In another thread, Bill_K writes: Wald, is one of the sources that does it the "wrong" way. But it seems that while the wrong way is rather "sloppy", it seems to work in practice. I' would like to see if this "slopiness" could lead to incorrect answers. If we imagine that parallel transport was defined by a vector field, rather than a curve, would you agree that we could use aμ = Uα∇αUμ ? Wald's argument is that parallel transport turns out to depend only on the values of the vector field along the curve. If I'm reading this right and Wald is correct, then _any_ vector field will give the right answer, as long as its orbit generates the curve in question. This would imply that while the formulation is sloppy, it's not so bad as to give wrong answers. I'd like to be sure I'm not missing something though,.