C FOR Loop Paradox: Unraveling the Mystery

[Myslius]

<<Unacceptable Link>>
Why in C's FOR object doesn't fit?

 

[yuiop]

Who is C? What is the object?

I assume you are talking about the barn and ladder paradox. If so I assume you mean the object to be the ladder and in the rest frame of the ladder the ladder does not appear to fit in the barn, because in the frame the barn is length contracted and is measured to be shorter than the ladder. in this reference frame, the ladder does not have to fit, because the doors are not simultaneously closed in this reference frame, so the ladder can stick out one end of the barn or other.

It is only in the reference frame of the barn that the doors are simultaneously closed, but that is not a problem, because in the reference frame, the ladder is length contracted relative to the barn and fits inside the barn with both doors closed.

 

[Myslius]

Have you looked at the link?

 

[jartsa]

I would guess it's because the person that made the animation did not make the red object lorentz contracted enough.

Even the leading edge does not seem to fit. With the tilting and with the the correct lorentz contraction it should just exactly fit.

 

[Myslius]

jartsa, you can make it Lorentz contracted till it becomes a line, still don't fit.

 

[yuiop]

Have you looked at the link?

Did not see the link for some reason. Yes, it looks like red B object if having a problem fitting inside the blue tube A in C's FOR, but I am not sure how accurate the animation is. It looks like there has been an attempt to take account of Thomas rotation when the red square B is moving diagonally. The degree of Thomas rotation depends on the order of the transformations and the error might be there.

In C's FOR, the red object should be length contracted in the vertical direction to the same extent as the inside of the blue tube and also length contracted in the horizontal direction to the same extend as in A's FOR, so it appears the animation is not accurate.

 

[jartsa]

jartsa, you can make it Lorentz contracted till it becomes a line, still don't fit.

Depends on the direction of the compression. Oh yes I see that if the direction of the compression is the same as the direction of the motion in the animation, then the line would not fit.

But the direction of the motion changes, when the the extra compression is caused by extra vertical speed. Motion becomes more vertical.

 

[Myslius]

"Length contraction is only in the direction parallel to the direction in which the observed body is traveling".
And so we have a problem... It doesn't care about vertical or horizontal contraction. If it were to compress in x and y direction equally, it's just stating that the object becomes smaller, but not length contracted.

But the direction of the motion changes, when the the extra compression is caused by extra vertical speed.

That's not relativistic length contraction description.

 

[yuiop]

This sketch shows how the red object actually would be skewed.

The general rule is that when an object is moving orthogonally to the intended boot direction, edges that are initially parallel to the intended boost direction will be rotated after the boost, while edges of the object that are orthogonal to the intended boost direction will not rotate.

 

[Myslius]

yuiop, yes, now it fits (when A moves vertically relative in C's coordinate system). Let's say A comes from the right to the left, doesn't fit.

 

[jartsa]

I see, horizontal edges stay horizontal, ok, thank you yuiop.No downwards motion of red rectangle - the side edges are vertical
Some downwards motion of red rectangle - the side edges are tilted
Huge amounts of downwards motion of red rectangle - the side edges are almost vertical again

At enormous vertical velocities time dialtion causes the sideways motion almost to stop, then there's no reason for the rectangle to be tilted.

 

[Dale]

The link in the OP is not acceptable to PF standards, so the thread must be closed.