Measuring procedure for Fermi Normal coordinates

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SUMMARY

Fermi normal coordinates are specifically designed for direct measurement of distances, aligning with concepts of born rigidity. Synge's book on General Relativity confirms that radar distance matches Fermi normal distance only in localized contexts. The discussion explores the feasibility of measuring Fermi normal distance at solar system scales, suggesting that detailed knowledge of the local metric and tracking one's own acceleration could theoretically allow conversion from radar ranging to Fermi-normal distance. However, practical applications remain elusive, with a conceptual method involving a chain of stationary observers proposed as a potential approach.

PREREQUISITES
  • Understanding of Fermi normal coordinates
  • Familiarity with General Relativity concepts, particularly from Synge's work
  • Knowledge of local metrics in spacetime
  • Basic principles of radar ranging techniques
NEXT STEPS
  • Research methods for measuring local metrics in General Relativity
  • Explore advanced concepts in Fermi normal coordinates
  • Investigate practical applications of radar ranging in astrophysics
  • Study the implications of acceleration tracking in relativistic contexts
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Physicists, astrophysicists, and researchers in General Relativity who are interested in the practical measurement of distances in curved spacetime.

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Locally, Fermi normal coordinates are designed to correspond with direct measurement of distances (born rigidity). I also discovered that Synge's book on GR establishes that very locally, radar distance must match Fermi normal distance, but not in general (obviously). What I am wondering is whether there is any conceivable procedure for measuring Fermi normal distance, say at solar system scale? I can't come up with anything other than: if you know the local metric in detail, and track your own acceleration, you can, in principle, convert from a radar ranging distance to a Fermi-normal distance. That is not very practical. Any operational way to do this?
 
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The only other thing that comes to mind is a large number of observers, all of whom are stationary with respect to you (you can use the radar notion of stationary), and using a "chain of observers" in a straight line to measure the distance. That's really more a conceptual appraoch than something you'd carry out in practice, though.

Knowing the local metric in detail is probably the most practical.
 

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