Fine structure constant

Physical constant
Surname	Fine structure constant
Formula symbol	${\displaystyle \alpha }$
Size type	dimensionless
value
SI	7th.297 352 5693 (11)e-3
Uncertainty  (rel.)	1.5e-10
Relation to other constants
${\displaystyle \alpha ={\frac {e^{2}}{4\pi \,\varepsilon _{0}\,\hbar \,c}}}$(in SI )
Sources and Notes
Source SI value: CODATA 2018 ( direct link )

Sommerfeld bust, Munich, LMU , Theresienstr. 37. Below the bust is the formula of the fine structure constant (given in the Gaussian system of units (ESU), which is often preferred in theoretical physics.)

The fine structure constant is a physical constant of the dimension number that indicates the strength of the electromagnetic interaction . It was in 1916 by Arnold Sommerfeld , the theoretical explanation of the splitting ( fine structure ) of spectral lines in the spectrum of the hydrogen atom introduced, so they will Sommerfeld constant or Sommerfeld fine structure constant called. ${\displaystyle \alpha }$

In quantum electrodynamics , the fine structure constant stands for the strength with which the exchange particle of the electromagnetic interaction, the photon , couples to an electrically charged elementary particle , for example an electron . It is therefore the electromagnetic coupling constant that determines how strong the (repulsive or attractive) forces are between electrically charged particles and how fast the electromagnetically caused processes, e.g. B. the spontaneous emission of light.

value

The value recommended by the Committee on Data for Science and Technology is:

${\displaystyle \alpha \ =7{,}297\,352\,569\,3(11)\cdot 10^{-3}\ =\ {\frac {1}{137{,}035\,999\,084\,(21)}},}$

where the bracketed digits denote the uncertainty in the last digits of the value. This uncertainty is given as the estimated standard deviation of the given numerical value from the actual value.

The most accurate value so far (accuracy ) was determined in 2018 with atomic interferometry : ${\displaystyle 2\cdot 10^{-10}}$

${\displaystyle {\frac {1}{\alpha }}=137{,}035\,999\,046(27)}$

The fine structure constant is linked to the elementary charge , Planck's quantum of action , the speed of light and the electric field constant as follows: ${\displaystyle e}$ ${\displaystyle h}$ ${\displaystyle c}$ ${\displaystyle \varepsilon _{0}}$

${\displaystyle \alpha \ =\ {\frac {1}{2c\,\varepsilon _{0}}}\;{\frac {e^{2}}{h}}=\ {\frac {1}{4\pi \,c\,\varepsilon _{0}}}\;{\frac {e^{2}}{\hbar \,}}.}$

The constants and have been assigned a fixed value in the International System of Units (SI). The fine structure constant is therefore linked directly and with identical measurement accuracy to the electrical field constant. ${\displaystyle e,h}$ ${\displaystyle c}$

Before the redefinition of the basic units in the SI in 2019, and were firmly defined, and, on the other hand, variables that had to be determined experimentally. For the measurement of the fine structure constant it was used that the reciprocal value of the von Klitzing elementary resistance can be determined from the quantum Hall effect and can be measured very precisely. ${\displaystyle c}$ ${\displaystyle \varepsilon _{0}}$ ${\displaystyle h}$ ${\displaystyle e}$ ${\displaystyle e^{2}/h}$

Comparison of the basic forces of physics

The strength of the electromagnetic interaction can only be compared directly with gravity , since both forces obey the same law of distance : The strength of the force decreases with the square of the distance.

If one wants to give the strength of the gravitation between two elementary particles, as indicated by the gravitational constant , in a dimensionless number like the fine structure constant, then this value depends on the mass of the two elementary particles. A larger dimensionless number is obtained for the strength between two relatively massive protons than for the strength between two electrons. But even for the attraction between two protons one only gets:

${\displaystyle \alpha _{G}\ ={\frac {G\,m_{p}^{2}}{\hbar \,c}}\ \approx \ 5{,}9\cdot 10^{-39}.}$

If you compare this value with the fine structure constant, which indicates the strength of the electrical repulsion between the two protons, you can see that the electromagnetic interaction is about 10 ³⁶ times stronger than gravity ( hierarchy problem ).

