» 
Arabic Bulgarian Chinese Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Malagasy Norwegian Persian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Thai Turkish Vietnamese
Arabic Bulgarian Chinese Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Malagasy Norwegian Persian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Thai Turkish Vietnamese

definition - Fine-structure_constant

definition of Wikipedia

   Advertizing ▼

Wikipedia

Fine-structure constant

                   

In physics, the fine-structure constant (usually denoted α, the Greek letter alpha) is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units. Arnold Sommerfeld introduced the fine-structure constant in 1916.

The current recommended value of α is 7.2973525698(24)×10−3 = 1/137.035999074(44).[1][2]

Contents

  Definition

Three equivalent definitions of α in terms of other fundamental physical constants are:

\alpha = \frac{e^2}{(4 \pi \varepsilon_0)\hbar c} = \frac{e^2 c \mu_0}{2 h} = \frac{k_\mathrm{e} e^2}{\hbar c},

where:

In electrostatic cgs units, the unit of electric charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1 and dimensionless. Then the expression of the fine-structure constant becomes the abbreviated

\alpha = \frac{e^2}{\hbar c}

an expression commonly appearing in physics literature.

  Measurement

Two example eighth-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 2010 CODATA recommended value of α is[3]

 \alpha = \frac{e^2}{(4 \pi \varepsilon_0) \hbar c} =  7.297\,352\,5698(24) \times 10^{-3}.

This has a relative standard uncertainty of 0.32 parts per billion.[3] For reasons of convenience, historically the value of the reciprocal of the fine-structure constant is often specified. The 2010 CODATA recommended value is given by[3]

 \alpha^{-1} = 137.035\,999\,074(44).

While the value of 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 α directly using the quantum Hall effect or the anomalous magnetic moment of the electron. The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant α (the magnetic moment of the electron is also referred to as "Landé g-factor" and symbolized as g). The most precise value of α obtained experimentally through the present is based on a new measurement of g using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved 891 four-loop Feynman diagrams:[4]

\alpha^{-1} = 137.035\,999\,084(51).

This measurement of α has a precision of 0.37 parts per billion. This value and uncertainty are about the same as the latest experimental results.[5]

  Erroneous 2006 recommended value

According to 2006 CODATA, the recommended value for α was 7.2973525376(50) x 10−3 = 1/137.035999679(94).[6] However, after the 2006 CODATA adjustment was completed, an error was discovered in one of the main data inputs.[7] Nevertheless, the 2006 CODATA recommended value was republished in 2008.[8] A revised standard value, taking recent research and adjustments to SI units into account, was published in June 2011.

  Physical interpretations

The fine-structure constant α has several physical interpretations. α is:

\alpha = \left( \frac{e}{q_\mathrm{P}} \right)^2.
  • The ratio of two energies: (i) the energy needed to overcome the electrostatic repulsion between two electrons a distance of d apart, and (ii) the energy of a single photon of wavelength \lambda = 2\pi d (from a modern perspective, of angular wavelength r = d ; see Planck relation):
\alpha = \frac{e^2}{4 \pi \varepsilon_0 d} \times \frac{\lambda}{h c} = \frac{e^2}{4 \pi \varepsilon_0 d} \times {\frac{2 \pi d}{h c}} = (\frac{e^2}{4 \pi \varepsilon_0 r} \times {\frac{r}{\hbar c}}) = \frac{e^2}{4 \pi \varepsilon_0 \hbar c}.
r_e = {\alpha \lambda_e \over 2\pi} = \alpha^2 a_0
\alpha = \frac{1}{4}\,Z_0\,G_0.

When perturbation theory is applied to quantum electrodynamics, the resulting perturbative expansions for physical results are expressed as sets of power series in α. Because α is much less than one, higher powers of α are soon unimportant, making the perturbation theory extremely 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.

