Brans-Dicke corrections to the gravitational Sagnac effect

The exact formulation for the effect of the Brans-Dicke scalar field on the gravitational corrections to the Sagnac delay in the Jordan and Einstein frames is presented. The results completely agree with the known parametrized post Newtonian factors in the weak-field region. The calculations also reveal how the Brans-Dicke coupling parameter <(<omega>)over bar> appears in various correction terms far different types of source or observer orbits. A first-order correction of roughly 2.83 x 10(-1) fringe shift for visible light is introduced by the gravity-scalar field combination far Earth-bound equatorial orbits. It is also demonstrated that the final predictions in the two frames do not differ. The effect of the scalar field on the geodetic and Lense-Thirring precession of a spherical gyroscope in a circular polar orbit around the Earth is also computed with an eye towards the Stanford Gravity Probe-B experiment currently in progress. The feasibility of optical and matter-wave interferometric measurements is discussed briefly.