# Why does length contraction happen only in the direction of motion?

1. Oct 10, 2011

Length contraction happens only in direction of motion. Never perpendicular to the motion.
My questions are
1) Why is it so?. For an observer in the same frame, it would mean a meter scale to give 2 different results. If by some means he is able to calculate the difference won't he be able to tell that he is in motion, thus violating POR?
2) What happens to the lengths neither perpendicular, nor parallel to the direction of motion?. Is the contraction according to trigonometry?

2. Oct 10, 2011

### phinds

For the observer "in the same frame" there is no perception of length contraction and he would see the stick appear the same no matter what way he oriented. It's the same as with time dilation. It is an artifact of different reference frames, not something perceived by the person IN the fast-moving reference frame.

3. Oct 10, 2011

### cbd1

But where it gets really tricky is when you try to convert this to general relativity. Is there length contraction in a gravitational field, as there would be in an accelerating reference frame? And, in that case, is the length contraction only in one direction?

4. Oct 10, 2011

### phinds

The length contraction is an artifact of different reference frames and yes, it occurs in one direction only (parallel to the lines of gravitational force). If I understand it correctly, the length contraction in a gravitational field is due to the fact that the light from the farther end of the meter stick is slowed down (red shifted) more by the tidal effect than is the light from the nearer end and this is what gives rise the perceptions of time dilation and length contraction.

Hm ... rereading what I just wrote, I see that it would seem (I think) that the different red shifts would cause the meter stick to look LONGER not shorter.

It's possible that I don't know what I'm talking about.

I'll shut up now.

5. Oct 10, 2011