Zitterbewegung and Quantum Jumps in Relativistic Schrödinger Theory

Abstract

Within the general framework of the relativistic Schrodinger theory, a new waveequation is identified which stands between Dirac's four-component spinorequation and the scalar one-component Klein–Gordon equation. It is atwo-component, first-order wave equation in pseudo-Riemannian spacetime which onone hand can take account of the Zitterbewegung (similar to the Dirac theory),but on the other hand describes spinless particles (just like the Klein–Gordontheory). In this way it is demonstrated that spin and Zitterbewegung areindependent phenomena despite the fact that both effects refer to a certain kindof internal motion. An extra variable for the internal motion can be introduced(similarly as in the Dirac theory) so that the new wave equation is reduced tothe Klein–Gordon case when the internal variable takes its trivial value and theinternal motion is not excited. The internal degree of freedom admits the occurenceof quasi-pure states (i.e., a special subset of the mixtures), which undergo atransition to a pure state in finite time. If the initial configuration is already apure state, this transition occurs in the form of a sudden jump to the final purestate. The coupling of the new wave field to gravity via the Einstein equationsmakes the Zitterbewegung manifest through the corresponding trembling of theextension of a Friedmann–Robertson–Walker universe.