- Fine-structure constant
The **fine-structure constant**or**Sommerfeld fine-structure constant**, usually denoted $alpha\; ,$, is thefundamental physical constant characterizing the strength of theelectromagnetic interaction .It is adimensionless quantity , and thus its numerical value is independent of the system of units used.: $alpha\; =\; frac\{e^2\}\{hbar\; c\; 4\; pi\; epsilon\_0\}\; =\; frac\{e^2\; c\; mu\_0\}\{2\; h\}\; =\; 7.297,352,570(5)\; imes\; 10^\{-3\}\; =\; frac\{1\}\{137.035,999,070(98)\}$ .

(numbers within parentheses are uncertainties), where $e\; ,$ is the

elementary charge , $hbar\; =\; h/(2\; pi)\; ,$ is the reducedPlanck constant , $c\; ,$ is thespeed of light in a vacuum, $epsilon\_0\; ,$ is thevacuum permittivity , and $mu\_0\; ,$ is themagnetic constant or vacuum permeability, a defined conversion factor.The defining expression and the value recommended by 2006 CODATA as reported by [

*http://physics.nist.gov/cgi-bin/cuu/Value?alph NIST reference on constants, units, and uncertainty*] is:: $alpha\; =\; frac\{e^2\}\{hbar\; c\; 4\; pi\; epsilon\_0\}\; =\; 7.297,352,5376(50)\; imes\; 10^\{-3\}\; =\; frac\{1\}\{137.035,999,679(94)\}$ .

However, after completion of the 2006 CODATA adjustment an error was discovered in one of the input data, leading to the first value given above.

The name of the fine-structure constant refers to its earliest use in the theory for the

fine structure of atomic energy spectra. However, its modern use is far from being as specialized as its name suggests.**Related definitions**The fine-structure constant can also be defined as

: $alpha\; =\; frac\{k\_e\; e^2\}\{hbar\; c\}\; =\; frac\{e^2\}\{2\; epsilon\_0\; h\; c\}$

where $k\_e\; ,$ is the electrostatic constant, $e\; ,$ is the

elementary charge , $hbar\; =\; h/(2\; pi)\; ,$ is thereduced Planck constant , $c\; ,$ is thespeed of light in a vacuum, and $epsilon\_0\; ,$ is theelectric constant .In electrostatic

cgs units, the unit ofelectric charge (the "Statcoulomb " or "esu of charge") is defined in such a way that the permittivity factor, $4\; pi\; epsilon\_0\; ,$, is the dimensionless constant 1. Then the fine-structure constant becomes: $alpha\; =\; frac\{e^2\}\{hbar\; c\}$ .

**Measurement**The definition of $alpha,$ contains several other constants which can be measured themselves.However,

quantum electrodynamics (QED) provides a way to measure $alpha,$ directlyusing thequantum Hall effect or theanomalous magnetic moment of the electron.QED predicts a relationship between the dimensionless magnetic moment of the

electron (or theLande g-factor , $g\; ,$) and the fine structure constant $alpha,$. A new measurement of $g\; ,$ using a one-electron quantum cyclotron, together with a QED calculation involving 891 four-loopFeynman diagrams , determines the most precise current value of $alpha,$:Citation

url=http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewFineStructureConstant.pdf

author1=G. Gabrielse

author2=D. Hanneke

author3=T. Kinoshita

author4=M. Nio

author5=B. Odom

title=New Determination of the Fine Structure Constant from the Electron g Value and QED

journal=Phys. Rev. Lett.

volume=97

issue=030802

date=2006-07-21

year=2006

doi=10.1103/PhysRevLett.97.030802

author=Gabrielse, G.

pages=030802 and Citation

url=http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewFineStructureConstant.pdf

author1=G. Gabrielse

author2=D. Hanneke

author3=T. Kinoshita

author4=M. Nio

author5=B. Odom

title=Erratum: New Determination of the Fine Structure Constant from the Electron g Value and QED Phys. Rev. Lett. 97, 030802 (2006)

journal=Phys. Rev. Lett.

volume=99

issue=039902

date=2007-06-24

year=2007

doi=10.1103/PhysRevLett.99.039902

author=Gabrielse, G.

pages=039902]: $alpha^\{-1\}\; =\; 137.035,999,068(96)$

i.e., a measurement with a precision of 0.70 ppb. The uncertainties are 10 times smaller than those of the nearest rival methods that include atom-recoil measurements. Comparisons of the measured and calculated values of $g\; ,$ test QED very stringently, and set a limit on any possible internal structure of the electron.

