Measuring procedure for Fermi Normal coordinates

In summary, Fermi normal coordinates are used for direct measurement of distances and are shown to match radar distance very locally, but not in general. It is possible to measure Fermi normal distance at a solar system scale by knowing the local metric and tracking acceleration, but this is not very practical. Another approach is using a chain of stationary observers, but this is also not a practical method.
  • #1
PAllen
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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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  • #2
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.
 

1. What are Fermi Normal coordinates?

Fermi Normal coordinates are a type of coordinate system used in general relativity to describe the spacetime around a massive object. In these coordinates, the distance from the massive object is measured along the worldlines of free-falling particles.

2. Why are Fermi Normal coordinates important?

They are important because they allow us to describe the effects of gravity on objects in a simple and intuitive way, without the need for complicated mathematical equations. They also allow us to make precise measurements of distances and times in curved spacetime.

3. How are Fermi Normal coordinates measured?

The measuring procedure for Fermi Normal coordinates involves first selecting a reference point, then measuring the distance from that point to the massive object along the worldlines of free-falling particles. This distance is then used to define the coordinates at that point, and the process is repeated at different points to create a coordinate system.

4. What are some applications of Fermi Normal coordinates?

Fermi Normal coordinates have been used in various astronomical and astrophysical studies, such as modeling the orbits of planets and satellites around massive objects, and studying the effects of gravitational waves on spacetime.

5. Are there any limitations to using Fermi Normal coordinates?

While Fermi Normal coordinates are useful for describing the spacetime around a single massive object, they are not suitable for describing the spacetime in more complex situations, such as multiple interacting objects. They also do not take into account the effects of matter and energy on spacetime.

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