According to the theory of the renormalization group, the value of the fine-structure constant (the strength of the electromagnetic interaction) grows logarithmically as the energy scale is increased. The observed value of α is 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 loops can contribute to the running. Therefore 1/137.036 is the value of the fine-structure constant at zero energy. Moreover, as the energy scale increases, the strength of the electromagnetic interaction approaches that of the other two fundamental interactions, a fact 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 makes quantum electrodynamics inconsistent beyond the perturbative expansions.

  History

Arnold Sommerfeld introduced the fine-structure constant in 1916, as part of his theory of the relativistic deviations of atomic spectral lines from the predictions of the Bohr model. The first physical interpretation of the fine-structure constant 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.[9] 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.

The fine-structure constant so intrigued physicist Wolfgang Pauli that he collaborated with psychologist Carl Jung in an extraordinary quest to understand its significance.[10]

  Is the fine-structure constant actually constant?

While the fine-structure constant is known to approach 1/128 at interaction energies above 80 GeV,[11] physicists have pondered for many years whether the fine-structure constant is in fact constant, i.e., whether or not its value differs by location and over time. Specifically, a varying α has been proposed as a way of solving problems in cosmology and astrophysics.[12][13][14][15] More recently, theoretical interest in varying constants (not just α) has been motivated by string theory and other such proposals for going beyond the Standard Model of particle physics. The first experimental tests of this question examined the spectral lines of distant astronomical objects, and the products of radioactive decay in the Oklo natural nuclear fission reactor. The findings were consistent with no change.[16][17][18][19][20][21]

More recently, improved technology has made it possible to probe the value of 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 α.[22][23][24][25] Using the Keck telescopes and a data set of 128 quasars at redshifts 0.5 < z < 3, Webb et al. found that their spectra were consistent with a slight increase in α over the last 10–12 billion years. Specifically, they found that

\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}.

In 2004, a smaller study of 23 absorption systems by Chand et al., using the Very Large Telescope, found no measureable variation:[26][27]

 \frac{\Delta \alpha}{\alpha_\mathrm{em}}= \left(-0.6\pm 0.6\right) \times 10^{-6}.

However, in 2007 simple flaws were identified in the analysis method of Chand et al., discrediting those results.[28][29] Nevertheless, systematic uncertainties are difficult to quantify and so the Webb et al. results still need to be checked by independent analysis, using quasar spectra from different telescopes.[citation needed]

King et al. have used Markov Chain Monte Carlo methods to investigate the algorithm used by the UNSW group to determine \Delta\alpha/\alpha from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for \Delta\alpha/\alpha for particular models.[30] This suggests that the statistical uncertainties and best estimate for \Delta\alpha/\alpha 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 α has changed in the past 2 billion years by 4.5 parts in 108. 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.[31][32][33][34]

In 2007, Khatri and Wandelt of the University of Illinois at Urbana-Champaign realized that the 21 cm hyperfine transition in neutral hydrogen of the early Universe leaves a unique absorption line imprint in the cosmic microwave background radiation.[35] They proposed using this effect to measure the value of 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 109 (4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on α is strongly dependent upon effective integration time, going as t−1/2. The European LOFAR radio telescope would only be able to constrain Δα/α to about 0.3%.[35] The collecting area required to constrain Δα/α to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at the present time.

In 2008, Rosenband et al.[36] used the frequency ratio of Al+ and Hg+ in single-ion optical atomic clocks to place a very stringent constraint on the present time variation of α, namely Δα̇/α = −1.6±2.3×10−17 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[37] 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.

In September 2010 researchers from Australia said they had identified a dipole-like structure in the fine-structure constant across the observable universe, using data on quasars 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, 10 billion years ago. Similarly, the constant appeared to have been smaller by a similar fraction in the northern direction, billions of years ago.[38][39][40]

In September and October 2010, after Webb's released research, physicists Chad Orzel and Sean M. Carroll suggested different approaches of how Webb's observations may be wrong. Orzel argues 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 triangles in the plotted graph of the quasars are so well-aligned (triangles, being the 3-omega of the data). On the other hand, Carroll suggested 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.[41][42]

In October 2011, Webb et al. reported[43] a variation in 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. "[I]ndependent VLT and Keck samples give consistent dipole directions and amplitudes...."

