If a gravitational wave is a wave of spacetime itself distor

If a gravitational wave is a wave of spacetime itself, distorting the very rulers and clocks that measure spacetime, then how is it possible to measure gravitational waves at all?

Solution

Yes, they do, but that distortion is not uniform in all directions. As in, if you will put two mirrors separated by a distance with the plane of the mirrors being perpendicular to the direction of propogation of the waves, the waves would change the \'amount of space\' between them, however, for another set of mirrors with their planes lying along the direction of the wave, ths \'amount of space\' would remain unchanged, hence the amont of time that light takes to travel along these two directions would become different, and that is detectable.

As in the case of LIGO detecting the gravitional waves, an L shaped set up was used. As discussed, as the gravitational waves pass through the set up, it changes the time needed by a light beam to travel between one pair of mirrors, while the time for the other pair reamains the same. We can measure this difference hence detecting the presence of gravitational waves.