Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by analyzing a classical theory of these fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some of the problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This (...) self-repulsion cannot be eliminated within classical field theory without also losing Coulomb interactions between distinct particles. But, electron self-repulsion can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After normal-ordering, the Coulomb term contains pieces describing attraction and repulsion between distinct particles and also pieces describing particle creation and annihilation, but no pieces describing self-repulsion. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot (...) get by without attributing energy to the electromagnetic field, matter may still have electromagnetic potential energy. Indeed, if we take the matter to be represented by the Dirac field, then it will possess potential energy. Thus, potential energy reappears. Upon field quantization, the potential energy of the Dirac field becomes an interaction term in the Hamiltonian operator of quantum electrodynamics. (shrink)