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Quantum mechanics as a solution to the classical self-force problem

Yehonatan Knoll

Abstract

It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent randomness observed in quantum mechanical scattering experiments and with the absence of any experimental support for such universality. In a recent paper [11], the statistical effect of radiative corrections to the motion of charged bodies has been derived from the basic tenets and does take a universal form, described by quantum mechanical wave equations -- again conforming with experiment. As that derivation assumes nothing about the size, mass or composition of the body, it is conjectured that quantum mechanics is the appropriate framework for dealing also with radiative corrections to the motion of macroscopic bodies.

Quantum mechanics as a solution to the classical self-force problem

Abstract

It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent randomness observed in quantum mechanical scattering experiments and with the absence of any experimental support for such universality. In a recent paper [11], the statistical effect of radiative corrections to the motion of charged bodies has been derived from the basic tenets and does take a universal form, described by quantum mechanical wave equations -- again conforming with experiment. As that derivation assumes nothing about the size, mass or composition of the body, it is conjectured that quantum mechanics is the appropriate framework for dealing also with radiative corrections to the motion of macroscopic bodies.

Paper Structure

This paper contains 22 sections, 118 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Manifestly scale covariant classical electrodynamics
  3. Scale covariance
  4. The basic tenets of CE
  5. The classical self-force problem
  6. Extended currents
  7. Extended Charge Dynamics
  8. The central ECD system
  9. The nature of particles in ECD
  10. Comparison with solitons
  11. The necessity for advanced solutions of Maxwell's equations
  12. The 'fine tuned' central ECD system
  13. ECD currents
  14. A semiclassical analysis of ECD
  15. ECD currents in the semiclassical approximation
  16. ...and 7 more sections

Figures (1)

  • Figure 1: A $1+1$ spacetime counterpart of our construction.