**Physical interpretation**There are several ways to interpret the reality of the Fine-structure constant, including:

# the square of the ratio of the elementary to Planck charges

# a ratio of certain energies

# the ratio between the electron velocity in Bohr's model of the atom and the speed of light

# a constant representing the strength of the interaction between electrons and photons

# the strength of the electromagnetic interaction, which may change, depending on the strength of the energy field. The fine-structure constant can be thought of as the square of the ratio of theelementary charge to thePlanck charge .: $alpha\; =\; left(\; frac\{e\}\{q\_P\}\; ight)^2$.

For any arbitrary length $s\; ,$, the fine-structure constant is the ratio of two energies: (i) the energy needed to bring two electrons from infinity to a distance of $s\; ,$ against their electrostatic repulsion, and (ii) the energy of a single photon of

wavelength equal to the same length scaled by 2π (i.e. $2\; pi\; s\; =\; lambda\; =\; frac\{c\}\{\; u\}\; ,$ where $u\; ,$ is the frequency of radiation associated with the photon):: $alpha\; =\; frac\{e^2\}\{4\; pi\; epsilon\_0\; s\}\; div\; h\; u\; =\; frac\{e^2\}\{4\; pi\; epsilon\_0\; s\}\; div\; frac\{h\; c\}\{2\; pi\; s\}\; =\; frac\{e^2\}\{4\; pi\; epsilon\_0\; hbar\; c\}.$

The fine structure constant is also the ratio between the electron velocity in the

Bohr atom and the speed of light. The square of alpha is the ratio between theelectron rest mass (511 keV) and theHartree energy (27.2 eV = 2 Ry).In the theory of

quantum electrodynamics , the fine structure constant plays the role of acoupling constant , representing the strength of the interaction between electrons and photons. Its value cannot be predicted by the theory, and has to be inserted based on experimental results. In fact, it is one of the twenty-odd "external parameters " in theStandard Model ofparticle physics .The fact that $alpha\; ,$ is much less than 1 allows the use of perturbation theory in quantum electrodynamics. Physical results in this theory are expressed as

power series in $alpha\; ,$, with higher orders of $alpha\; ,$ increasingly unimportant. In contrast, the large value of the corresponding factors inquantum chromodynamics makes calculations involving thestrong force extremely difficult.In the

electroweak theory , one that unifies theweak interaction withelectromagnetism , the fine-structure constant is absorbed into two other coupling constants associated with the electroweak gauge fields. In this theory, the electromagnetic interaction is treated as a mixture of interactions associated with the electroweak fields.According to the theory of

renormalization group , the value of the fine-structure constant (the strength of the electromagnetic interaction) depends on theenergy scale . In fact, it growslogarithm ically as the energy is increased. The observed value of $alpha\; ,$ is associated with the energy scale of the electron mass; the energy scale does not run below this because the electron (and thepositron ) is the lightest charged object whose quantum loops can contribute to the running. Therefore, we can say that 1/137.036 is the value of the fine-structure constant at zero energy. Moreover, as the energy scale increases, the electromagnetic interaction approaches the strength of the other two interactions, which is important for the theories ofgrand unification . If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as theLandau pole . This fact makes quantum electrodynamics inconsistent beyond theperturbative expansions.**History**The fine-structure constant was originally introduced into physics in 1916 by

Arnold Sommerfeld , as a measure of the relativistic deviations inatom icspectral line s from the predictions of theBohr model .Historically, the first physical interpretation of the fine-structure constant, $alpha\; ,$, was the ratio of the velocity of the electron in the first circular orbit of the relativistic

Bohr atom to thespeed of light in vacuum. Equivalently, it was the quotient between the maximum 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 of the hydrogenic spectral lines.**Is the fine structure constant really constant?**Physicists have been wondering for many years whether the fine structure constant is really a constant, i.e., whether or not its value is different at different times or in different places. Historically, a varying $alpha\; ,$ has been proposed as a means to solve some of the perceived cosmological problems of the day. [

