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Alpha – The Fine Structure Constant

Alpha- The Fine Structure Constant

Alpha – The Fine Structure Constant “[1/137] is one of the greatest damn mysteries of physics: a magic number that comes to use 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.’” –Richard P. Feynman, QED

The fine structure constant is a unit less physical parameter that has the approximate value of 1/137. It is the measure of the strength of the electromagnetic force. It is usually denoted by the lower case Greek letter, alpha. It was first introduced in 1916 by Arnold Sommerfeld (a teacher of Werner Heisenberg)  in order to explain the fine structure of energy levels found in the hydrogen atom. The fine structure constant is defined as:


The physical origin of this constant pertains to the closely spaced groups of optical spectrum lines of gases, like hydrogen. Optical spectrum lines are unique in a particular element because they have their own specific energy levels; it is like an element’s “finger print”.

Our understanding of the fine structure constant has evolved since its initial introduction by Sommerfeld. Alpha is now considered to be the coupling constant for the electromagnetic force, just like there are coupling constants for the gravitational force, the weak nuclear force, and the strong nuclear force.

The fine structure constant is quite mysterious and has baffled many physicists, mathematicians and anybody else who has been concerned because there are several bizarre numerical coincidences involving the digits 137. Especially coincidences involving other unit less mathematical constants such as e, pi, and the golden ratio. Here are a few interesting examples of numerical coincidences (note that these are approximate values):

Here is a comical quote from Leon Lederman’s book The God Particle that pokes fun at Wolfgang Pauli’s obsession with the number 137:

“One of the wonderful (but unverified) stories in physics emphasizes the importance of 137 as well as illustrating the arrogance of theorists. As indicated by this story, a remarkable Austrian scientific physicist of Swiss influence, Wolfgang Pauli, went to paradise, we are guaranteed, and, as a result of his greatness in material science, was given a group of people with God.

‘Pauli, you’re allowed one question. What do you want to know? Pauli immediate asked the one question that he has labored in vain to answer for the last decade of his life. “Why is alpha equivalent to one more than one hundred thirty-seven?”

God grinned, grabbed the chalk, and started composing conditions on the chalkboard. She turned to Pauli, who waved his hand. ‘Das ist falsch! [That’s baloney!]”

This anecdote not only illustrates the arrogance of some theorists as Lederman pointed out, but  perhaps how absurd nature may seem to us because it does not always conform to our understanding and what we perceive as reason. Or ironically, God not knowing the answer and Pauli calls Her on it.

Oddly enough, there have been recent discoveries that the fine structure constant, may not be so constant.

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