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 is defined as\n:\nwhere
e is the
charge of an
electron, π is
pi, =
h/(2π) is
Dirac's constant,
c is the
speed of light in vacuum and ε
0 is the
permittivity of the vacuum.
In
cgs units, electrical charges are measured in a way which results in the factor 4πε
0 becoming equal to one:\n:
Since α is a dimensionless quantity, its numerical value is independent of the system of units used. This value is\n:\nbut it is commonly listed by the value of its inverse,\n:
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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. In the
standard model, the fine-structure constant is inserted to the theory externally.
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.
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 Système international d'unités
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 \nESO 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.
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
\n*http://physics.nist.gov/cuu/Constants/alpha.html\n*http://scienceworld.wolfram.com/physics/FineStructureConstant.html
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