The existence of gravitational waves was a hotly debated topic after Einstein introduced general relativity.
Indeed, Einstein and Rosen concluded in 1936 that gravitational plane waves do not exist, but this conclusion turned out to be wrong.
It was Richard Feynman who came up with a thought experiment that eventually led to a rigorous mathematical foundation for the understanding of gravitational waves and their physical effects on material objects.
Feynman's argument is called the "sticky bead" thought experiment. Quoting from the Wikipedia page:
"Feynman’s gravitational wave detector: It is simply two beads sliding freely (but with a small amount of friction) on a rigid rod. As the wave passes over the rod, atomic forces hold the length of the rod fixed, but the proper distance between the two beads oscillates. Thus, the beads rub against the rod, dissipating heat."