Self-force and inertia. Old light on new ideas
The title problem of this book is worked out in great detail. The reader is guided from basic concepts of electrodynamics, relativity and relativistic dynamics to consider simple models of rigid charge distributions and the problem of inertia. It is well known that the energy of the electromagnetic field of a point charge is infinite. For that reason, quantum electrodynamics, as well as other quantum field theoretical descriptions of point particles, require renormalization. This method, although non-esthetic in some sense, works so well that it is accepted as natural without contemplating the reasons the book likes to remind us of. The author goes a further step ahead. Transducing the problem to point masses in general relativity, he works on the idea that the emergence of inertia may be explained in this way. Eventually, the generation of mass spectra in modern elementary particle physics is considered and related to the idea of extended massive particles. After the introduction (chapter 1), the classical electromagnetic field and the motion of charged point particles are considered. Larmor's formula for the radiated power is compared with a formula due to Feynman (chapter 2). Chapter 3 begins with the derivation of the (momentum-derived) electromagnetic mass of the electron whose charge is assumed to be uniformly distributed over a spherical shell of radius \(a\). Section two of this chapter is essential in that fundamental ideas about the emergence of inertia are exhibited. Inertia may result for an elementary particle like the electron from a mechanical rest mass and the electromagnetic mass. For a nucleon it may result from the rest masses, kinetic energies, and binding energies of its elementary constituents whose rest masses may have mechanical and field dynamical origins. The discrepancy between a momentum-derived or an energy-derived rest mass of the electron leads over to the next sections which are devoted to aspects of the the self-force. The chapter concludes with a program, a simple \textit{Toy Electron} consisting of two point charges \(q_e/2\) separated by the distance \(d\) in its rest-frame is worked out in chapters 6 through 11. In chapter 4 the main features of general relativity needed are described. In chapter 5 an electron model, a bit more complicated than the toy model is considered. It consists of two plane parallel disks of radius \(a\) centered by a perpendicular axis at a distance \(d\gg a\), each carrying the uniformly distributed charge \(q_e/2\). The energy-derived mass and the momentum.derived masses for longitudinal and transversal motion w.r.t. the axis are calculated in the classical and the relativistic case. Hints for more general applications of the model are given. Chapter 6 is the first of five chapters devoted to the toy model. Here the self force in case of linear transversal motion w.r.t. the model axis is considered. After calculating explicitly the self force, which vanishes when the system has constant velocity, the Laurent expansion with respect to \(d\) shows up to \({\mathcal O}(d)\) that there is a term proportional to \(1/d\) in opposite direction of the acceleration. Hence, for sufficiently small \(d\) it contributes to the inertia. For \(d\rightarrow 0\), i.e., the toy model approaching a point charge, this term diverges confirming the necessity of mass renormalization. The constant term is due to the radiation reaction. Chapters 7 through 9 treat the axial linear motion, the transverse rotational motion and the axial linear motion. The results are summarized in chapter 10. Remarkably, the self-force-derived masses coincide with the momentum-derived ones for each of the models under consideration, for the toy model moving in a transversal direction they also coincide with the energy-derived mass, but for longitudinal motion of the toy model and the spherical charged shell the energy-derived is smaller by the factor \(1/2\). This discrepancy is the subject of chapter 11. Attempts to solve the problem by F. Rohrlich, T. Boyer and P. Moylan are represented and discussed in great detail. The electron models in consideration rely on the rigidity of the charge distribution but rigidity is only well defined in the inertial rest frame. However, the derivation of the electromagnetic mass is based on accelerated motions and, hence, a serious problem arises. This problem is extensively discussed in chapter 12. How inertial masses are considered in modern particle physics is described in chapter 13. The basic idea is, that there are truly elementary particles and others are consisting in bound states of the former. The mass of a compound particle should be the result of the masses of the components, their kinetic energy and the binding energy. But only the leptons can exist as isolated systems whereas the quarks do not. So the inertial quark mass can at best be determined indirectly. Modern particle physics is getting around this problem in a more abstract manner and correct results are obtained. Since inertia is basic in classical and relativistic dynamics it would be very satisfying to understand particle masses more directly on this basis. The author stresses at several places that the aim of this book ``has certainly not been to reject the standard model out of hand, nor to advocate a return to pre-quantum methods of calculation, or anything of the sort''. The only purpose is to remind that there is nice old light which possibly may fruitful illuminate new ideas. Chapter 14 contains commented summaries of the main chapters 2 through 13. Formulas in this book are cited by their number as well as the page. This book is written very well and can be best recommended to any physicist contemplating on foundations of physics. Especially, it can be recommended to students after they have finished the basic courses. They may read this book with pleasure and profit.
scientific article; zbMATH DE number 5654758