I'm reading a book about unification of general relativity and quantum physics. The author states that one of the axioms of GR is background-independence, meaning that space-time has no external reference points. All distances and motions in space-time are relative. On the other hand, the standard interpretation of gravity according to GR states that two objects fall toward each other because their straight-line geodesics intersect as the objects travel through curved space-time. Every book I've read about GR gives the same explanation. However, the very notion of traveling along geodesics through curved space-time clearly violates background independence, which is the basis of GR. If all objects are traveling together "through" space-time (being background-independent), then where could they be "traveling" to? What makes them travel? What is their "destination"? Is there another way to interpret gravity within the context of GR without violating background independence?