Geodesic Particle Paths Inside a Nonrotating, Homogeneous, Spherical Body

Abstract

Proceeding from a solution of field equations that are improved versions of Einstein's nonvacuum gravitational field equations one is able to calculate precisely the trajectories of particles traveling inside a nonrotating, homogeneous, spherical body. Application of the results to the conditions of recent measurements of neutrino flight times between a source point A at CERN's European Laboratory for Particle Physics and a point B in either of two detectors (ICARUS or OPERA) at LNGS (Laboratori Nazionale del Gran Sasso), separated by a euclidean distance d(A,B) = 731 km, predicts for the flight time from A to B of a 2 eV neutrino launched with energy 17 GeV, as measured by a clock at B synchronized to a similar clock at A, approximately d/c + 9.3 x 10^{-16} sec. But as measured by inertial observers along the path the predicted flight time is approximately d/c - 2.6 x 10^{-9} sec and the predicted path length is approximately d - 8.4 x 10^{-7} m, which yields c + 321 m/sec for the predicted average inertially referenced speed of the neutrino from A to B.