Spin in stationary gravitational fields and rotating frames

Abstract

Abstract.A spin motion of particles in stationary spacetimes is investigated in the framework of the classical gravity and relativistic quantum mechanics. We bring the Dirac equation for relativistic particles in nonstatic spacetimes to the Hamiltonian form and perform the Foldy-Wouthuysen transformation. We show the importance of the choice of tetrads for description of spin dynamics in the classical gravity. We derive classical and quantum mechanical equations of motion of the spin for relativistic particles in stationary gravitational fields and rotating frames and establish the full agreement between the classical and quantum mechanical approaches.

Detection of gravitational frame dragging using orbiting qubits

“…However, we have to recall that spin and curvature are coupled in a non-trivial manner [27]. As a consequence, the motion of spinning particles, either classical or quantum, does not follow geodesics [28,29,30,31,32]. It is also known that the deviation from geodetic motion is very small, except for the case of supermassive compact objects and/or ultra-relativistic test particles [33,34,35,36].…”

“…In that case the tangential speed of the particle = v c u u t 3 0 as seen by the hovering observer and which is associated with the circular orbits verify < v c 0.9 t (see figure 1). Those kinds of spin-curvature couplings that may affect also the equation for the parallel transport of spin have been considered by several authors in the past [28][29][30][44][45][46] (cf footnote 2). At leading order such additional forces and torques manifest by the coupling between the spin of the particle and the spin of the rotating source of the gravitational field [30].…”