Editing Zero-point energy (section)

=== Lamb shift ===
{{Main|Lamb shift}}
[[File:Hydrogen fine structure.svg|thumb|[[Fine structure]] of energy levels in hydrogen – relativistic corrections to the [[Bohr model]]]]

The quantum fluctuations of the electromagnetic field have important physical consequences. In addition to the Casimir effect, they also lead to a splitting between the two [[energy level]]s {{math|<sup>2</sup>''S''<sub>{{sfrac|1|2}}</sub>}} and {{math|<sup>2</sup>''P''<sub>{{sfrac|1|2}}</sub>}} (in [[term symbol]] notation) of the [[hydrogen atom]] which was not predicted by the [[Dirac equation]], according to which these states should have the same energy. Charged particles can interact with the fluctuations of the quantized vacuum field, leading to slight shifts in energy;{{sfnp|Itzykson|Zuber|1980|p=80}} this effect is called the Lamb shift.<ref>
{{cite journal
 |last=Hawton |first=M.
 |year=1993
 |title=Self-consistent frequencies of the electron–photon system
 |journal=[[Physical Review A]]
 |volume=48 |issue=3 |pages=1824–1831
 |bibcode=1993PhRvA..48.1824H
 |doi=10.1103/PhysRevA.48.1824
 |pmid=9909797
}}</ref> The shift of about {{val|4.38|e=-6|u=eV}} is roughly {{val|e=-7}} of the difference between the energies of the 1s and 2s levels, and amounts to 1,058&nbsp;MHz in frequency units. A small part of this shift (27&nbsp;MHz ≈ 3%) arises not from fluctuations of the electromagnetic field, but from fluctuations of the electron–positron field. The creation of (virtual) electron–positron pairs has the effect of screening the Coulomb field and acts as a vacuum dielectric constant. This effect is much more important in muonic atoms.{{sfnp|Le Bellac|2006|p=381}}