From my understanding, we are not really moving "anywhere." By this, I mean direction is not absolute. Walking north, in terms of spacetime curvature, is the same as walking south. The only way in which we are moving is through spacetime. A guy going 70mph on a train in Paris is moving through spacetime the same as a guy in NYC on a train going 70mph, minor gravitational effects aside. Okay, here's where it starts to get confusing for me, and I will not attempt to be perfectly rigorous in my interpretation, as I foolishly did before. My pup is asleep (at rest). She is moving (relatively) through spacetime only at the rate at which the earth is rotating relative to other planets, stars, or whatever, but in the reference frame we're using here, she's at rest. Suddenly my pup awakens because she can smell the piece of bacon I put in her food bowl. She gets on all four paws and races toward the bacon. At this point she is accelerating, and this is where I'm getting confused. If she is accelerating relative to the earth beneath her paws (correct me if that is not correct), could we also say that it's the earth beneath her paws that is accelerating in the opposite "direction"? There is something occurring among space, motion, and acceleration that is very confusing to me. It seems that "space" (and its "contraction") is creating this idea of accelerated motion, when it's not really happening.