2026/07/28 by G. Jordan Maclay
Physics and Astronomy · #quant-ph
published as Physics 2023, 5(3), 883-894; · 13 pages, 5 figures, 1 table, Revised version submitted to arXiv 7/28/2026
arxiv created 2026/07/28 · arxiv updated 2026/07/31
\abstractThe Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman and Power demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. By using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, we can obtain an expression for the size of the region of vacuum energy for each frequency \texorpdfstringωω around the H atom due to the Lamb shift. The ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of virtual quanta. For energies \texorpdfstringE=ℏωE=hbar omega eV less than 1 eV, the radius of the positive energy region is approximately 14. 4/E Angstroms. For a vacuum fluctuation of wavelength \texorpdfstringλlambda the radius is \texorpdfstring(α/2π)λ(alpha/2pi) lambda. Thus, for long wavelengths, the region has macroscopic dimensions. The energy-time Uncertainty Relation predicts a maximum possible radius that is larger than this by a factor of \texorpdfstring1/ 4α1/(4 alpha). \keywordBethe; radiative shift; shift spectral density; spectral volume; vacuum fluctuations; vacuum field; Lamb shift; QED; energy field, renormalization, zero point fluctuations; hydrogen atom.