Geodesic Particle Paths Inside a Nonrotating, Homogeneous, Spherical Body

TL;DR

This paper derives precise particle trajectories inside a nonrotating spherical body using improved Einstein field equations, and applies the results to neutrino flight times, predicting minute deviations from the speed of light.

Contribution

It provides a new method to calculate particle paths inside spherical bodies and applies it to neutrino timing experiments, offering refined predictions of neutrino travel times.

Findings

Predicted neutrino flight time is slightly longer than d/c when measured by synchronized clocks.

Inertial observer measurements suggest neutrinos travel faster than light by about 321 m/sec.

Path length inside the sphere is marginally shorter than the Euclidean distance.

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.