cite book
|author=A. S. Eddington
|year=1956
|chapter=The Constants of Nature
|editor=J.R. Newman
|title=The World of Mathematics
|volume=2 |pages=1074–1093
|publisher=[[Simon & Schuster]]
|isbn=
|oclc=
|lccn=
}}</ref> This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not [[almost integer|approximately the integer]] 137, but precisely the [[integer]] [[137 (number)|137]].<ref>{{Cite journal|last=Whittaker|first=Edmund|date=1945|title=Eddington's Theory of the Constants of Nature|journal=The Mathematical Gazette|volume=29|issue=286|pages=137–144|doi=10.2307/3609461|jstor=3609461}}</ref> Other physicists neither adopted this conjecture nor accepted his arguments but by the 1940s experimental values for {{math|{{sfrac|1|''α''}}}} deviated sufficiently from 137 to refute Eddington's argument.<ref>{{cite journal
|author=H. Kragh
|year=2003
|title=Magic Number: A Partial History of the Fine-Structure Constant
|journal=[[Archive for History of Exact Sciences]]
|volume=57 |issue=5 |pages=395–431
|doi=10.1007/s00407-002-0065-7|jstor=41134170
|doi-broken-date=2019-08-18
}}</ref>

The fine-structure constant so intrigued physicist [[Wolfgang Pauli]] that he collaborated with psychoanalyst [[Carl Jung]] in a quest to understand its significance.<ref>{{cite journal
|author1=P. Varlaki |author2=L. Nadai |author3=J. Bokor |year=2008
|title=Number Archetypes and Background Control Theory Concerning the Fine Structure Constant
|url=http://uni-obuda.hu/journal/Varlaki_Nadai_Bokor_14.pdf
|journal=[[Acta Polytechnica Hungarica]]
|volume=5 |issue=2 |pages=71
|doi=
}}</ref> Similarly, [[Max Born]] believed that would the value of alpha differ, the universe would degenerate. Thus, he asserted that {{sfrac|1|137}} is a law of nature.<ref>{{cite book
|author = A. I. Miller
|year = 2009
|title = Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung
|page = 253
|publisher = [[W.W. Norton & Co.|W.W. Norton & Co]]
|isbn = 978-0-393-06532-9
|quote = '''Max Born''': If alpha were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy.
|url = https://archive.org/details/isbn_9780393065329
}}</ref>

[[Richard Feynman]], one of the originators and early developers of the theory of [[quantum electrodynamics]] (QED), referred to the fine-structure constant in these terms:

{{quote|There is a most profound and beautiful question associated with the observed coupling constant, {{math|''e''}} – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!|{{cite book
|author=Richard P. Feynman
|author-link=Richard Feynman
|year=1985
|title=QED: The Strange Theory of Light and Matter
|publisher=[[Princeton University Press]]
|page=129
|isbn=978-0-691-08388-9
|title-link=QED: The Strange Theory of Light and Matter
}}}}

Conversely, statistician [[I. J. Good]] argued that a numerological explanation would only be acceptable if it could be based on a good theory that is not yet known but "exists" in the sense of a [[Platonic Ideal]].<ref>{{cite book
|author=I. J. Good
|year=1990
|chapter=A Quantal Hypothesis for Hadrons and the Judging of Physical Numerology |editor1=G. R. Grimmett |editor2=D. J. A. Welsh |title=Disorder in Physical Systems
|publisher=[[Oxford University Press]]
|page=141
|isbn=978-0-19-853215-6
|quote = '''[[I. J. Good]]''': There have been a few examples of numerology that have led to theories that transformed society: see the mention of Kirchhoff and Balmer in Good (1962, p. 316) … and one can well include Kepler on account of his third law. It would be fair enough to say that numerology was the origin of the theories of electromagnetism, quantum mechanics, gravitation.... So I intend no disparagement when I describe a formula as numerological. When a numerological formula is proposed, then we may ask whether it is correct. … I think an appropriate definition of correctness is that the formula has a good explanation, in a Platonic sense, that is, the explanation could be based on a good theory that is not yet known but ‘exists’ in the universe of possible reasonable ideas.
}}</ref>

Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community.

In the early 21st century, multiple physicists, including [[Stephen Hawking]] in his book ''[[A Brief History of Time]]'', began exploring the idea of a [[multiverse]], and the fine-structure constant was one of several universal constants that suggested the idea of a [[fine-tuned universe]].<ref name=":2">{{cite book |author=Stephen Hawking |year=1988 |title=A Brief History of Time |url=https://archive.org/details/briefhistoryofti00step_1 |url-access=registration |publisher=Bantam Books |isbn=978-0-553-05340-1 |pages=[https://archive.org/details/briefhistoryofti00step_1/page/7 7], 125|author-link=Stephen Hawking }}</ref>

==Quotes==
{{quote|The mystery about ''α'' is actually a double mystery. The first mystery – the origin of its numerical value {{math|''α'' ≈ 1/137}} – has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized.|{{cite book
|author = M. H. MacGregor
|year = 2007
|title = The Power of Alpha
|page= [https://books.google.com/books?id=jdloDQAAQBAJ&lpg=PP1&hl=de&pg=PA69 69]
|publisher = [[World Scientific]]
|isbn = 978-981-256-961-5
}}}}

==See also==
*[[Dimensionless physical constant]]
*[[Electric constant]]
*[[Gravitational coupling constant]]
*[[Hyperfine structure]]
*[[Planck's constant]]
*[[Speed of light]]

==References==
{{Reflist|40em}}

==External links==
{{wikiquote}}
*[[Stephen L. Adler]], [http://lss.fnal.gov/archive/1972/pub/Pub-72-059-T.pdf "Theories of the Fine Structure Constant α"] FERMILAB-PUB-72/059-T
*[http://physics.nist.gov/cuu/Constants/alpha.html "Introduction to the constants for nonexperts"], adapted from the ''[[Encyclopædia Britannica]]'', 15th ed. Disseminated by the [[NIST]] web page.
*[http://physics.nist.gov/cuu/Constants/codata.pdf CODATA recommended value of α], as of 2010.
*[https://www.goodreads.com/quotes/tag/fine-structure-constant Quotes About Fine Structure Constant]
*[http://scienceworld.wolfram.com/physics/FineStructureConstant.html "Fine Structure Constant"], Eric Weisstein's World of Physics website.
*[[John D. Barrow]], and John K. Webb, [http://www.sciam.com/article.cfm?articleID=0005BFE6-2965-128A-A96583414B7F0000&ref=sciam "Inconstant Constants"], ''[[Scientific American]]'', June 2005.
*{{cite web|last=Eaves|first=Laurence|title=The Fine Structure Constant|url=http://www.sixtysymbols.com/videos/finestructure.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|authorlink=Laurence Eaves|year=2009}}

[[Category:Concepts in physics]]
[[Category:Dimensionless numbers]]
[[Category:Electromagnetism]]
[[Category:Fundamental constants]]