Why does the circle appear as an ellipse when moving at different velocities?

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Discussion Overview

The discussion revolves around the perception of a circle as an ellipse when observed from different inertial frames, particularly when one frame is in motion relative to the other. It explores the implications of length contraction in special relativity and how observers in different frames perceive measurements of radii of a circle under motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that when a circle is in motion along the x-axis, the radius in that direction contracts, leading to the appearance of an ellipse from the perspective of an observer in motion.
  • Others argue that an observer at rest with respect to the circle would not notice any contraction and would measure the circle as a circle before and after acceleration.
  • A participant suggests that while the ruler used to measure the radius along the direction of motion is also contracted, the radius perpendicular to the motion remains unchanged, leading to different measurements.
  • Another viewpoint is that if both observers measure the same radius in different directions and find them equal, the moving observer would not conclude they are in motion.
  • Some participants express uncertainty about how an observer could detect motion if all measurements yield the same results.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus, as multiple competing views remain regarding the implications of length contraction and the ability to detect motion relative to a circle.

Contextual Notes

The discussion highlights limitations in understanding how measurements are affected by relative motion and the assumptions about the observers' frames of reference. There are unresolved questions about the nature of measurements and the perception of motion.

ShayanJ
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Imagine a circle lying on xy plane and initially at rest w.r.t. frame S.
Then S' comes and gets the circle and moves it with velocity v along x axis.
The radius which is along x axis,should be contracted but not other radii and this means that the circle becomes an ellipse and because its sth that needs only a comparison between two not aligned radii,S' will notice the deformation and so S' realizes that he is moving but this can't be true.
What's wrong?
thanks
 
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Shyan said:
...,S' will notice the deformation and so S' realizes that he is moving but this can't be true.
What's wrong?
All that tells him, is that he moving relative to the circle. There is no issue with that. You can detect that you are moving relative to a circle without moving at speeds that make length contraction obvious. There is nothing that forbids detecting motion relative to another object.
 
No No,you didn't get what I meant.
S' is at rest relative to the circle.
When motion starts,contraction occurs for the radius along the x axis.
S' compares this radius with others and sees the difference so he realizes he is moving.
 
Shyan said:
No No,you didn't get what I meant.
S' is at rest relative to the circle.
When motion starts,contraction occurs for the radius along the x axis.
S' compares this radius with others and sees the difference so he realizes he is moving.

Ah, OK. S' accelerated with the circle to a new constant velocity relative to S. S measures the circle to be shortened along the x-axis relative to the y-axis after the acceleration. S' on the other hand (who is co-moving with the circle) always sees and measures the circle to be a circle before and after the acceleration.
 
Shyan said:
No No,you didn't get what I meant.
S' is at rest relative to the circle.
When motion starts,contraction occurs for the radius along the x axis.
S' compares this radius with others and sees the difference so he realizes he is moving.

He will not be able to detect any contraction. He measures the radius with a contracted ruler, so he finds the radius to be the same in every direction.
 
There is a point here.
Yes,he measures the radius with a contracted ruler but only along x axis.
Imagine he has a ruler.He places it along the radius which is in direction of motion.
That radius is contracted and so the ruler.
Then he takes the ruler and places it along the radius which is,e.g. perpendicular to the direction of motion so not the radius nor the ruler is contracted.
Because of this,he measures different radii and so he sees the circle to be an ellipse.
 
Shyan said:
There is a point here.
Yes,he measures the radius with a contracted ruler but only along x axis.
Imagine he has a ruler.He places it along the radius which is in direction of motion.
That radius is contracted and so the ruler.
Then he takes the ruler and places it along the radius which is,e.g. perpendicular to the direction of motion so not the radius nor the ruler is contracted.
Because of this,he measures different radii and so he sees the circle to be an ellipse.

The ruler and the cicle only contract in the direction of motion. When he measures the contracted radius (the one parallel to the direction of motion), he does so with a contracted ruler. They are both contracted by the same amount, so he measures the same length he would if he were at rest. When he measures the uncontracted radius (the one perpendicular to the direction of motion), he does so with an uncontracted ruler. Both measurements will be the same.
 
Yes.
Imagine [; L_0=30 \ cm ;].
S and S',while both at rest,measure the radii to be [; 30 \ cm ;].
S' begins motion.Then S measures the radius along the direction of motion,to be less than [; 30 \ cm ;].
But S' measures that to be [; 30 \ cm ;] but when he measures other radii,he is like S and again gets [; 30 \ cm ;]
But I think he should realize the difference between two [; 30 \ cm \ s;] as S understands.
 
Shyan said:
Yes.
Imagine [; L_0=30 \ cm ;].
S and S',while both at rest,measure the radii to be [; 30 \ cm ;].
S' begins motion.Then S measures the radius along the direction of motion,to be less than [; 30 \ cm ;].
But S' measures that to be [; 30 \ cm ;] but when he measures other radii,he is like S and again gets [; 30 \ cm ;]
But I think he should realize the difference between two [; 30 \ cm \ s;] as S understands.

I'm not sure what you're confused about. If he gets 30 cm in every direction then why would he conclude that he is moving?
 
  • #10
Both S and S' also get the same 30 cm for e.g. a rod.
But S sees the rod,which is at rest w.r.t. S',smaller.
Now when S' looks at a rod along the direction of motion and another perpendicular to it,its like the situation above.Its like S comparing his rod with S' 's contracted rod.
He notices the difference.(at least as I think)
 

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