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kent davidge
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Is it difficult to show that a Fermi-Walker "rotation" happens only in the plane formed by a particle four-acceleration and four-velocity?
kent davidge said:Is it difficult to show that a Fermi-Walker "rotation" happens only in the plane formed by a particle four-acceleration and four-velocity?
I can't see directly from the definition. So I am trying to prove/show it. I guess we need to show that a vector in the plane formed by the four-acceleration and four-velocity, when rotated, still lies in the same plane. Correct?PeterDonis said:Since it follows directly from the definition of Fermi-Walker transport, I would say no.
kent davidge said:I can't see directly from the definition.
kent davidge said:I guess we need to show that a vector in the plane formed by the four-acceleration and four-velocity, when rotated, still lies in the same plane. Correct?
I find it hard to show that an infinitesimal Lorentz boost in the ##u-a## plane gives as a result your equation 1.8.5.vanhees71 said:You can find a derivation of Fermi-Walker transport in terms of old-fashioned Ricci calculus here:
https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf
Fermi-Walker is a mathematical tool used in the study of general relativity to describe the motion of a particle in a curved spacetime. It shows the rotation of a particle in the plane of its 4-acceleration and 4-velocity by calculating the change in the direction of the 4-velocity vector as the particle moves along its worldline.
Understanding rotation in the plane of 4-acceleration and 4-velocity is important in the study of general relativity because it allows us to accurately describe the motion of particles in curved spacetime. This is crucial in understanding the behavior of objects in the presence of massive bodies, such as planets and stars.
Fermi-Walker is closely related to the concept of parallel transport, which describes the movement of a vector along a curved path without changing its direction. In the case of Fermi-Walker, the vector being transported is the 4-velocity vector of a particle, and the path is the particle's worldline.
Yes, Fermi-Walker can be applied to any type of motion in curved spacetime, as long as the motion can be described by a 4-velocity vector. This includes both geodesic motion (the natural motion of a particle in a curved spacetime) and non-geodesic motion (where the particle is under the influence of external forces).
While Fermi-Walker is a useful tool in the study of general relativity, it does have limitations. It assumes that the spacetime is stationary and that the particle is moving along a smooth and continuous path. Additionally, it does not take into account the effects of quantum mechanics, which are necessary for understanding the behavior of particles at a very small scale.