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kent davidge
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Is the wikipedia definition of Fermi coordinates accurate? https://en.wikipedia.org/wiki/Fermi_coordinates
kent davidge said:Is not that the definition of Riemann coordinates?
Actually, the metric on origin curve will still be Minkowski, even though the connection coefficients will not vanish on this curve. Even if such coordinates are further extended to allow frame rotation (also done in MTW), the metric exactly on the origin world line remains Minkowski.PeterDonis said:As far as it goes, yes, it looks OK, although it is phrased in terms of Riemannian geometry, i.e., locally Euclidean, instead of locally Minkowski.
Note that some textbooks (such as MTW) use the term "Fermi normal coordinates" in a broader sense, as coordinates adapted to a timelike curve, which does not necessarily have to be a geodesic. In the non-geodesic case, the definition has to be broadened somewhat, since the metric will not be exactly Minkowski on the curve and not all of the Christoffel symbols will vanish on the curve.
can you tell me what page is this discussed in mtw?PAllen said:Actually, the metric on origin curve will still be Minkowski, even though the connection coefficients will not vanish on this curve. Even if such coordinates are further extended to allow frame rotation (also done in MTW), the metric exactly on the origin world line remains Minkowski.
pp. 327 - 332, in my edition.kent davidge said:can you tell me what page is this discussed in mtw?
PAllen said:the metric on origin curve will still be Minkowski
I've been looking. Are you sure that the coordinates they construct there are Fermi coordinates?PAllen said:pp. 327 - 332, in my edition.
It is a generalization of Fermi coordinates to allow both rotation around and proper acceleration of the origin world line. If you restrict to the case where the basis is Fermi-Walker transported, and there is no proper acceleration, you end up with traditional Fermi coordinates. But the literature has never been consistent about how restrictive the definition of Fermi coordinates should be, and there are authors who have called the full construction presented in MTW as Fermi Normal Coordinates. Note that at the top of p. 332 they show the reduction to the restrictive definition.kent davidge said:I've been looking. Are you sure that the coordinates they construct there are Fermi coordinates?
I'm asking you that because I'm having a hard time matching what they do with the definitions of Fermi coordinates found across the web.
How is it possible that the metric remains Minkowskian when its derivatives don't vanish along the curve?PAllen said:the metric on origin curve will still be Minkowski, even though the connection coefficients will not vanish on this curve
kent davidge said:How is it possible that the metric remains Minkowskian when its derivatives don't vanish along the curve?
kent davidge said:How is it possible that the metric remains Minkowskian when its derivatives don't vanish along the curve?
Umm, f(x) = x is zero at x=0, what is its derivative there? F(x,y) =xy is zero along either axis, but what about the partial derivatives on the axes? It’s really that simple an idea.kent davidge said:How is it possible that the metric remains Minkowskian when its derivatives don't vanish along the curve?
kent davidge said:they say "for small t" the coordinates take the form (t,0,0,0).
kent davidge said:that's not what they seem to be describing there
kent davidge said:they are describing a geodesic on which the coordinates are centered
kent davidge said:wouldn't it be a mistake of them to say that it's only for small t?
Fermi coordinates are a set of coordinates used to describe the position and movement of objects in a curved space, such as in general relativity. They are named after physicist Enrico Fermi.
Fermi coordinates are unique because they are defined in terms of the observer's reference frame. This means that they can be used to describe the position and movement of objects relative to an observer, rather than a fixed point in space.
Fermi coordinates are important in the field of general relativity, as they allow us to describe the behavior of objects in a curved space. They are also used in other areas of physics, such as in the study of black holes and gravitational waves.
To calculate Fermi coordinates, we first need to define a reference frame or observer. Then, we use mathematical equations to transform the coordinates of an object in a curved space to its coordinates in the observer's reference frame.
Yes, Fermi coordinates can be used in any type of curved space, as long as we have a defined reference frame or observer. They are not limited to any specific type of space or geometry.