# Why is the symmetry of measurements in SR no longer valid in GR?

In special relativity, we know that if an inertial observer $$A$$, having a relative motion WRT an inertial observer $$B$$, attributes, say, time dilation and length contraction to respectively $$B$$'s clocks and rulers, $$B$$ can do the same to $$A$$'s too.

However, I want to know why this is not the case in general relativity. Assume $$A$$ is located on a massive planet, and $$B$$ is a Schwarzschild observer both at rest WRT the planet. If $$B$$ measures $$A$$'s clocks run slower and his ruler contracted, $$A$$ detects vice versa, i.e., $$B$$'s clocks run faster and his ruler is possibly expanded. Why is this the case? What happens to symmetry? Is it because, in the latter example, one observer ($$A$$) is non-inertial and the other one ($$B$$) is inertial?

Moreover, please explain which ruler (radial or tangential) is contracted or expanded, and in which directions the speed of light is measured smaller or greater than $$c$$ from the viewpoint of both $$A$$ and $$B$$.

As far as I remember, radial rulers are left unchanged from the viewpoint of both of these observers. Is it correct?

• By a "Schwarzschild observer", do you mean "an observer at rest at a great distance from the planet"? (I'm guessing so, since otherwise observer $B$ isn't inertial any more than observer $A$ is.) Dec 10, 2019 at 22:40
• @MichaelSeifert Yes, I do. Dec 11, 2019 at 7:39