  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 α to change by 4%, stellar fusion would not produce carbon, so that carbon-based life would be impossible. If α were > 0.1, stellar fusion would be impossible and no place in the universe would be warm enough for life as we know it.[44]

  Numerological explanations

As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long fascinated physicists. 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:

There is a most profound and beautiful question associated with the observed coupling constant, 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!

Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 0-691-08388-6 

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.[45] This led him in 1929 to conjecture that its reciprocal was precisely the integer 137. Other physicists neither adopted this conjecture nor accepted his arguments but by the 1940s experimental values for 1/α deviated sufficiently from 137 to refute Eddington's argument.[46] Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. For example, the mathematician James Gilson suggested (earliest archive.org entry dated December 2006 [1]), that the fine-structure constant has the value:

 \alpha = \frac{\cos \left(\pi/137 \right)}{137} \ \frac{\tan \left(\pi/(137 \cdot 29) \right)}{\pi/(137 \cdot 29)} \approx \frac{1}{137.0359997867},

29 and 137 being the 10th and 33rd prime numbers. In 2007, the difference between the CODATA value for α and this theoretical value was about 3×10−11, about 6 times the standard error for the measured value, but as of 2010 CODATA correction the difference became much greater.

  Quotes

The mystery about α is actually a double mystery. The first mystery – the origin of its numerical value α ≈ 1/137 has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized.
—Malcolm H. Mac Gregor, M.H. MacGregor (2007). The Power of Alpha. World Scientific. p. 69. ISBN 978-981-256-961-5 
If alpha [the fine-structure constant] 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.
—Max Born, A.I. Miller (2009). Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung. W.W. Norton & Co. p. 253. ISBN 978-0-393-06532-9 

