Before the recent LIGO result, there was already not much doubt that gravitational effects propagated at c, but the evidence was indirect. To what extent does the LIGO result test this directly, and how will this be improved in the future?(adsbygoogle = window.adsbygoogle || []).push({});

The H1 and L1 instruments are separated by 3002 km, which corresponds to ##T=10## ms at the speed of light. The time delay for a signal propagating at speed ##v## and arriving from an angle ##\theta## with respect to the H1-L1 line would be ##T(c/v)\cos\theta##. The actual time delay in the GW150914 events was 7 ms (caption to fig. 1 in the PRL paper). So I guess this doesn't actually test anything. If the time delay had been *longer* than ##T##, then it would have falsified GR's prediction of ##v=c## by proving ##v<c##.

I suppose if they see a statistically significant number of events, then comparing the probability distribution of the time delays with a statistical prediction of the curve should give a measurement of ##v##.

They localized the source of GW150914 to a certain arc (less than a full circle) in the sky. I haven't seen any details of how this was done, but my guess is that they assume ##v=c## to determine##\theta##, and probably polarization constraints eliminate part of the resulting circle...?? Once the European detectors come online, are there good prospects for doing triangulation, so that we would get an independent measurement of ##\theta##?

The LIGO result puts strict limits on dispersion, so in that sense it gives us a direct determination of possible *differences* between values of ##v## for waves of different frequencies.

If future gravitational wave events can be correlated with electromagnetic signals such as gamma-ray bursts, I guess that would also be pretty clear evidence.

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# I LIGO and speed of propagation of gravity

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