Undergrad A textbook passage describing coordinate lines in physical space

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SUMMARY

The discussion centers on the concept of geodesics in curved space as described in the textbook "Gravitation" by Misner, Thorne, and Wheeler (2017). It highlights that in curved space, geodesics appear curved relative to straight lines in the coordinate system. The participants express a desire to reference a specific passage that illustrates this concept from a first-person perspective, which is distinct from the third-person view presented in the textbook's figures. The search for a quotable sentence related to this topic remains unresolved.

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gnnmartin
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TL;DR
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.
 
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This might help. Gravitation, Misner, Thorne & Wheeler, 2017, page 4:
1745422098549.png

AM
 
gnnmartin said:
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.
 
Andrew Mason said:
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.
 
Thanks.
 

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