The synchronization problem in covariant relativistic dynamics

John R. Fanchi

Paweł Caban, Jakub Rembieliński

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.

John R. Fanchi

Theodore Garavaglia

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a generalized Hamiltonian dynamics and to a covariant Schrödinger type equation is shown. Examples for relativistic potential problems are solved. Mathematically and physically acceptable probability densities for the Klein-Gordon equation and for the Dirac equation are derived, and a new continuity equation for each case is given. The quantum distribution for mass is discussed, and unambiguous representations of four-velocity and four-acceleration operators are given.

F. Reuse