1. Nov 25, 2013

### Myslius

Why in C's FOR object doesn't fit?

Last edited by a moderator: Nov 25, 2013
2. Nov 25, 2013

### 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.

3. Nov 25, 2013

### Myslius

Have you looked at the link?

4. Nov 25, 2013

### 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.

5. Nov 25, 2013

### Myslius

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

6. Nov 25, 2013

### yuiop

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.

Last edited: Nov 25, 2013
7. Nov 25, 2013

### jartsa

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.

8. Nov 25, 2013

### 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.

That's not relativistic length contraction description.

9. Nov 25, 2013

### 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.

#### Attached Files:

• ###### Thomas rotation.jpg
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10. Nov 25, 2013

### 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.

Last edited: Nov 25, 2013
11. Nov 25, 2013

### 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.

12. Nov 25, 2013

### Staff: Mentor

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