Mass, energy, and the electron

Abstract

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle–antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.