External and internal motion in Relativistic Schrödinger Theory

T. Beck, M. Sorg

Young‐Sea Huang

Ya.I. Frenkel

Thomas B. Mieling

The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While previous models of such effects were predominantly restricted to linearized gravity and often required quantum particles to follow prescribed world-lines, this letter shows how such phenomena can be understood using generally covariant semi-classical approximations in the framework of quantum field theory in curved space-times. This method provides a unification and generalization of previously established results, but also predicts new effects such as an influence of internal energies on field amplitudes, as well as correction terms to the internal Schrödinger equation that give rise to Berry phases.

Salvatore Esposito

From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of mass, and an ``internal'' one, whose presence disappears in the classical limit. The latter is caused by the spin of the particle, whatever is its actual value (different from zero). The quantum potential in the Schrodinger equation, which is responsible of the quantum effects of the system, is then completely determined from the properties of the internal motion, and its ``unusual'' properties have a simple and physical explanation in the present context. From the impossibility to fix the initial conditions relevant for the internal motion follows, finally, the need of a probabilistic interpretation of quantum mechanics.

Frank V. Kowalski