  See also

  References

  1. ^ "CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2011. http://physics.nist.gov/cgi-bin/cuu/Value?alphinv. Retrieved 2011-06-23. 
  2. ^ "CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2011. http://physics.nist.gov/cgi-bin/cuu/Value?alph. Retrieved 2011-06-23. 
  3. ^ a b c P.J. Mohr, B.N. Taylor, and D.B. Newell (2011), "The 2010 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 6.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. Available: http://physics.nist.gov/constants [Thursday, 02-Jun-2011 21:00:12 EDT]. National Institute of Standards and Technology, Gaithersburg, MD 20899.
  4. ^ D. Hanneke, S. Fogwell, G. Gabrielse (2008). "New Measurement of the Electron Magnetic Moment and the Fine Structure Constant". Physical Review Letters 100 (12): 120801. Bibcode 2008PhRvL.100l0801H. DOI:10.1103/PhysRevLett.100.120801. PMID 18517850. http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2008/HarvardElectronMagneticMoment2008.pdf. 
  5. ^ Rym Bouchendira; Pierre Cladé; Saïda Guellati-Khélifa; François Nez; François Biraben (2010). "New determination of the fine-structure constant and test of the quantum electrodynamics". Physical Review Letters 106 (8). arXiv:1012.3627. Bibcode 2011PhRvL.106h0801B. DOI:10.1103/PhysRevLett.106.080801. 
  6. ^ "Fine Structure Constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 2006. http://physics.nist.gov/cgi-bin/cuu/Value?alph. Retrieved 11 September 2009. 
  7. ^ G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom (2007). "Erratum: New Determination of the Fine Structure Constant from the Electron g Value and QED [Phys. Rev. Lett. 97, 030802 (2006)]". Physical Review Letters 99 (3): 039902. Bibcode 2007PhRvL..99c9902G. DOI:10.1103/PhysRevLett.99.039902. 
  8. ^ P.J. Mohr, B.N. Taylor, D.B. Newell (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Reviews of Modern Physics 80 (2): 633. Bibcode 2008RvMP...80..633M. DOI:10.1103/RevModPhys.80.633. http://physics.nist.gov/cuu/Constants/RevModPhys_80_000633acc.pdf. 
  9. ^ "Introduction to the Constants for Nonexperts – Current Advances: The Fine-Structure Constant and Quantum Hall Effect". The NIST Reference on Constants, Units, and Uncertainty. NIST. http://physics.nist.gov/cuu/Constants/alpha.html. Retrieved 11 April 2009. 
  10. ^ P. Varlaki, L. Nadai, J. Bokor (2008). "Number Archetypes and Background Control Theory Concerning the Fine Structure Constant". Acta Polytechnica Hungarica 5 (2): 71. http://uni-obuda.hu/journal/Varlaki_Nadai_Bokor_14.pdf. 
  11. ^ P.J. Mohr (NIST) (2010). "Physical Constants.". Particle Data Group. http://pdg.lbl.gov/2011/reviews/rpp2011-rev-phys-constants.pdf. Retrieved 21 December 2011. 
  12. ^ E.A. Milne (1935). Relativity, Gravitation and World Structure. Clarendon Press. 
  13. ^ P.A.M. Dirac (1937). "The Cosmological Constants". Nature 139 (3512): 323. Bibcode 1937Natur.139..323D. DOI:10.1038/139323a0. 
  14. ^ G. Gamow (1967). "Electricity, Gravity, and Cosmology". Physical Review Letters 19 (13): 759. Bibcode 1967PhRvL..19..759G. DOI:10.1103/PhysRevLett.19.759. 
  15. ^ G. Gamow (1967). "Variability of Elementary Charge and Quasistellar Objects". Physical Review Letters 19 (16): 913. Bibcode 1967PhRvL..19..913G. DOI:10.1103/PhysRevLett.19.913. 
  16. ^ J.-P. Uzan (2003). "The Fundamental Constants and Their Variation: Observational Status and Theoretical Motivations". Reviews of Modern Physics 75 (2): 403–455. arXiv:hep-ph/0205340. Bibcode 2003RvMP...75..403U. DOI:10.1103/RevModPhys.75.403. 
  17. ^ J.-P. Uzan (2004). "Variation of the Constants in the Late and Early Universe". arXiv:astro-ph/0409424 [astro-ph]. 
  18. ^ K. Olive, Y.-Z. Qian (2003). "Were Fundamental Constants Different in the Past?". Physics Today 57 (10): 40–45. Bibcode 2004PhT....57j..40O. DOI:10.1063/1.1825267. 
  19. ^ J.D. Barrow (2002). The Constants of Nature: From Alpha to Omega—the Numbers That Encode the Deepest Secrets of the Universe. Vintage. ISBN 0-09-928647-5. 
  20. ^ J.-P. Uzan, B. Leclercq (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Springer Praxis. ISBN 978-0-387-73454-5. 
  21. ^ F. Yasunori (2004). "Oklo Constraint on the Time-Variability of the Fine-Structure Constant". Astrophysics, Clocks and Fundamental Constants. Lecture Notes in Physics. Springer Berlin. pp. 167–185. ISBN 978-3-540-21967-5. http://www.springerlink.com/content/20dt5p8t8ene319q/. 
  22. ^ J.K. Webb et al. (1999). "Search for Time Variation of the Fine Structure Constant". Physical Review Letters 82 (5): 884–887. arXiv:astro-ph/9803165. Bibcode 1999PhRvL..82..884W. DOI:10.1103/PhysRevLett.82.884. 
  23. ^ M.T. Murphy et al. (2001). "Possible evidence for a variable fine-structure constant from QSO absorption lines: motivations, analysis and results". Monthly Notices of the Royal Astronomical Society 327 (4): 1208. arXiv:astro-ph/0012419. Bibcode 2001MNRAS.327.1208M. DOI:10.1046/j.1365-8711.2001.04840.x. 
