Model-dependence of Shapiro time delay and the 'speed of gravity/speed of light' controversy

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 analysing 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 ≠ 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.