The fine-structure constant

Arnold Sommerfeld

One of the latest scientific advances of 2020 was a new, more precise measurement of the fine-structure constant. The last value officially accepted in 2018 by the Committee for Data on Science and Technology (CODATA) is equal to 1/137.035999084. The value obtained in December 2020 is equal to 1/137.035999206. It will be seen that the difference with the previous value is very small and affects only the seventh decimal place.

But what is the fine-structure constant? It's a dimensionless constant, defined by the following formula:

Where α is the fine-structure constant, e the charge of the electron (the elemental charge), ε₀ the permittivity of vacuum, c the speed of light, and h the Planck constant.

What is the importance of the fine-structure constant? It gives a measure of the intensity of the electromagnetic interaction (attractions and repulsions) between charged particles. It was named in 1916 by its discoverer, Arnold Sommerfeld, who found it by studying the fine structure of the spectral lines of the hydrogen atom (hence its name). For that reason, it is also called sometimes the Sommerfeld constant.

Arthur Eddington

It is usual to give the inverse value of this constant, as we did above, which is very close to 137. In fact, Arthur Eddington proposed in 1929 that its value should be exactly equal to 137, but this conjecture was not confirmed by increasingly precise measurements of the constant.

The fine-structure constant has several interesting physical interpretations. Let's look at a few:

• The quotient between the energy required to overcome the electrostatic repulsion of two electrons located at a certain distance, and the energy of a photon whose wavelength is the same distance.
• The quotient between the speed of an electron in the first orbit of the hydrogen atom and the speed of light in vacuum.
• One of the 19 parameters that had to be adjusted in the standard model of particle physics, whose value is not fixed by the model (see this post in my blog).
• According to Richard Feynman, the inverse of this constant would be the maximum atomic number of an atom that would be compatible with the Bohr model, which means that it's not probable that we'll find elements with more than 137 protons in their nucleus (the maximum reached so far is 118).
• The quotient between the electrostatic repulsion and the gravitational attraction of two elementary particles with the Planck mass and a charge equal to that of the electron.

Interestingly (I say this because of the coincidence of names) the fine-structure constant is one of the constants that seems to have been finely tuned, so that the existence of life in the universe may be possible. It has been calculated that, if its value were different from its actual value by more than 4% in either direction, then either no carbon or no oxygen would be generated inside stars. Without carbon or oxygen, life as we know wouldn't be possible.

There is a debate, dating back to the eighties, about whether this constant is really constant, or whether its value has changed during the history of the universe. In 1999, after studying the spectral lines of distant galaxies and quasars, an Australian team asserted that the value of the fine-structure constant has varied by 5.7×10^-8 percent in the last 10 to 12 billion years. Other studies carried out later have not yielded totally convincing results, although the idea is spreading that perhaps this constant might not be as constant as was supposed. What no one has the faintest idea is about the reason for this change, assuming it is real, although string theory, which in forty years has not been able to find a single convincing confirmation, holds that many of the universal constants might, after all, not be constant at all.

The same post in Spanish

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Manuel Alfonseca