# Physics/Essays/Fedosin/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 7.29735257×10^{−3}.
^{[1]}

## Definition[edit]

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

where:

*e*is the elementary charge;*h*is the Planck constant;*ħ*=*h*/2π is the Dirac constant or reduced Planck constant;*c*is the speed of light in vacuum;*ε*_{0}is the electric constant;*m*_{S}is the Stoney mass;- is the gravitoelectric gravitational constant of selfconsistent gravitational constants;
- is the gravitational constant;
- µ
_{0}is the vacuum permeability; *k*_{e}is the Coulomb constant;*R*_{K}is the von Klitzing constant;*Z*_{0}is the impedance of free space;*q*_{p}is the Planck charge;*m*_{P}is the Planck mass;*M*_{p}is the mass of proton;*M*_{e}is the mass of electron;*G*_{s}is the strong gravitational constant;- β is the magnetic coupling constant.

In electrostatic cgs units, the unit of electric charge, the statcoulomb, is defined so that the Coulomb constant, *k*_{e}, or the permittivity factor, 4π*ε*_{0}, is 1 and dimensionless. Then the expression of the fine structure constant becomes the abbreviated

an expression commonly appearing in physics literature.

## Bohr model[edit]

In the Bohr model of hydrogen atom *α* is connected to the atom parameters for the first energy level

where is the speed of electron’s matter at the Bohr radius .

On the other hand

where is the Compton wavelength of the electron, is the classical electron radius, is the Rydberg constant for wavelength.

The next equation for *α* is

where is the magnetic flux quantum, is the electron magnetic flux for the first energy level, is the magnetic field in electron disc with flat surface area , and is velocity circulation quantum for electron.

Another equation for *α* is

where m^{2}/s

is the strong gravitational torsion flux quantum, which is related to proton and to its velocity circulation quantum,

and the strong gravitational electron torsion flux for the first energy level of hydrogen atom is

while is the gravitational torsion field of strong gravitation in electron disc.

The Bohr model for hydrogen system at the level of star introduces *α* in such way:

where and – mass of the star-analogue of proton and the planet-analogue of electron, respectively, – stellar Dirac constant, – characteristic speed of stars matter.

## See also[edit]

Many of articles in Vikiversity make reference to the fine structure constant, or discuss its relationship to other physical quantities. Examples are:

- Planck scale
- Stoney scale
- Strong gravitational constant
- Selfconsistent gravitational constants
- Selfconsistent electromagnetic constants
- Gravitational characteristic impedance of free space
- Magnetic coupling constant
- Monopoles

## References[edit]

- ↑ "CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2011. Retrieved 2011-06-23.