Zitterbewegung and quantum jumps in relativistic Schrodinger theory

Within the general framework of the relativistic Schrodinger theory, a new wave equation is identified which stands between Dirac's four-compooonent s pinor equation and the scalar one-component Klein-Gordon equation. It is a two-component, first-order wave equation in pseudo-Riemannian spacetime whi ch on one hand can take account of the Zitterbewegung (similar to the Dirac theory), but on the other hand describes spinless particles (just like the Klein-Gordon theory). In this way it is demonstrated that spin and Zitterb ewegung are independent phenomena despite the fact that both effects refer to a certain kind of internal motion. An extra variable for the internal mo tion can be introduced (similarly as in the Dirac theory) so that the new w ave equation is reduced to the Klein-Gordon case when the internal variable takes its trivial value and the internal motion is not excited. The intern al degree of freedom admits the occurence of quasi-pure states (i.e., a spe cial subset of the mixtures), which undergo a transition to a pure state in finite time. If the initial configuration is already a pure state, this tr ansition occurs in the form of a sudden jump to the final pure state. The c oupling of the new wave field to gravity via the Einstein equations makes t he Zitterbewegung manifest through the corresponding trembling of the exten sion of a Friedmann-Robertson-Walker universe.