Fine Structure Constant

1 / 137.03597

These days the word genius is applied to just about everything, football, cooking, acting, you name it someone will say "oh yeah that guy, absolute genius, he's amazing". This is a shame because for me it actually takes something away from people who really are geniuses.

A Genius (plural geniuses) is something or someone embodying exceptional intellectual ability, creativity or originality typically to a degree that is associated with the achievement of unprecedented insight.

In other words, something or someone truly, truly amazing. Someone who will be remembered long after they have gone on their way. Newton, Mozart Einstein, The Beatles and for me and many others... Richard Feynman.

The reason why I love Feynman is not because he was absolutely fantastic at Physics, or that he put together some of the greatest Physics lecture notes ever. It's not that he could explain the most complicated ideas really clearly, though he could. It was that fact that he was not afraid to say that he didn't know things in Physics. In fact he often drew attention to them.

He won the Nobel Prize for his work on Quantum Electro Dynamics, a brilliant theory that has so far stood the test of time. It has given Physics some of the most accurate predictions ever and these have been backed up time and again by experiment. It really is brilliant. Now, you would think that having come up with something this clever, you would spend your time giving yourself a little pat on the back and saying "yep, hit that mark with that one", instead, Feynman says this...

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 fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where 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." 

Oh cool is that?! Wins a Nobel prize and then points out that there is a number used in a part of his theory, a number that he as not got the first clue about where it comes from or what it is means?!

How can you not love him?

So, what is this magic number? It is called the fine structure constant and has an approximate value of 1/137. It was first introduced to the world in 1916 by Arnold Sommerfeld.  It is defined by the equation below

where:

• e is the elementary charge;
• ħ = h/2π, known as the reduced Planck constant
• c is the speed of light in a vacuum

e, is the charge that an electron has. We don't know why it has this charge, it just does. c,  we don't know why light travels at this speed, it just does. h, Plancks constant, or the proprotionality constant, relates the frequency of light to energy, again we have no idea why it has the value it does.

So to summarise, we have 3 values that we don't really know why they have the values they do. But more interestingly when we multiple the charge on an electron by itself and divide by the speed of light and then divide by Plancks constant you end up with a number 1/137. A unitless constant which props up in various place in Physics. Can't help thinking that once we crack this fella we will be making a real big break through.