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

[ShayanJ]

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

 

[yuiop]

...,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.

 

[ShayanJ]

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.

 

[yuiop]

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.

 

[elfmotat]

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.

 

[ShayanJ]

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.

 

[elfmotat]

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.

 

[ShayanJ]

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.

 

[elfmotat]

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?

 

[ShayanJ]

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)