The Relativistic Kinematics of the de Broglie Phase Wave

Abstract

If we postulate that a linearly-moving particle is accompanied by an in-phase plane wave (a phase wave), then the de Broglie phase-wave velocity follows as a consequence of the requirement of relativistic invariance. This is the usual formulation of this problem. If we alternately assume that the de Broglie phase wave is a real kinematic excitation produced by the motion of the particle, then its properties follow directly from the equations of special relativity when they are taken in the (unfamiliar) perturbative limit of very small excitation energies. The equations of “perturbative special relativity” are set forth, and some of their consequences are discussed.

This work was performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.