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References:
Textbook chapter on Fine Structure: https://t.ly/PLM4
Sommerfeld's original paper: https://t.ly/qrAF
Good Wiki description: https://t.ly/f4iK

Chapters:
0:00 Historical context of Fine Structure Constant
2:54 What is the interpretation of Fine Structure Constant?
4:25 How is alpha useful?
6:44 How Arnold Sommerfeld found it
10:04 How is alpha measured?
10:36 Why is 1/137 significant?
12:40 Where did fine structure constant come from?
13:50 Fine Structure constant is NOT constant!

Summary:
This constant represented by the Greek letter alpha is just a dimensionless number, so no matter what units you use, it will always have the same value, about 1/137. If it was different by just 4%, life may not exist. What is the Fine Structure Constant? What does it mean? And why is it important?

At one time it was believed to be exactly 1/137, but today we have measured it more precisely, and it is not exactly that. it is now one of the most precisely measured constants. There is more than one way to interpret it. It is the ratio of the energy needed to overcome the electrostatic repulsion of two electrons, and the energy of a photon with the wavelength lambda λ.

The simplest way to think of it is the ration of the speed of an electron in a classical orbit to the speed of light. In other words, the speed of an electron orbiting an atom is about 1/137th the speed of light.

The number is directly related to the strength of the electromagnetic force. The higher the value, the greater the strength of attraction between an electron and a proton, and, the greater the repulsion between two of the same charges. One way to think of the fine structure constant is like coulomb’s constant expressed in dimensionless units.

This constant is found everywhere because in our macro world, the two fundamental forces we directly experience most are gravity and electromagnetism. Since electromagnetism determines chemistry, alpha is critical for life.

In Feynman diagrams, Alpha is related to the probability that an electron will emit or absorb a photon. It was German theoretical physicist, Arnold Sommerfeld who introduced it in 1916 when he was expanding the Bohr model of the atom. Prior to his work, Niels Born's model of the atom failed to explain the observed light emission of atoms. The energy levels appeared to split into two, whereas Bohr's model only predicted one. Those additional levels were very close to each other. But they indicated that Bohr’s model was incomplete. Sommerfeld was able to show that there is finer structure to the atom, that it has suborbitals.

Alpha can be measured experimentally at cyclotron accelerators by accelerating an electron in a magnetic field, and measuring its magnetic moment. The electron acts like a spinning bar magnet. The magnetic moment is related to the strength and direction of the magnetic field created by this electron. The alpha value can then be figured out from this measurement.

Why is this number 1/137 so significant? First, it’s a small number. This means that electromagnetism is relatively weak at least compared to the strong nuclear force. Consequently, electrons orbit on average, at a substantial distance away from the proton, which allows electrons to be available for exchange with other atoms, so that chemistry can take place. And thus life is possible. However, this number is not too large, because otherwise atoms would not form in the first place.

In 1957, English astronomer Fred Hoyle and others found that the abundance of carbon in the universe could be explained only if the fine structure constant had a value that made the nuclei of helium atoms more likely to fuse to produce carbon nuclei than otherwise. They calculated that if this constant was different by 4%, Carbon and Oxygen may not have existed.

What determines the value of α? Some believe it was set at the moment of the big bang due to the initial conditions from quantum fluctuations. Others think that there are tiny hidden dimensions that fix the value.

Is alpha really a constant? No. Alpha changes as a function of the energy, according to QED. It is very close 1/137 at zero Kelvin which is roughly the temperature of the universe, and at room temperature. But at 10^15 Kelvin near the big bang, it would would have been around 1/127, but after a few minutes it would have reached 1/137 as today.
#finestructureconstant
So why do we then call it a constant, if it actually isn’t? The answer is for most practical purposes in our current universe, it is constant.