Effect of finite mass on gravitational transit time

Abstract

The dependence of the gravitational transit time on the mass of the particle is derived in this paper. The result confirms, as might be expected, that for highly relativistic particles the effect of a finite mass on the gravitational time delay is negligible compared to special-relativistic effects. As an application, the travel times of photons and the relativistic neutrinos from SN1987A are calculated to show explicitly the negligible effect a finite neutrino mass has on the arguments of Longo and Krauss and Tremaine who used the nearly simultaneous arrival of photons and neutrinos as a test of the Einstein equivalence principle.