*cite book*] [

last=Milne

first=Edward Arthur

authorlink=Arthur Milne

title = Relativity, Gravitation and World Structure

publisher = The Clarendon press

date = 1935

location = Oxford*P. A. M. Dirac, Nature*] [**139**, 323(1937)*G. Gamow, Phys. Rev. Lett.*] More recently, theoretical interest in varying constants (not just $alpha\; ,$) has been motivated by**19**, 757 and 913 (1967).string theory and other such proposals for going beyond theStandard Model of particle physics. The first experimental tests of this question, most notably examination ofspectral line s of distant astronomical objects and of radioactive decays in theOklo natural nuclear fission reactor , found results consistent with no change. [*cite journal*] [

last = Uzan

first = Jean-Philippe

authorlink = Jean-Philippe Uzan

title = The fundamental constants and their variation: observational status and theoretical motivations

journal = Reviews of Modern Physics

volume = 75

pages = 403–455

publisher =American Physical Society

date = 2003

url = http://arxiv.org/abs/hep-ph/0205340

accessdate = 2006-08-12

doi = 10.1103/RevModPhys.75.403*cite journal*] [

last = Uzan

first = Jean-Philippe

authorlink = Jean-Philippe Uzan

title = Variation of the constants in the late and early universe

journal = astro-ph/0409424

publisher =arXiv

date = 2004

url = http://arxiv.org/abs/astro-ph/0409424

accessdate = 2006-08-12*cite journal*] [

last = Olive

first = Keith

authorlink = Keith Olive

coauthors = Qian, Yong-Zhong

title = Were Fundamental Constants Different in the Past?

journal =Physics Today

volume = 57

issue = 10

pages = 40–5

publisher =American Institute of Physics

date = 2003

doi = 10.1063/1.1825267*cite book*] [

last = Barrow

first = John D.

authorlink = John D. Barrow

title = The Constants of Nature: From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe

publisher = Vintage

date = 2002

location = London

id = ISBN 0-09-928647-5*cite book*] [

last = Uzan

first = Jean-Philippe

authorlink = Jean-Philippe Uzan

coauthors = Bénédicte Leclercq

title = The natural laws of the universe - Understanding fundamentral constants

publisher = Springer Praxis

date = 2008

location = Berlin Heidelberg New-York

id = ISBN 978-0-387-73454-5*cite book*]

last = Fujii

first = Yasunori

title = Astrophysics, Clocks and Fundamental Constants

chapter = Oklo Constraint on the Time-Variability of the Fine-Structure Constant

pages = 167-185

chapterurl = http://www.springerlink.com/content/20dt5p8t8ene319q/

url = http://www.springerlink.com/content/yvjtrlw7grcn/

publisher =Springer Berlin

isbn = 978-3-540-21967-5

date = 2004

series = Lecture Notes in Physics

location = HeidelbergMore recently, technology improvements have made it possible to probe the value of $alpha\; ,$ at much larger distances and to much greater accuracy. In 1999, a team lead by

John K. Webb of theUniversity of New South Wales claimed the first detection of a variation in $alpha\; ,$. [*cite journal*] [

last = Webb

first = John K.

authorlink = John K. Webb

coauthors = et al

title = Search for Time Variation of the Fine Structure Constant

journal = Physical Review Letters

volume = 82

issue = 5

pages = 884–887

publisher =American Physical Society

date = 1999

url = http://arxiv.org/pdf/astro-ph/9803165

accessdate = 2006-08-12

doi = 10.1103/PhysRevLett.82.884*M. T. Murphy et al, Mon. Not. Roy. Astron. Soc.*] [**327**, 1208 (2001)*cite journal*] [

last = Webb

first = John K.

authorlink = John K. Webb

coauthors = et al

title = Further Evidence for Cosmological Evolution of the Fine Structure Constant

journal = Physical Review Letters

volume = 87

issue = 9

pages = 091301

publisher =American Physical Society

date = 2001

url = http://arxiv.org/pdf/astro-ph/0012539

accessdate = 2006-08-12

doi = 10.1103/PhysRevLett.87.091301*M.T. Murphy, J.K. Webb and V.V. Flambaum, Mon. Not R. astron. Soc.*] Using the**345**, 609 (2003)Keck telescopes and a data set of 128quasars atredshifts 0.5alpha , over the last 10-12 billion years. Specifically, they found that :$frac\{Delta\; alpha\}\{alpha\}\; stackrel\{mathrm\{def\{=\}\; frac\{alpha\; \_mathrm\{then\}-alpha\; \_mathrm\{now\{alpha\_mathrm\{now\; =\; left(\; -0.57pm\; 0.10\; ight)\; imes\; 10^\{-5\}.$

