A textbook passage describing coordinate lines in physical space

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Discussion Overview

The discussion revolves around the representation of coordinate lines in curved space, particularly in relation to geodesics and their depiction in a textbook. Participants are exploring the nuances of how these concepts are illustrated and referenced in literature, specifically in the context of Misner, Thorne, and Wheeler's work.

Discussion Character

  • Exploratory, Technical explanation, Meta-discussion

Main Points Raised

  • One participant recalls a textbook passage that illustrates how coordinate lines appear to 'swoop' through physical space in curved geometry.
  • Another participant references a specific page in the textbook "Gravitation" by Misner, Thorne, and Wheeler, suggesting it may contain relevant information.
  • A participant notes that the curvature of geodesics relative to straight lines in the coordinate system is not exclusive to curved spaces, mentioning that curved coordinates in flat spacetime also yield curved representations of inertial paths.
  • One participant expresses a desire for a more quotable description from the textbook that captures a first-person perspective of someone experiencing curved space.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specific passage or description sought. Multiple viewpoints regarding the representation of coordinate lines and geodesics are present, with some participants providing references while others seek additional clarification.

Contextual Notes

There is an indication that the discussion may depend on specific interpretations of curved coordinates and the visual representation of geodesics, which may not be universally agreed upon.

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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