The strong interaction has an energy-dependent ('running') coupling constant. The comparison value for the force between two nucleons in the atomic nucleus is

${\displaystyle \alpha _{s}\ \cong \ 1.}$

If one compares the decay rates from strong and weak decays, one obtains a coupling constant of for the weak force

${\displaystyle \alpha _{w}\ =\ 10^{-7}\ \ldots \ 10^{-6}.}$

Temporal constancy

The answer to the question of whether the fine structure constant varies over time or has not changed since the Big Bang is of considerable theoretical interest. Previous considerations and measurements have so far not shown any significant change .

Experiments and measurements are carried out on very different time scales:

• Laboratory experiments, for example with atomic clocks , can limit the relative change over time to a maximum of (-1.6 ± 2.3) × 10 ⁻¹⁷ / year. ${\displaystyle \alpha }$
• The observation of absorption lines of quasars improves this accuracy by one to two orders of magnitude, although the treatment of systematic errors is difficult and so far both significantly positive and zero results have been published. A final evaluation of all data is still pending.
• The consideration of the primordial nucleosynthesis does not reveal any changes for times immediately after the Big Bang, but with greater uncertainty.
• The natural reactor Oklo and the isotope distribution in meteorites were also used for estimations.

Energy dependence

In elementary particle physics , the fine structure constant also depends on the energy. The fine structure constant for the mass of the Z boson is (91 GeV). The interaction is shielded by electron- positron pairs that exist briefly out of the vacuum (see vacuum fluctuation ). The particles get closer at higher energies and thus there are fewer electron-positron pairs between them, which shield the interaction. ${\displaystyle \alpha \approx {\frac {1}{128}}.}$

In all conventional applications, e.g. B. in spectroscopy , the energies are typically only a few eV , which means that the energy dependence is negligible.

Occurrence in physics

• Fine structure splitting in atoms . ${\displaystyle \sim (Z\cdot \alpha )^{2}}$
• Spectral absorption of a graphene layer , . ${\displaystyle \sim \pi \cdot \alpha }$

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.

"It has been a mystery since it was discovered over fifty years ago, and all good theoretical physicists hang this number on their walls and worry about it."

- Richard P. Feynman

Web links

Commons : Fine structure constant  - collection of images, videos and audio files

Individual evidence and receipts

1. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed June 6, 2019 .  Value for . ${\displaystyle \alpha }$
2. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed June 6, 2019 .  Value for . ${\displaystyle {\frac {1}{\alpha }}}$
3. ↑ Richard H. Parker, Chenghui Yu, Weicheng Zhong, Brian Estey, Holger Müller: Measurement of the fine-structure constant as a test of the Standard Model, Science 360 ​​(2018) 191-95, abstract
4. ↑ Rainer Scharf: Record measurement of the fine structure constants , Pro Physik, April 13, 2018
5. ^ Rohlf, James William: Modern Physics from a to Z0 , Wiley 1994
6. ↑ John D. Barrow : Varying Constants , Phil. Trans. Roy. Soc. Lond. A363 (2005) 2139-2153, online
7. ↑ Jean-Philippe Uzan: The fundamental constants and their variation: observational status and theoretical motivations , Rev.Mod.Phys. 75 (2003) 403, online
8. ↑ T. Rosenband: Frequency Ratio of Al + and Hg + Single-Ion Optical Clocks; Metrology at the 17th Decimal Place , Science, Vol 319, March 28, 2008
9. ↑ MT Murphy, JK Webb, VV Flambaum: Further Evidence for a Variable Fine-Structure Constant from Keck / HIRES QSO Absorption Spectra . In: Monthly Notices of the Royal Astronomical Society . 345, 2003, p. 609. arxiv : 1008.3907 . doi : 10.1046 / j.1365-8711.2003.06970.x .
10. ^ R. Quast, D. Reimers, SA Levshakov: Probing the variability of the fine-structure constant with the VLT / UVES , Astron. Astrophys. 415 (2004) L7, online
11. ^ HV Klapdor-Kleingrothaus , A. Staudt: Particle physics without accelerators . Teubner, 1995, ISBN 3-519-03088-8
12. ↑ Yasunori Fujii: Oklo Constraint on the Time-Variability of the Fine-Structure Constant , in: SG Karshenboim and E. Peik (eds.), Astrophysics, Clocks and Fundamental Constants , Lecture Notes in Physics 648, Springer 2004, p. 167 -85, doi: 10.1007 / 978-3-540-40991-5_11 , arxiv: hep-ph / 0311026
13. ↑ Christoph Berger: Elementarteilchenphysik, From the basics to modern experiments, Springer 2006, 2nd edition, p. 194
14. ^ QED - The strange theory of light and matter, Princeton University Press 1985, p. 129