Wikipedia's article on torsion includes the following excerpt:
Suppose that an observer is moving along a geodesic, and carries with herself a system of rigid straight measuring rods (a coordinate system). Each rod is a straight segment; a geodesic. Assume that each rod is parallel transported along the trajectory. The fact that these rods are physically carried along the trajectory means that they are Lie-dragged, or propagated so that the Lie derivative of each rod along the tangent vanishes.
I don't understand the last sentence, which seems to equate Lie dragging with physically dragging an object. That's certainly a nice physical interpretation for something I thought was just a mathematical tool, but I can't see how Lie dragging is even relevant here.
- Why is Lie dragging needed to describe what happens when you hold a ruler? Isn't that just parallel transport of the vector pointing along the ruler?
- Along what vector field are we doing the Lie dragging? Isn't there only one vector around, the observer's velocity?