I A textbook passage describing coordinate lines in physical space

[gnnmartin]

TL;DR Summary

A picture illustrating coordinate lines 'swooping' through physical space.

In curved space, geodesics are curved relative to lines which are straight in the coordinate system. I remember seeing a text book that illustrated the corollary, the coordinate lines 'swooping' through physical space. I wish to reference it. I thought it was in 'Gravitation' by Milner Thorn & Wheeler, but if it is, I can't find it now.

 

[Andrew Mason]

This might help. Gravitation, Misner, Thorne & Wheeler, 2017, page 4:

AM

 

[Ibix]

In curved space, geodesics are curved relative to lines which are straight in the coordinate system.

Just to note, this isn't particular to curved spaces. If you have curved coordinates in flat spacetime, inertial paths will be represented by curved lines in coordinate space.

 

[gnnmartin]

This might help. Gravitation, Misner, Thorne & Wheeler, 2017, page 4:
View attachment 360283
AM

Thanks. I was aware of the M T &W's figure, but it is rather a 'third person' view annd not very quotable. The description I thought I remember reading talks about a first person view: someone in curved space visualising the coordinates. I thought I remembered a rather snappy quotable sentence, but can't remember it or whose it was.

 

[gnnmartin]

Thanks.