The Lorentz-Dirac equation in light of quantum theory

Bahram Mashhoon

The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.

Masao Ozaki, Shigeru Sasabe

Following Crisp's method based on neoclassical theory for a radiating electron, we have derived the nonrelativistic Lorentz-Dirac equation from quantum mechanics by means of Ehrenfest's theorem. It is found that the dipole approximation is essential to obtain the correct form of the equation of motion.

Bahram Mashhoon

The nonlocal theory of accelerated systems is extended to the propagation of Dirac particles. The implications of nonlocality for the phenomenon of spin-rotation coupling are discussed. The Lorentz-invariant nonlocal Dirac equation is presented for certain special classes of accelerated observers.