Fine-structure constant

The fine-structure constant is a fundamental physical constant. Scientists often call it the Sommerfeld constant. It is represented by the Greek letter alpha. This number quantifies the strength of the electromagnetic interaction. This interaction occurs between elementary charged particles. It describes how an elementary charge couples with the electromagnetic field. One unique feature is that it is a dimensionless quantity. This means the value does not change based on your system of units. It is a pure number that describes a rule of our universe.

To understand how this constant works, we must look at its mathematical definition. It is defined by several other physical constants. These include the elementary charge, which is the charge of an electron. It also involves the Planck constant and the reduced Planck constant. The speed of light and the electrical permittivity of space are also required. The magnetic permeability of space is part of the calculation too. By combining these specific values, scientists can determine the strength of electromagnetic coupling. Since 2019, most of these components have exact values in the SI system. Only the electrical permittivity of space lacks an exact defined value.

Different systems of measurement handle this constant in various ways. In the electrostatic CGS system, the constant is often expressed simply as alpha. High energy physics uses a system called natural units. In natural units, scientists set certain values for mass, distance, and time to one. This changes how the formula looks, but the constant remains the same. In atomic units, the constant is also expressed differently. Regardless of the system, the constant primarily determines the behavior of the elementary charge. It acts as a scaling factor for how particles interact through light and electricity.

The history of this constant began with precise observations of light. In 1887, Michelson and Morley measured the spectral lines of the hydrogen atom. They noticed tiny gaps in the light patterns. In 1916, Arnold Sommerfeld introduced the fine-structure constant to explain these gaps. He was extending the Bohr model of the atom. He included elliptical orbits and how mass changes with velocity. Later, Paul Dirac provided an exact formula in 1928. His work used a linear relativistic wave equation. Eventually, the theory of quantum electrodynamics, or QED, showed its true importance. QED explains how electrons and photons interact.

Measuring this constant requires incredible precision. The current recommended value for alpha is approximately 0.00729735256(13). Many scientists prefer to use the reciprocal, which is about 137.035999166. One way to measure it is through the anomalous magnetic moment of the electron. This is a tiny deviation in how an electron behaves in a magnetic field. Another method uses the quantum Hall effect. Scientists also use the A.C. Josephson effect and photon recoil in atom interferometry. In 2023, a measurement used a quantum cyclotron apparatus. This method reached a very high level of accuracy.

Scientists also study how the constant changes at different energy scales. In quantum electrodynamics, the strength of the interaction grows as energy increases. This is known as the renormalization group. At the energy scale of an electron's mass, we see the standard value. However, at much higher energies, such as the scale of a Z boson, the value changes. At about 90 GeV, the effective value is approximately 1/127. This increase is important for grand unification theories. These theories try to connect the different fundamental forces of nature. If the theory were perfectly exact, the constant might actually diverge at a point called the Landau pole.

Finally, researchers wonder if the constant changes over time or space. Some theories, like string theory, suggest physical constants might vary. Scientists have tested this by looking at distant quasars. A team led by John K. Webb claimed to find a slight increase in alpha over 10 to 12 billion years. They used the Keck telescopes to study 128 quasars. Other studies, like those using the Very Large Telescope, found no change. Researchers also look at the Oklo natural nuclear fission reactor. So far, most data shows the constant is stable. It remains consistent to at least 10 digits of accuracy.