how do you measure a change of 1/10,000 of a proton diameter with a laser?
Optical lasers wavelengths are in the few thousands of angstroms (angstrom = 10^-10 meters). But a proton is 10^-15 meters in diameter, and 1/10,000 of that is 10^-19 meters, or one billionth of a photon of visible light.
So, how can you use such large photons to see such a small change in length?
Also, how do you know the size of the black holes involved, at such a distance?