I thought Einstein’s conclusion was that if the sun’s mass suddenly vanished, the earth would fly off tangentially like a ball being twirled on a string if the string broke. There would be no lag, as if the gravitational “wave” had to travel the 93 million miles.
Possible experimental measurements
The speed of gravity (more correctly, the speed of gravitational waves) can be calculated from observations of the orbital decay rate of binary pulsars PSR 1913+16 (the Hulse–Taylor binary system noted above) and PSR B1534+12. The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%.[18] However, according to PPN formalism setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed cannot be infinite.
In September 2002, Sergei Kopeikin and Edward Fomalont announced that they had made an indirect measurement of the speed of gravity, using their data from VLBI measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of the bright radio source quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.
Several physicists, including Clifford M. Will and Steve Carlip, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, Hideki Asada in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.[20] However, Kopeikin and Fomalont continue to vigorously argue their case and the means of presenting their result at the press-conference of AAS that was offered after the peer review of the results of the Jovian experiment had been done by the experts of the AAS scientific organizing committee. In later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time null cone in two – one for gravity and another one for light, the authors claimed that Asada's claim was theoretically unsound.[21] The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors[22][23] but was never properly employed by Asada and/or the other critics.
Stuart Samuel also suggested that the experiment did not actually measure the speed of gravity because the effects were too small to have been measured.[24] A response by Kopeikin and Fomalont challenges this opinion.
It is important to understand that none of the participants in this controversy are claiming that general relativity is "wrong". Rather, the debate concerns whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions. A comprehensive review of the definition of the speed of gravity and its measurement with high-precision astrometric and other techniques appears in the textbook Relativistic Celestial Mechanics in the Solar System.
Direct measurements of gravitational waves
The first direct observation of gravitational waves, from the merger of a pair of black holes, on 14 September 2015 (announced by the LIGO and Virgo collaborations on 11 February 2016[27][28][29]), allowed a more direct measurement of their speed. The extent of any deviation of the speed of gravitational waves (vg) from the speed of light (c) can be parameterized in terms of the mass of the hypothetical graviton. The graviton is an elementary particle that plays the role of force carrier in quantum theories about gravity, and is expected to be massless. If it was not massless, gravitational waves would propagate below lightspeed, with lower frequencies (ƒ) being slower than higher frequencies, leading to dispersion of the waves from the merger event.[30] No such dispersion was observed.[30][31] The observations of the inspiral give an upper limit on the mass of the graviton of 2.1×10−58 kg, corresponding to 1.2×10−22 eV/c2 or a Compton wavelength (λg) of greater than 1013 km, roughly 1 light-year.[27][30] Using the lowest observed wave frequency of 35 Hz, this translates to a lower limit on vg such that the upper limit on 1-vg /c is ~ 4×10−19.