Localization problem in quantum mechanics and preferred frame

Abstract

In this paper the localization problem in the relativistic quantum mechanics is considered in the framework of a nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincaré covariance but (at least formally) distinguishes an inertial frame. Our analysis has been focused mainly on the problem of existence of a proper position operator for massive particles. We have found the explicit form of the position operator and have demonstrated that in the preferred frame our operator coincides with the Newton–Wigner one. Moreover, full algebra of observables consisting of position operators and fourmomentum operators is manifestly Poincaré covariant in this framework. Our results support expectations of other authors (Bell [1], Eberhard [3]) that a consistent formulation of quantum mechanics demands existence of a preferred frame.