Fine-structure constant: Encyclopedia II - Fine-structure constant - Physical interpretation

Fine-structure constant - Physical interpretation

For any arbitrary length , the fine-structure constant is the ratio of two energies: (i) the energy needed to bring two electrons from infinity to a distance of against their electrostatic repulsion, and (ii) the energy of a single photon of wavelength .

Historically, the first physical interpretation of the fine-structure constant, , was the ratio of the velocity of the electron in the first circular orbit of the Bohr atom to the speed of light in vacuum. It appears naturally in Sommerfeld's analysis and determines the size of the splitting or fine-structure of the hydrogenic spectral lines.

In the theory of quantum electrodynamics, the fine structure constant plays the role of a coupling constant, representing the strength of the interaction between electrons and photons. Its value cannot be predicted by the theory, and has to be inserted based on experimental results. In fact, it is one of the twenty-odd "external parameters" in the Standard Model of particle physics.

The fact that is much less than 1 allows the use of perturbation theory in quantum electrodynamics. Physical results in this theory are expressed as power series in , with higher orders of increasingly unimportant. In contrast, the large value of the corresponding factors in quantum chromodynamics makes calculations involving the strong force extremely difficult.

In the electroweak theory, one that unifies the weak interaction with electromagnetism, the fine-structure constant is absorbed into two other coupling constants associated with the electroweak gauge fields. In this theory, the electromagnetic interaction is treated as a mixture of interactions associated with the electroweak fields.

According to the theory of renormalization group, the value of the fine-structure constant (the strength of the electromagnetic interaction) depends on the energy scale. In fact, it grows logarithmically as the energy is increased. The observed value of is associated with the energy scale of the electron mass; the energy scale does not run below this because the electron (and the positron) is the lightest charged object whose quantum loops can contribute to the running. Therefore, we can say that 1/137.036 is the value of the fine-structure constant at zero energy. Moreover, as the energy scale increases, the electromagnetic interaction approaches the strength of the other two interactions, which is important for the theories of grand unification. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the Landau pole. This fact makes quantum electrodynamics inconsistent beyond the perturbative expansions.

Adapted from the Wikipedia article "Physical interpretation", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki