lepton being the electron and since it is the lightest in mass, the most numerous due to the energy–time uncertainty principle as mentioned above; e.g., virtual electron–positron pairs. Such charged pairs act as an electric dipole. In the presence of an electric field, e.g., the electromagnetic field around an electron, these particle–antiparticle pairs reposition themselves, thus partially counteracting the field (a partial screening effect, a dielectric effect). The field therefore will be weaker than would be expected if the vacuum were completely empty. This reorientation of the short-lived particle–antiparticle pairs is referred to as vacuum polarization. Electric and magnetic fields Extremely strong electric and magnetic fields cause an excitation of electron–positron pairs. Maxwell's equations are the classical limit of the quantum electrodynamics which cannot be described by any classical theory. A point charge must be modified at extremely small distances less than the reduced Compton wavelength (). To lowest order in the fine-structure constant, , the QED result for the electrostatic potential of a point charge is: This can be understood as a screening of a point charge by a medium with a dielectric permittivity, which is why the term vacuum polarization is used. When observed from distances much greater than , the charge is renormalized to the finite value . See also the Uehling potential. The effects of vacuum polarization become significant when the external field approaches the Schwinger limit, which is: These effects break the linearity of Maxwell's equations and therefore break the superposition principle. The QED result for slowly varying fields can be written in non-linear relations for the vacuum. To lowest order , virtual pair production generates a vacuum polarization and magnetization given by: this polarization and magnetization has not been directly measured. Vacuum polarization tensor The vacuum polarization is quantified by the vacuum polarization tensor which describes the dielectric effect as a function of the four-momentum p carried by the photon. Thus the vacuum polarization depends on the momentum transfer, or in other words, the electric constant is scale dependent. In particular, for electromagnetism we can write the fine-structure constant as an effective momentum-transfer-dependent quantity; to first order in the corrections, we have where and the subscript 2 denotes the leading order-e correction. The tensor structure of is fixed by the Ward identity. Note Vacuum polarization affecting spin interactions has also been reported based on experimental data and also treated theoretically in QCD, as for