A time operator in the simulations of the Dirac equation

Simulations of the Dirac equation have allowed to mimic measurably the predicted unusual characteristics of the electron motion, e.g. Zitterbewegung and Klein paradox that are beyond current technical capabilities. In this paper, it is shown that a Bose-Einstein condensate experiment carried out corroborates these results, but in addition exhibits a particular feature of an observable represented by a Dirac self-adjoint time operator introduced in relativistic quantum mechanics.