Fine-structure constant

Tiny bits of matter have a pull. This pull is called an electric charge. There is a special number for this pull.

This number tells us how strong the pull is. It helps bits of matter talk to light. A man named Arnold Sommerfeld named it. He found it in 1916.

Scientists use this number to study atoms. Atoms are the tiny building blocks of everything. This number stays the same everywhere.

We can measure this number in many ways. Some ways use light from far away. Other ways use tiny tools in a lab.

It is a very important rule of our world. It helps us understand how things work.

Everything in our world is made of tiny parts. Some of these parts have an electric charge. This charge lets them interact with light. Scientists use a special number to measure this strength. This number is called the fine-structure constant.

Arnold Sommerfeld named this constant in 1916. He used it to help explain how atoms work. He looked at the lines of light from hydrogen atoms. These lines have a very fine structure. This number tells us how much the parts of an atom pull on each other.

The value of this constant is about 1/137. This number does not change based on how we measure it. It is a pure number. Scientists have many ways to find its exact value. Some use tiny tools in a lab. Others study light from very far away in space.

Some people wonder if this number ever changes. They look at old light from the early universe. So far, most tests show the number stays the same. It seems to be a steady rule for our world.

The fine-structure constant is a very special number in physics. It is also called the Sommerfeld constant. This number tells us how strong the electromagnetic interaction is between tiny charged particles. This interaction is the way particles like electrons pull or push on each other using electricity and magnetism. Scientists use the Greek letter alpha to represent this constant. It is a dimensionless quantity. This means the number stays the same no matter what system of units you use. It is a fundamental rule of our universe.

This constant works by linking several other important parts of nature together. It connects the elementary charge to the electromagnetic field. To find its value, scientists look at the charge of an electron and the speed of light. They also use the Planck constant, which helps describe tiny particles. They even use the electrical permittivity of space. By using these pieces, they can calculate the strength of the interaction. The value is approximately 1/137. This number helps scientists predict how light and matter will act together.

History shows how we slowly learned about this number. In 1887, Michelson and Morley measured the light lines of hydrogen atoms very precisely. Later, in 1916, Arnold Sommerfeld introduced this constant. He was trying to improve the Bohr model of the atom. He used it to explain the tiny gaps in the light patterns of hydrogen. In 1928, Paul Dirac found an exact formula for this structure. Later, the theory of quantum electrodynamics, or QED, showed its true importance. This theory explains how electrons and photons interact.

Scientists use many different ways to measure this number today. One way is to look at the anomalous magnetic moment of the electron. This is a special property of how an electron behaves in a magnetic field. Another method uses the quantum Hall effect. They can also use the A.C. Josephson effect or photon recoil. In 2023, one very precise measurement used a special tool called a quantum cyclotron. This tool helped scientists reach a very high level of accuracy. They compare these different results to make sure they all agree.

It is interesting to think about how this constant relates to everything else. For example, the strength of this interaction changes at different energy scales. At very high energies, like the scale of a Z boson, the value changes to about 1/127. Some scientists wonder if the constant changes over very long periods of time. They look at light from distant quasars or old nuclear reactors in Oklo. So far, most evidence shows the constant stays the same. It remains a steady part of the laws of physics.

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.