  24. ^ J.K. Webb et al. (2001). "Further Evidence for Cosmological Evolution of the Fine Structure Constant". Physical Review Letters 87 (9): 091301. arXiv:astro-ph/0012539. Bibcode 2001PhRvL..87i1301W. DOI:10.1103/PhysRevLett.87.091301. PMID 11531558. 
  25. ^ M.T. Murphy, J.K. Webb, V.V. Flambaum (2003). "Further Evidence for a Variable Fine-Structure Constant from Keck/HIRES QSO Absorption Spectra". Monthly Notices of the Royal Astronomical Society 345 (2): 609. arXiv:astro-ph/0306483. Bibcode 2003MNRAS.345..609M. DOI:10.1046/j.1365-8711.2003.06970.x. 
  26. ^ H. Chand et al. (2004). "Probing the Cosmological Variation of the Fine-Structure Constant: Results Based on VLT-UVES Sample". Astronomy & Astrophysics 417 (3): 853. arXiv:astro-ph/0401094. Bibcode 2004A&A...417..853C. DOI:10.1051/0004-6361:20035701. 
  27. ^ R. Srianand et al. (2004). "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". Physical Review Letters 92 (12): 121302. arXiv:astro-ph/0402177. Bibcode 2004PhRvL..92l1302S. DOI:10.1103/PhysRevLett.92.121302. PMID 15089663. 
  28. ^ M.T. Murphy, J.K. Webb, V.V. Flambaum (2007). "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"". Physical Review Letters 99 (23): 239001. Bibcode 2007PhRvL..99w9001M. DOI:10.1103/PhysRevLett.99.239001. 
  29. ^ M.T. Murphy, J.K. Webb, V.V. Flambaum (2008). "Revision of VLT/UVES Constraints on a Varying Fine-Structure Constant". Monthly Notices of the Royal Astronomical Society 384 (3): 1053. arXiv:astro-ph/0612407. Bibcode 2008MNRAS.384.1053M. DOI:10.1111/j.1365-2966.2007.12695.x. 
  30. ^ J. King, D. Mortlock, J. Webb, M. Murphy (2009). "Markov Chain Monte Carlo methods applied to measuring the fine-structure constant from quasar spectroscopy". arXiv:0910.2699 [astro-ph]. 
  31. ^ R. Kurzweil (2005). The Singularity Is Near. Viking Penguin. pp. 139–140. ISBN 0-670-03384-7. 
  32. ^ S.K. Lamoreaux, J.R. Torgerson (2004). "Neutron Moderation in the Oklo Natural Reactor and the Time Variation of Alpha". Physical Review D 69 (12). arXiv:nucl-th/0309048. Bibcode 2004PhRvD..69l1701L. DOI:10.1103/PhysRevD.69.121701. 
  33. ^ E.S. Reich (30 June 2004). "Speed of Light May Have Changed Recently". New Scientist. http://www.newscientist.com/article/dn6092-speed-of-light-may-have-changed-recently.html. Retrieved 30 January 2009. 
  34. ^ "Scientists Discover One Of The Constants Of The Universe Might Not Be Constant". ScienceDaily. 12 May 2005. http://www.sciencedaily.com/releases/2005/05/050512120842.htm. Retrieved 30 January 2009. 
  35. ^ a b R. Khatri, B.D. Wandelt (2007). "21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant". Physical Review Letters 98 (11): 111301. arXiv:astro-ph/0701752. Bibcode 2007PhRvL..98k1301K. DOI:10.1103/PhysRevLett.98.111301. PMID 17501040. 
  36. ^ T. Rosenband et al. (2008). "Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place". Science 319 (5871): 1808–12. Bibcode 2008Sci...319.1808R. DOI:10.1126/science.1154622. PMID 18323415. 
  37. ^ J.D. Barrow, H.B. Sandvik, J. Magueijo (2001). "The Behaviour of Varying-Alpha Cosmologies". Phys.Rev.D65:063504,2002. arXiv:astro-ph/0109414. 
  38. ^ H. Johnston (2 September 2010). "Changes spotted in fundamental constant". Physics World. http://physicsworld.com/cws/article/news/43657. Retrieved 11 September 2010. 
  39. ^ J.K.Webb et al.; King, J. A.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B. (23 August 2010). "Evidence for spatial variation of the fine-structure constant". Physical Review Letters. arXiv:1008.3907. Bibcode 2011PhRvL.107s1101W. DOI:10.1103/PhysRevLett.107.191101. 
  40. ^ J. A. King (2010). Searching for variations in the fine-structure constant and the proton-to-electron mass ratio using quasar absorption lines (PhD thesis). University of New South Wales. http://handle.unsw.edu.au/1959.4/50886. 
  41. ^ Chad Orzel (September 14). "Why I'm skeptical about changing Fine-Structure constant". http://scienceblogs.com/principles/2010/09/_httpksjtrackermitedu20100907e.php. 
  42. ^ Sean Corroll (October 18). "The fine-structure constant is probably constant". http://blogs.discovermagazine.com/cosmicvariance/2010/10/18/the-fine-structure-constant-is-probably-constant/. 
  43. ^ J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, and M. B. Bainbridge (2011). "Indications of a Spatial Variation of the Fine Structure Constant". Physical Review Letters 107 (19). Bibcode 2011PhRvL.107s1101W. DOI:10.1103/PhysRevLett.107.191101. 
  44. ^ J.D. Barrow (2001). "Cosmology, Life, and the Anthropic Principle". Annals of the New York Academy of Sciences 950 (1): 139–153. Bibcode 2001NYASA.950..139B. DOI:10.1111/j.1749-6632.2001.tb02133.x. 
  45. ^ A.S Eddington (1956). "The Constants of Nature". In J.R. Newman. The World of Mathematics. 2. Simon & Schuster. pp. 1074–1093. 
  46. ^ H. Kragh (2003). "Magic Number: A Partial History of the Fine-Structure Constant". Archive for History of Exact Sciences 57 (5): 395. DOI:10.1007/s00407-002-0065-7. 

