# Special relativity & length contraction

1. Sep 24, 2007

### Denton

Ive heard that length contraction does not occur when the movement of the object is perpendicular to the observer. Is this correct?

Say two identical rings were travelling at eachother at relativistic speeds, whilst the observer is perpendicular to them. Ring A would see ring B contract and therefore pass through whereas ring B would see ring A contract and go through it. Since both cant contract AND pass through eachother as seen by the perpendicular observer, it does not apply to perpendicular frames of reference.

2. Sep 24, 2007

### JesseM

What do you mean when you talk about movement that is "perpendicular to the observer"? "Observers" don't have one single angle that they measure things, they have coordinate systems which cover all of space. For any object, no matter what the direction, in the observer's own coordinate system the object's length will be contracted along the axis parallel to its direction of motion in that coordinate system, and uncontracted along the axis perpendicular to its direction of motion.
This isn't very clear. Is the plane of each ring (the plane where the ring appears to be 'lying flat') perpendicular to its direction of motion? If so, only the ring's thickness will be contracted, its diameter won't be.

Last edited: Sep 24, 2007
3. Sep 24, 2007

### Denton

oh right perpendicular to the object, not the observer. Never mind me.

4. Sep 24, 2007

### rbj

let's say you have what you see as a perfect cubical shaped box when it is in your frame of reference (not moving relative to you). let's say the sides of the box are aligned with some perpendicular x, y, and z axes. now let's say that you fly that box past you in the direction of the x axis at some relativistic speed. the length of the side of the box along the x axis will be contracted, from your perspective, while the lengths of the sides along the y and z axes will not be contracted. the box will no longer look like a cube but will look squished in the x axis sense of direction, the same direction of relative movement.