Chapter 28: Electromagnetic Mass & Radiation Reaction

Electromagnetic Mass & Radiation Reaction from The Feynman Lectures on Physics systematically investigates the foundational shortcomings of classical electrodynamics when attempting to describe fundamental particles, focusing primarily on the concept of electromagnetic mass. The analysis begins by calculating the total electrostatic field energy stored in the field of a point charge. By treating the charge as distributed over a tiny sphere of radius a, the energy derived is found to be inversely proportional to a. This result immediately highlights a catastrophic theoretical dilemma: if the particle is truly a point charge (radius a approaches zero), the required self-energy becomes infinite, an issue that classical physics struggles to fully resolve. The discussion then advances to a charge moving at a small, uniform velocity v (lesser than) c, where the field momentum carried by the electromagnetic field is calculated. Relating the energy U to mass and comparing the momentum P to the classical momentum leads to the determination of the electromagnetic mass. Although this mass is consistent with relativistic dependence on velocity, the resulting energy calculation is mathematically inconsistent with the mass derived from momentum, a renowned puzzle often referred to as the 4/3 problem. This discrepancy necessitates the theoretical introduction of non-electrical stresses, known as Poincaré stresses, to ensure the electron model is relativistically complete and consistent. The chapter briefly addresses historical attempts to modify Maxwell's theory to circumvent the infinite energy and self-force issues, mentioning theoretical approaches by figures like Born, Infeld, and Dirac. Finally, the perspective shifts to the nuclear force field, drawing an analogy where strong interactions are mediated by particles, specifically mesons (or pions), instead of photons. Applying principles from field theory leads to a modification of the wave equation, resulting in the Yukawa potential, which successfully describes the characteristic short-range nature of nuclear forces. The differences in mass observed between charged and neutral particles, like the proton and neutron, are examined as evidence suggesting an electromagnetic contribution to particle mass.