A more recent, smaller, study of 23 absorption systems by Chand et al. using the

Very Large Telescope found nomeasureable variation: [*H. Chand et al., Astron. Astrophys.*] [**417**, 853 (2004)*R. Srianand et al., Phys. Rev. Lett.*]**92**, 121302 (2004).:$frac\{Delta\; alpha\}\{alpha\_mathrm\{em=\; left(-0.6pm\; 0.6\; ight)\; imes\; 10^\{-6\}.$ The Chand et al. result apparently rules out variation at the level claimed by Webb et al., although there are still concerns about systematic uncertainties. Surveys to provide additional data are ongoing. All other astrophysical results to date are consistent with no variation. [

*cite journal*]

last = Barrow

first = John D.

authorlink = John D. Barrow

title = Varying Constants

journal =Philosophical Transactions of the Royal Society

volume = 363

pages = 2139–2153

publisher =Royal Society

date = 2005

url = http://arxiv.org/pdf/astro-ph/0511440

accessdate = 2006-08-12Very recently, Khatri and Wandelt of the University of Illinois at Urbana-Champaignrealized that the 21 cm hyperfine transition in neutral hydrogen in the early Universe leaves a unique absorption line imprint in the cosmic microwave background radiation. [

*Citation*] They proposed using this effect to measure the value of $alpha$ 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 $10^\{9\}$ (4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on $alpha$ is strongly dependent upon effective integration time, going as $t^\{-1/2\}$. The

last1 = Khatri

first1 = Rishi

last2 = Wandelt

first2 = Benjamin D.

author2-link = Benjamin D. Wandelt

title = 21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant

journal =Physical Review Letters

volume = 98

pages = 111301

publisher =American Physical Society

date = 2007

url = http://arxiv.org/abs/astro-ph/0701752

accessdate = 2007-07-09

doi = 10.1103/PhysRevLett.98.111301LOFAR telescope would only be able to constrain $Deltaalpha/alpha$ to ~0.3% [*Citation*] . The collecting area required to constrain $Deltaalpha/alpha$ to the current level of quasar constraints is on the order of 100$km^2$, which is impracticable at present.

last1 = Khatri

first1 = Rishi

last2 = Wandelt

first2 = Benjamin D.

author2-link = Benjamin D. Wandelt

title = 21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant

journal =Physical Review Letters

volume = 98

pages = 111301

publisher =American Physical Society

date = 2007

url = http://arxiv.org/abs/astro-ph/0701752

accessdate = 2007-07-09

doi = 10.1103/PhysRevLett.98.111301**Anthropic explanation**One controversial explanation of the value of the fine-structure constant invokes the

anthropic principle and argues that the value of the fine-structure is what it is because stable matter and therefore life and intelligent beings could not exist if the value were anything else. For instance, were $alpha,$ to change by 4%,carbon would no longer be produced in stellar fusion. If $alpha,$ were greater than 0.1, fusion would no longer occur in stars. [*cite journal*]

last = Barrow

first = John D.

authorlink = John D. Barrow

title = [*http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1749-6632.2001.tb02133.x Cosmology, Life, and the Anthropic Principle*]

journal = Annals of the New York Academy of Sciences

volume = 950

issue = 1

pages = 139–153

date = 2001

doi = 10.1111/j.1749-6632.2001.tb02133.x

doi_brokendate = 2008-06-25The fine structure constant plays a central role in John Barrow and

Frank Tipler 's broad-ranging discussion ofastrophysics ,cosmology ,quantum physics ,teleology , and theanthropic principle . []John D. Barrow andFrank J. Tipler , 1986. "The Anthropic Cosmological Principle". Oxford University Press.**Numerological explanations**As a dimensionless constant which does not seem to be directly related to any

mathematical constant , the fine-structure constant has long been an object of fascination to physicists.Richard Feynman , one of the founders of quantum electrodynamics, referred to it as "one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man." [*cite book|first=Richard P.|last=Feynman|authorlink=Richard Feynman|title=*]

year=1985|publisher=Princeton University Press|id=ISBN 0-691-08388-6|pages=129In 1929,

Arthur Eddington conjectured that its reciprocal was precisely theinteger 137, constructed numerological arguments that the value could be "obtained by pure deduction", and related it to theEddington number , his estimate of the number of protons in the Universe. Other physicists neither adopted this conjecture nor accepted his arguments, and by the 1940s, experimental values for frac|1|α deviated sufficiently from 137 to reject that value. [*Helge Kragh, "Magic Number: A Partial History of the Fine-Structure Constant", "Archive for History of Exact Sciences"*]**57**:5:395 (July, 2003) doi|10.1007/s00407-002-0065-7Recently the mathematician [

