How about proper length in curved spacetime? Let's consider the radial distance between two spherical shells in Schwarzschild spacetime. The proper distance between them follows from the spacelike form of the metric with ##dt=0## for simultaneity. So I think having the r-values of the shells the proper distance calculated by this should equal the rest length of a rod between them, correct? But how would two observers, one on each shell, measure the proper distance between them? Is that possible with the knowledge of the frequency shift they see each other?