- #1
hawkdron496
- 19
- 3
- TL;DR Summary
- Trying to understand a trick Carroll uses to derive the geodesic equation by extremizing proper time
On pages 106-107 of Spacetime & Geometry, Carroll derives the geodesic equation by extremizing the proper time functional. He writes:
What I am unclear on is the step in 3.47. I understand that the four velocity is normalized to -1 for timelike paths, but if the value of f is fixed, how can we vary it at all?
What I am unclear on is the step in 3.47. I understand that the four velocity is normalized to -1 for timelike paths, but if the value of f is fixed, how can we vary it at all?