Thank you. My comment about the preferred reference frame is a little embarrassing to me. There is nothing wrong with preferring a frame which matches geodesics closely. Furthermore, the distances which one measures in that frame are invariant with respect to metric, in that picking a...
Thx Re: Scaling Paradox.
Thank you, Justin Levy. I wrote a lot because I wanted my paradox to be understood by someone who is new to differential geometry. Jargon can speed or impede communication. Your reply confirmed a suspicion of mine which I have not seen explicitly stated in a text...
Differential geometry (which includes general relativity) often introduces the length differential, expressed as ds2=gabdxadxb, to introduce the covariant form of the metric tensor gab. However, this formulation scales ds2 incorrectly. The appearance of an index as a superscript, as in dxa...