Neutron Interference in the Gravitational Field of a Ring Laser

Measuring the gravitational inertial frame dragging effect has been attempted in the recent Gravity Probe B experiment. With the accuracy of the results under scrutiny from the community, and the expense of repeating the experiment in the near future too high, new ways of demonstrating gravitational frame dragging could result in more accurate results sooner. A number of analyses of neutron interference effects due to various metric perturbations have been found in the literature. However, the approach of each author depends on a specific metric. I will present a new general technique giving the Foldy-Wouthuysen transformed Hamiltonian for a Dirac particle in the most general linearized space-time metric. I will then apply this new technique to calculate the phase shift on a neutron beam interferometer due to the gravitational field of a ring laser which contains the gravitational frame dragging effect