Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy

TL;DR

This paper analyzes whether the Shapiro time delay measurement depends on the speed of gravity or light, concluding that the dependence is theory-specific and current observations mainly reflect the speed of light.

Contribution

It demonstrates that the question of dependence on the speed of gravity or light is ill-posed outside specific theory classes, clarifying the interpretation of recent measurements.

Findings

The dependence on $c$ or $c_g$ varies with the chosen theory class.

Current observations are not precise enough to measure the speed of gravity.

In many theories close to general relativity, the delay depends primarily on $c$.

Abstract

Fomalont and Kopeikin have recently succeeded in measuring the velocity-dependent component of the Shapiro time delay of light from a quasar passing behind Jupiter. While there is general agreement that this observation tests the gravitomagnetic properties of the gravitational field, a controversy has emerged over the question of whether the results depend on the speed of light, $c$, or the speed of gravity, $c_g$. By analyzing the Shapiro time delay in a set of ``preferred frame'' models, I demonstrate that this question is ill-posed: the distinction can only be made in the context of a class of theories in which $c\ne c_g$, and the answer then depends on the specific class of theories one chooses. It remains true, however, that for a large class of theories ``close enough'' to general relativity, the leading contribution to the time delay depends on $c$ and not $c_g$; within this class, observations are thus not yet accurate enough to measure the speed of gravity.