*http://www.maths.qmul.ac.uk/~jgg/ James Gilson*] has suggested [*http://www.fine-structure-constant.org/*] that the fine-structure constant has the value::$alpha\; =\; frac\{cos\; left(pi/137\; ight)\}\{137\}\; frac\{\; an\; left(pi/(137\; cdot\; 29)\; ight)\}\{pi/(137\; cdot\; 29)\}\; approx\; frac\{1\}\{137.0359997867\}$ ,

29 and 137 being the 10

^{th}and 33^{rd}prime number s. This deviates from the 2006CODATA value for α by about one standard uncertainty of measurement, but by more than seven standard deviations from the best α value currently known (2007).**Quotes*** "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 π 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!" — Richard P. Feynman, "QED: The Strange Theory of Light and Matter", Princeton University Press 1985, p. 129.

* "The mystery about $alpha,$ is actually a double mystery. The first mystery -- the origin of its numerical value $alpha,$ ~ 1/137 -- has been recognized and discussed for decades. The second mystery -- the range of its domain --is generally unrecognized." -- Malcolm H. Mac Gregor, "The Power of $alpha,$ " Singapore: World Scientific Publishing Company, 2007, p. 69Citation |isbn = 9789812569615 .**See also***

Coupling constant s

*Fundamental physical constant **External links***" [

*http://physics.nist.gov/cuu/Constants/alpha.html Introduction to the constants for nonexperts,*] " adapted from the "Encyclopedia Britannica ", 15th ed. Disseminated by theNIST web page.

* [*http://physics.nist.gov/cuu/Constants/codata.pdf CODATA recommended value of α,*] as of 2006.

*" [*http://scienceworld.wolfram.com/physics/FineStructureConstant.html Fine structure constant,*] " Eric Weisstein's World of Physics website.

*John D. Barrow , and Webb, John K., " [*http://www.sciam.com/article.cfm?articleID=0005BFE6-2965-128A-A96583414B7F0000&ref=sciam Inconstant Constants,*] " "Scientific American ", May 2005.**References**

*Wikimedia Foundation.
2010.*

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**fine structure constant**— smulkiosios sandaros konstanta statusas T sritis Standartizacija ir metrologija apibrėžtis Apibrėžtį žr. priede. priedas( ai) Grafinis formatas atitikmenys: angl. fine structure constant vok. Feinstrukturkonstante, f rus. константа тонкой… … Penkiakalbis aiškinamasis metrologijos terminų žodynas**fine structure constant**— smulkiosios sandaros konstanta statusas T sritis fizika atitikmenys: angl. fine structure constant vok. Feinstrukturkonstante, f rus. постоянная тонкой структуры, f pranc. constante de la structure fine, f … Fizikos terminų žodynas**fine-structure constant**— A dimensionless constant, equal to 7.297351 x 10 3 (approximately 1/137), given by 2π times the square of the electron charge, divided by the product of the speed of light and Planck s constant … Dictionary of automotive terms**fine-structure constant**— noun The fundamental physical value α, presumed to be constant, that characterizes the strength of the electromagnetic force … Wiktionary**fine-structure constant**— ¦ ̷ ̷ ˈ ̷ ̷ ̷ ̷ noun : a dimensionless constant that is a measure of the strength of electromagnetic interactions of subatomic particles and that has an approximate value of 0.0073 or 1/137 symbol α … Useful english dictionary**fine structure**— /fuyn/, Physics. a group of lines that are observed in the spectra of certain elements, as hydrogen, and that are caused by various couplings of the azimuthal quantum number and the angular momentum quantum number. Cf. hyperfine structure. [1915… … Universalium**Fine structure**— Interference fringes, showing fine structure (splitting) of a cooled deuterium source, viewed through a Fabry Pérot étalon. In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to first order… … Wikipedia**STRUCTURE ET FONCTION**— L’étude de la relation entre les structures et les fonctions est au cœur même de la biologie. Cette relation s’exprime chez les êtres vivants par l’adaptation des premières aux secondes et pose une série de problèmes absolument fondamentaux,… … Encyclopédie Universelle**Fine-tuned Universe**— The fine tuned Universe is the idea that the conditions that allow life in the Universe can only occur when certain universal physical constants lie within a very narrow range, so that if any of several fundamental constants were only slightly… … Wikipedia**Dimensionless physical constant**— In physics, a dimensionless physical constant (sometimes fundamental physical constant) is a universal physical constant that is dimensionless having no unit attached, so its numerical value is the same under all possible systems of units. The… … Wikipedia