In physics, the fine-structure constant, also known as Sommerfeld’s constant, is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary particles. This constant is expressed by combining several other fundamental constants of nature: α= e²⁄4πεhc
where e is the charge on the electron, c is the speed of light, h is Planck’s constant and ε is the permittivity of free space.
α is the fine-structure constant = 1/137.035999173(35). This is the most precise value of α obtained experimentally ( as of 2012) based on a measurement of g ( Lande g-factor, the magnetic moment of the electron) using the “quantum cyclotron” apparatus, together with a calculation via the theory of QED that involved 12,672 tenth-order Feynman diagrams: This measurement of α has a precision of 0.25 parts per billion.
So the main question is how significant is this fine-structure constant ?
The importance of this constant is that it measures the strength of the electromagnetic interaction and because the constant is so small that QED works so amazingly well as a quantum theory of electromagnetism. Richard Feynman, the original developer of the theory of QED, referred to the fine-structure constant as follows:
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 50 years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know what 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 Feynman (1985). QED: the strange Theory of Light and Matter. Princeton University Press. p129. ISBN 0-691-08388-6.
Is the fine-structure constant actually constant?
Physicists have pondered about this question for a long time whether its value differs by location and over time. A varying α has been proposed for the purpose of solving problems in cosmology as well as in astrophysics. String theory and the physics beyond the Standard Model of particle physics are also expressing interest in whether the accepted physical constants actually vary. Some theories 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.
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.