As far as I can understand, the gravitational waves also slow down on interaction with matter similar to light rays. I am trying to understand if we can measure this?
Suppose we put two detectors on 2 opposite side of the globe and measure the time difference with the help of LIGO detectors. Then, we follow up for the location of the black holes with the help of some other em-observations. Now, we know the predicted time difference that should occur if the gravitational waves are travelling at the speed of light and the observed time difference. The difference of these 2 should be because of the slowdown of gravitational waves caused by the earth. Has such a calculation been done before?