Taking  (the Planck constant divided by ),  (the speed of light), and  (the electromagnetic coupling constant i.e. a measure of the strength of the electromagnetic force (where  is the absolute value of the electronic charge and  is the vacuum permittivity)) we can form a dimensionless quantity called the fine-structure constant:
The fine-structure constant is the coupling constant of quantum electrodynamics (QED) determining the strength of the interaction between electrons and photons. It turns out that the fine-structure constant is not really a constant at all owing to the zero-point energy fluctuations of the electron-positron field. The quantum fluctuations caused by zero-point energy have the effect of screening electric charges: owing to (virtual) electron-positron pair production, the charge of the particle measured far from the particle is far smaller than the charge measured when close to it.
The Heisenberg inequality where , and ,  are the standard deviations of position and momentum states that:
It means that a short distance implies large momentum and therefore high energy i.e. particles of high energy must be used to explore short distances. QED concludes that the fine-structure constant is an increasing function of energy. It has been shown that at energies of the order of the Z boson rest energy,  90 GeV, that:
rather than the low-energy . The renormalization procedure of eliminating zero-point energy infinities allows the choice of an arbitrary energy (or distance) scale for defining . All in all,  depends on the energy scale characteristic of the process under study, and also on details of the renormalization procedure. The energy dependence of  has been observed for several years now in precision experiment in high-energy physics.