GR & Coriolis Forces: Inertial Trajectories & Resources

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Discussion Overview

The discussion revolves around the implications of General Relativity (GR) in relation to Coriolis forces on a solid spherically symmetric body, particularly in a frame of reference where the body's rotation is considered eliminated. Participants explore whether trajectories influenced by Coriolis forces can be classified as geodesic paths and seek references for further understanding.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions how GR accounts for Coriolis forces when the rotation of a solid body is eliminated, asking if the resulting trajectories are inertial and geodesic.
  • Another participant argues that defining a non-rotating frame of reference for a rotating body is impossible, as each point on the body has a different and constantly changing frame, implying that such a frame would be accelerating.
  • A third participant highlights the distinction between relative and absolute acceleration, suggesting that all observers agree on what is accelerating, which raises questions about the equivalence principle.
  • One participant proposes a Newtonian perspective, stating that in a rotating frame, Coriolis forces appear as pseudo-forces, while in a non-rotating frame, the motion is seen as straight-line motion without pseudo-forces.
  • There is a discussion about the implications of defining a frame with zero acceleration and how this relates to gravitational fields, with some participants questioning the consistency with the equivalence principle.
  • Another participant acknowledges the possibility of defining a local frame where rotation is absent but emphasizes that this frame is not inertial, thus introducing acceleration considerations.

Areas of Agreement / Disagreement

Participants express differing views on the nature of frames of reference in relation to rotating bodies and Coriolis forces. There is no consensus on whether the trajectories can be considered inertial or geodesic, and the discussion remains unresolved regarding the implications for the equivalence principle.

Contextual Notes

Participants note limitations in defining frames of reference and the implications of acceleration, particularly in relation to the equivalence principle and the nature of inertial versus non-inertial frames.

dand5
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How does GR account for coriolis forces on a solid spherically symmetric body in a frame of reference where the solidy body rotation has been eliminated?
Are these trajectories inertial, as in if a free falling object has an initial velocity along the angle between the plane of rotation and the axis of rotation, are the coriolis trajectories geodesic paths?
Also please let me know of any good references that might help me
understand this.
Thanks in advance for any replies.
 
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dand5 said:
How does GR account for coriolis forces on a solid spherically symmetric body in a frame of reference where the solidy body rotation has been eliminated?

It appears that you meant that solid body is in fact rotating then you attempt to define a frame of reference for which it is not rotating. First of all it is not possible to define such a frame of reference when each point in the body not only has a different frame of reference but the frame of reference for each point is constantly changing. By constantly changing frames of reference means that it is accelerating, i.e. constantly changing either direction or magnitude of motion. Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating. Observers can only disagree on how much acceleration. The only frame of reference in which the body is not rotating is when the body is not rotating in any frame of reference meaning no coriolis forces.
 
my_wan said:
Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating.
This seems to fly in the face of the equivalence principle.
my_wan said:
Observers can only disagree on how much acceleration.
This is better. There is a frame in which an observer would say that zero is how much. The observer attributes observations to the fact that there is a gravitational field.

There is a frame in which the rotation of the body is eliminated, but it is not an inertial frame.
 
My $.02

Relativity explains rotating frames with Christoffel symbols, but I don't really think that's the type of explanation that's being asked for here.

So let's go with the Newtonian explanation.

If you are on a rotating body, you experience a Coriolis pseudo-force if you adopt a rotating coordinate system.

If you are on a rotating body and you use a non-rotating coordinate system, there are no pseudo-forces, and the body that was experienceing the coriolis psuedo-force in the rotating coordinate system is seen to be moving in a straight line in the non-rotating coordiante system.
 
my_wan said:
Note that acceleration is not relative. All observers regardless of the frame of reference agree on what is and isn't accelerating.
jimmysnyder said:
This seems to fly in the face of the equivalence principle.

Why? I do not see how my statement implies that gravitational and inertial mass are not equivalent.

my_wan said:
Observers can only disagree on how much acceleration.
jimmysnyder said:
There is a frame in which an observer would say that zero is how much. The observer attributes observations to the fact that there is a gravitational field.

Zero how? No wait, first you defined a frame with zero acceleration. Then you say the observer attributes the observations (observations presumably meaning g forces) to a gravitational field. So you have g forces with zero acceleration? If that's not a violation of the Principle of Equivalence I don't know what is. The only frame for which you could say acceleration is zero is one moving -at- the speed of light relative to the sphere. Even that is debatable.
jimmysnyder said:
There is a frame in which the rotation of the body is eliminated, but it is not an inertial frame.

Here you have conceded that the frame is not an inertial frame, which -means- it is accelerating.

To be fair it is possible to define a frame for which locally (meaning for a given infinitesimal point within the sphere) there is no rotation, only acceleration. This is what is meant when it's said that the Principle of Equivalence only applies locally. Globally it is always possible to to prove a spin even without referring to an outside frame of reference. Just try to operate a gyroscope inside such a spinning sphere.
 

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