Classical theory of spinning particles

Summary

The exact relativistic classical equations taking radiation reaction into account for the rotation and translation of apoint dipole are given for the case where the dipole is always a pure magnetic dipole in the rest system. These equations are entirely free from any singularities. It is shown that the mass M, angular momentum of the spin I and magnetic moment g₂ are three entirely independent constants with no connection between them. The cross-section for the scattering of light by a dipole is given by formula (56). This formula shows that due to radiation reaction the scattering actually decreases as ω⁻² for very high frequenciesω, instead of increasing as ω² when radiation reaction is neglected. The quantum mechanical formula for the scattering of neutral mesons by neutrons is shown to go wrong at energiesħ ω ≳ 3 μ due to neglect of the effects of radiation damping. The classical formula (56) can still be correctly applied in the range 3μ <ħ ω < M, where the quantum formula is wrong, M being the neutron mass. Finally reasons are given for thinking that the quantum theory of the electron fails at energies above about √3 × 137m due to neglect of the effect of radiation damping on the spin, and the quantum theory of the meson and its inter-action with the electromagnetic field at √6 × 137μ.