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Fine-structure constant
The fine-structure constant, often denoted by the Greek letter α, is a dimensionless quantity frequently encountered in atomic physics; it is generally considered to be a fundamental physical constant. It was introduced into physics by A. Sommerfeld in 1916, and is sometimes called the "Sommerfeld fine-structure constant". In the theory of quantum electrodynamics, it represents the strength of the interaction between electrons and photons.
The fine-structure constant α is defined as
where e is the charge of an electron, π is pi, 
=h/(2π) is Planck's constant, c is the speed of light in vacuum and ε0 is the permittivity of the vacuum.
Since α is a dimensionless quantity, its numerical value is independent of the system of units used. This value (CODATA Dec.2003) is
- α = 0.007297352568(24),
but it is commonly listed by the value of its inverse,
- α - 1 = 137.03599911(46).
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Physical interpretation
The fine-structure constant has been of interest to physicists because its value does not seem to be directly related to any obvious mathematical constant.
For any arbitrary length l the fine-structure constant is the ratio of two energies: the energy needed to bring two electrons from infinity into distance l against their electrostatic repulsion and the energie of single photon of wavelngth l/2π.
The small value of the fine-structure constant is important in allowing calculations using quantum electrodynamics. Quantum electrodynamics allows one to break up a quantum mechanical problem into a power series of α and the small value of α creates a situation in which the terms corresponding to higher orders of α become unimportant. By contrast, the large value of the corresponding factors in quantum chromodynamics make calculations involving the strong force extremely difficult.
In the standard model, the fine-structure constant is inserted to the theory externally.
In the electroweak theory, one that unifies the weak interaction with electromagnetism, the fine-structure constant is not quite fundamental; it is derived from two other coupling constants associated with the gauge groups SU(2) and U(1), respectively (the electromagnetic interaction is a mixture of the interactions associated with these two groups).
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.
α in the cgs System of Units
In cgs units, electrical charges are measured in a way which results in the factor 4πε0 becoming equal to one:
α in the International System of Units
CIPM (1988) Recommendation 2, PV 56; 20 states that the von Klitzing constant (RK ≡ 2/(e·KJ)) should be considered to have the exact value of 25 812.807 Ω. It turns out the fine structure constant can be expressed as α ≡ μ0·c/(2·RK), where μ0 is the permeability of the vacuum. Hence the value of α is:
α ≈ 7.297 352 695 151 880 527 139 074 809 266 57×10-3
(since π appears in μ0, there are an infinite number of digits in the value of α)
CIPM (1988) Recommendation 1, PV 56; 19 similarly fixes the value of the Josephson constant (KJ ≡ 2·e/h) at exactly 4,835 979×1014 Hz/V. Although this step has not been taken yet, one can use these definitions to redefine the kilogram (the last SI base unit to be still based on a prototype) from physical first principles.
Is α really constant?
Physicists have been wondering whether the fine structure constant is really a constant, i.e. whether it always had the same value over the history of the universe, as some theories had been suggested which implied this not to be the case. First experimental tests of this question, most notably examination of spectral lines of distant astronomical objects and of the Oklo natural fission reactor, have not hinted any changes.
Recent improvements in astronomical techniques brought first hints in 2001 that α in fact might change its value over time. (For a brief article see (1) ). However in April 2004, new and more-detailed observations on quasars made using the UVES spectrograph on Kueyen , one of the 8.2-m telescopes of ESO's Very Large Telescope array at Paranal (Chile), puts limits to any change in α at 0.6 parts per million over the past ten thousand million years. (See ESO press release or (2) ).
As this limit contradicts the 2001 results, the question on whether α is constant or not is open again and the correctness of the contradicting experiments is currently (as of 2004) hotly debated by the scientists involved.
However, there is another sense in which α is definitely not constant. 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 as the energy is increased - which is described by a positive beta-function. The value 1/137.03604 is associated with the very low energy scales; the value of the fine-structure constant essentially does not "run" below the energy scale equal to the electron mass 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 fine-structure constant increases (logarithmically) with the energy scale, it 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.
Arthur Eddington and the fine structure constant
The physicist Arthur Eddington at one time thought that α, which had been measured at approximately 1/136, should be exactly 1/136, based on aesthetic and numerological arguments. Measurements have currently shown this not to be the case. Around 1938, when another measurement showed α to have a value nearer 1/137, Eddington constructed an argument relating the number 136+1 to the Eddington number. This was his estimate of the number of electrons in the Universe.
External links
- http://physics.nist.gov/cuu/Constants/alpha.html
- http://scienceworld.wolfram.com/physics/FineStructureConstant.html