The fine structure constant (approx. 1/137) is the value of Coulomb's constant in Planck units.
kC = 1/137 Planck force (Planck length)2/(Elementary charge)2.
This is essentially what is meant by it's conventional description as "the coupling constant for the electromagnetic force." In symbols:
kC = 1/137 FP l P2/e2.
Equivalence of this to an older definition is shown at the bottom of the page. The conventional symbol for the constant is alpha. The NIST website has a well-written fairly up-to-date essay on alpha.
http://physics.nist.gov/cuu/Constants/alpha.html
This is part of the NIST essay "Introduction to the constants for nonexperts" which is mostly adapted from a 1971 article by Barry Taylor but which has been updated in places. I quote: "Our view of the fine-structure constant has changed markedly since Sommerfeld introduced it over 80 years ago. We now consider alpha the coupling constant for the electromagnetic force and similar to those for the other three known fundamental forces or interactions of nature: the gravitational force, the weak nuclear force, and the strong nuclear force..." [I have added the emphasis.]
Alpha applies at distances within the atomic nucleus as well as interatomic distances and at macroscopic scale. Over this wide range of distances there is so-called "vacuum polarization" screening, the screening by virtual particle pairs which buffers and reduces electromagnetic interaction. At high energies produced experimentally in accelerators interactions can be studied at distances so small that this screening partly breaks down and the effective values of alpha are greater than 1/137. Some people like to say that "alpha is bigger at small distances" and the NIST article talks about this. Such "small distances" are roughly one percent of the Compton wavelength of a proton — orders of magnitude less than the width of familiar nuclear building blocks — and represent a rather special area of interest. There is also recently publicized evidence of a fraction of a percent different alpha in the early universe. (One can see the effect of alpha in hydrogen lines, so one can look at very old light to see if there has been variation over time.) Such exceptions to constancy notwithstanding, alpha is well-defined, fundamental to much of physics and chemistry, and one of the most precisely measured physical constants. The NIST currently gives alpha inverse as 137.035 999 76 with standard uncertainty 0.000 000 50. The relative standard uncertainty 3.7 x 10-9 is unusually small.
http://physics.nist.gov/cgi-bin/cuu/Value?alphinv|search_for=abbr_in!
The fine structure constant was first identified and named in 1916 by Arnold Sommerfeld, Heisenberg's teacher, who was studying fine patterns in spectral lines. Alpha is central to Quantum Electrodynamics. Its value is unexplained. Richard Feynmann made the famous remark that every physicist should have a piece of paper with alpha on it tacked to the wall (as a reminder to try to understand why it is what it is.)
For people who like algebra:
Planck force (Planck length)2 = h-bar c
This follows from basic facts about Planck quantities, namely:
Planck force = c4/G
(Planck length)2 = h-bar G/c3.
As a consequence we have that
kC = alpha Planck force (Planck length)2/e2 = alpha h-bar c/e2.
and this is evidently equivalent to the usual definition of alpha, namely:
alpha = kCe2/h-bar c
In the usual definition one often sees the Coulomb constant written as (4pi epsilono)-1 instead of kC.
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Copyright © 2002 by Leonard Cottrell. All rights reserved.