  External links

   
               

 

All translations of Fine-structure_constant


sensagent's content

  • definitions
  • synonyms
  • antonyms
  • encyclopedia

Dictionary and translator for handheld

⇨ New : sensagent is now available on your handheld

   Advertising ▼

sensagent's office

Shortkey or widget. Free.

Windows Shortkey: sensagent. Free.

Vista Widget : sensagent. Free.

Webmaster Solution

Alexandria

A windows (pop-into) of information (full-content of Sensagent) triggered by double-clicking any word on your webpage. Give contextual explanation and translation from your sites !

Try here  or   get the code

SensagentBox

With a SensagentBox, visitors to your site can access reliable information on over 5 million pages provided by Sensagent.com. Choose the design that fits your site.

Business solution

Improve your site content

Add new content to your site from Sensagent by XML.

Crawl products or adds

Get XML access to reach the best products.

Index images and define metadata

Get XML access to fix the meaning of your metadata.


Please, email us to describe your idea.

WordGame

The English word games are:
○   Anagrams
○   Wildcard, crossword
○   Lettris
○   Boggle.

Lettris

Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.

boggle

Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !

English dictionary
Main references

Most English definitions are provided by WordNet .
English thesaurus is mainly derived from The Integral Dictionary (TID).
English Encyclopedia is licensed by Wikipedia (GNU).

Copyrights

The wordgames anagrams, crossword, Lettris and Boggle are provided by Memodata.
The web service Alexandria is granted from Memodata for the Ebay search.
The SensagentBox are offered by sensAgent.

Translation

Change the target language to find translations.
Tips: browse the semantic fields (see From ideas to words) in two languages to learn more.

last searches on the dictionary :

4067 online visitors

computed in 0.140s

   Advertising ▼

I would like to report:
section :
a spelling or a grammatical mistake
an offensive content(racist, pornographic, injurious, etc.)
a copyright violation
an error
a missing statement
other
please precise:

Advertize

Partnership

Company informations

My account

login

registration

   Advertising ▼