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The fine-structure constant is a dimensionless quantity, and its numerical value is independent of the system of units used. The value recommended by CODATA (as of December 2003) is
It can be defined as
where e is the elementary charge, π is pi, is Planck's constant divided by 2π, c is the speed of light in a vacuumCherenkov effect in a "swimming pool" nuclear reactor. The effect is due to electrons moving faster than the speed at which light moves in water. The speed of light (denoted as c reputedly from the Latin celeritas "speed", and also known as Einstein's con, and ε0 is the permittivityIn electromagnetism, permittivity ε is a measure of how much a medium changes to absorb energy when subject to an electric field. It is defined as the ratio D / E where D is the electric displacement by the medium and E is the electric field stren of the vacuum.
In electrostatic cgs units, electrical charges are measured in a way that results in the factor 4πε0 becoming equal to one:
For any arbitrary length s, the fine-structure constant is the ratio of two energies: (i) the energy needed to bring two electrons from infinity to a distance of s against their electrostatic repulsion, and (ii) the energy of single photon of wavelength s/2π.
In the theory of quantum electrodynamicsQuantum electrodynamics QED is a quantum field theory of electromagnetism. QED describes all phenomena involving electrically charged particles interacting by means of the electromagnetic force and has been called "the jewel of physics" for its extremely, the fine structure constant plays the role of a coupling constantIn physics, a coupling constant usually denoted , is a number that determines the strength of an interaction. For example, the fine-structure constant is a coupling constant that determines the strength of the electromagnetic force. In quantum relativisti, 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 ModelThe Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. It is a quantum field theory, and consistent with both quantum mecha of particle physicsParticle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called high energy physics because many elementary particles do not occur under normal circumstances in.
The fact that α is much less than 1 allows the use of perturbation theoryIn quantum mechanics, perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system and gradually turn on an additional "perturbing" Hamiltonian repre in quantum electrodynamics. Physical results in this theory are expressed as power series in α, with higher orders of α 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.
As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long been an object of fascination to physicists. Richard Feynman, one of the founders of quantum electrodynamics, referred to it as "one of the greatest damn mysteries of physics: a magic number that comes to use with no understanding by man." Towards the end of his life, the physicist Arthur Eddington constructed numerological "proofs" that 1/α was an exact integer, even relating it to the Eddington number, his estimate of the number of electrons in the Universe. Experiments have since shown that 1/α is definitely not an integer.
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 α 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 1/137.03604 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.
One controversial explanation of the value of the fine-structure constant invokes the anthropic principle and argues that the value of the fine-structure is what it is because stable matter and therefore life and intelligent beings could not exist if the value were something else.