Equivalence between electromagnetic self-energy and self-mass

A cornerstone of physics, Maxwell's theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the energy and inertial mass of the field around an electron do not obey Einstein's famous equation, $E=mc^2$, but instead fulfill this relation with a factor of 4/3 on the left-hand side. Many famous physicists, including Max Born, Enrico Fermi, Paul Dirac, Wolfgang Pauli and Richard Feynman, have contributed to the debate of this so-called 4/3-problem. However, only few suggestions have contained a satisfactory solution and they have been overlooked, misunderstood, or forgotten. Here, a comprehensive solution of this century-old problem is presented. It turns out that relativistic effects are important even at low velocities, and it is shown that equivalence between field energy and mass is restored when these effects are included properly in rigid-body acceleration of the electron.