Narrow Results

I present the theory and analysis behind the experiment by Fomalont and Kopeikin involving Jupiter and quasar J0842+1845 that purported to measure the speed of gravity. The computation of the v_J/c correction to the gravitational time delay difference relevant to the experiment is derived, where v_J is the speed of Jupiter as measured from Earth. Since the v_J/c corrections are too small to have been measured in the Jupiter/quasar experiment, it is impossible that the speed of gravity was extracted from the data, and I explain what went wrong with the data analysis. Finally, mistakes are shown in papers by Fomalont and Kopeikin intended to rebut my work and the work of others.

A v_J/c correction to the Shapiro time delay seems verified by a 2002 Jovian observation by VLBI. In this Essay, this correction is interpreted as an effect of the aberration of light in an optically refractive medium which supplies an analog of Jupiter's gravity field rather than as a measurement of the speed of gravity, as it was first proposed by other authors. The variation of the index of refraction is induced by the Lorentz invariance of the weak gravitational field equations for Jupiter in a uniform translational slow motion with velocity v_J=13.5 km/s. The correction on time delay and deflection is due not to the Kerr (or Lense-Thirring) stationary gravitomagnetic field of Jupiter, but to its Schwarzschild gravitostatic field when measured from the barycenter of the solar system.

Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that measuring the extrinsic gravitomagnetic field is equivalent to testing the relativistic effect of the aberration of gravity caused by the Lorentz transformation of the gravitational field. We show that the recent Jovian deflection experiment is a null-type experiment testing the Lorentz invariance of the gravitational field (aberration of gravity), thus, confirming existence of the extrinsic gravitomagnetic field associated with the orbital motion of Jupiter with accuracy 20%. We comment on physically inadequate interpretations of the Jovian deflection experiment given by a number of researchers who are not experts in modern VLBI techniques and the subtleties of JPL ephemeris. We propose to measure the aberration of gravity effect more accurately by observing the gravitational deflection of light by the Sun and processing VLBI observations in the geocentric frame with respect to which the Sun is moving with velocity ~30 km/s.

A recent review article by S. Samuel "On the Speed of Gravity and the Jupiter/Quasar Measurement" published as Int. J. Mod. Phys. D13, 1753 (2004), provides the reader with a misleading "theory" of the relativistic time delay in the general theory of relativity. Furthermore, it misquotes original publications by Kopeikin and Fomalont and Kopeikin related to the measurement of the speed of gravity by VLBI. We summarize the general relativistic principles of the Lorentz-invariant theory of the propagation of light in a time-dependent gravitational field, derive a Lorentz-invariant expression for the relativistic time delay, and finally explain why Samuel's "theory" is conceptually incorrect and confuses the speed of gravity with the speed of light.

The observation of Shapiro time delay of quasar light passing near Jupiter¹ generated considerable excitement, but also considerable controversy. The disagreements involve two distinct issues: (i) Is there a v_J/c term in the time delay that is large enough to detect? (ii) If so, is the factor of c in the delay the "speed of gravity" c_g or the "speed of light" c? I will comment briefly on each.