Light and divergences: History and outlook

TL;DR

This paper reviews the historical development, current understanding, and future prospects of quantum vacuum phenomena, focusing on divergences in quantum electrodynamics and the running of the fine-structure constant.

Contribution

It provides a comprehensive overview of the evolution of ideas related to vacuum quantum properties and discusses a simple model linking Maxwell's displacement to vacuum polarization.

Findings

Vacuum filled with quantum fluctuations and virtual particles.

The fine-structure constant varies with energy, known as 'running'.

A simple model describes low-energy vacuum polarization effects.

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.