Liénard–Wiechert potentials and the electromagnetic memory effect

Classical electrodynamics is one of the most well-tested and understood theories in physics. After more than a century of history, it may be surprising that such an established theory still makes predictions that have not yet been experimentally verified. A noteworthy example is the memory effect—a prediction that an electromagnetic pulse with nonzero ∫E dt can leave a lasting influence long after it has passed. This influence is manifested in a transverse velocity “kick” on a distant test charge. This simple remark lies at the heart of modern investigations of the low-energy behavior of gravity, electrodynamics, and gauge theories and awaits confirmation (or refutation) through experiments. From a pedagogical perspective, this current research topic beautifully epitomizes how standard concepts from undergraduate electrodynamics can still lead to new physics. In this work, we use the Liénard–Wiechert solutions for the electromagnetic fields of moving charges to understand what the memory effect is, where it comes from, and how it could be experimentally probed in the near future. We also discuss the connections between the memory effect and other important topics in fundamental physics, as well as the search for memory in modern gravitational wave observatories.