Light and divergences: History and outlook

Abstract

All experimental evidence {indicates} that the vacuum is not void, but filled with something truly quantum. This is reflected by terms such as {zero-point} fluctuations, and Dirac's sea of virtual particle-antiparticle pairs, and last but not least the vacuum is the medium responsible for Maxwell's displacement current. While quantum electrodynamics (QED) is an exceptionally successful theory, it remains a perturbative framework rather than a fully self-contained one. Inherently, it includes singularities and divergences, which prevent the precise calculation of fundamental quantities such as the fine-structure constant $\alpha$. Any direct attempt to compute $\alpha$ results in divergent values. However, and most remarkable, what can be determined is how $\alpha$ ``runs", meaning how it varies with energy or exchanged momentum. In this article, we review the historical development of these ideas, the current state of knowledge, and ongoing efforts to find ways to move further. This includes a simple model to describe vacuum polarization in the low-energy regime, when considering only small (linear) deviations from the equilibrium {state}, relating {Maxwell's displacement} in the vacuum, to the quantum properties of the vacuum.