- #36
- 24,488
- 15,021
That's exactly my point, but remember the very heated discussion we had in these forums, when I dared to make the point that a reference frame is not simply an abstract "coordinate patch" in a pseudo-Riemannian manifold but something made of real things in the lab ;-)).robphy said:In grad school, learning more tensorial methods and the abstract-index notation from Wald's text helped.
But it wasn't until I learned about operational definitions of distance and time measurements via radar-methods on a spacetime diagram from Geroch, did things finally click for me. For me, I could now tie together the verbiage of introductory texts, the notations of vectors and tensors in coordinate form and in abstract-index form, and physics connected to observation using light signals and clocks (which is more relativistic in spirit than rods and clocks).
FACK.robphy said:On my own in grad school, I stumbled upon Yaglom's "A simple non-Euclidean geometry and its physical basis", which introduced me to Klein and the Cayley-Klein geometries. I also tumbled upon Schouten's "Ricci Calculus" and "Tensor Analysis for Physicists", which introduced me to visualizing tensors.
Ideally, one really should try to be fluent in (and fluid in, in the sense of "being able to inter-connect") all of these methods.
My $0.03.