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Experiments have since shown that Eddington was wrong; to six significant digits, the reciprocal of the fine-structure constant is 137.036.
For reasons of convenience, historically the value of the reciprocal of the fine-structure constant is often specified.
If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the Landau pole.
As such, the fine-structure constant is just an alternative expression of the elementary charge; 0.30282212 in terms of the natural unit of charge.
According to some theorists there are some very special circumstances in which changes in the fine-structure constant can be measured as a change in dimensionful physical constants.
The coupling constant sets the magnitude of the force of interaction; for example, in quantum electrodynamics, the fine-structure constant is a coupling constant.
The atomic length scale is meters and is given by the size of hydrogen atom (i.e., the Bohr radius (approximately 53 pm)) which is set by the electron's Compton wavelength times the fine-structure constant: .
Paul Davies and collaborators have suggested that it is in principle possible to disentangle which of the dimensionful constants (the elementary charge, Planck's constant, and the speed of light) of which the fine-structure constant is composed is responsible for the variation.