A Relativity-Related Thought Experiment that has Given me Trouble

1. Jul 26, 2012

Math Buddy

Hello everyone, I'm not a physics major or anything but I have an interest in math and physics. I do know the basics of relativity and with what I know I can't make sense of this. (I came up with this on my drive home after a long calculus lecture, in case you're wondering.)

Imagine that you have an extremely long rope (held taught, without any slack). So long, in fact, that it spans from one side of the universe to the other (assume the rope has no elasticity). Imagine that at each end of this long rope are two different people. Now, one of these people suddenly pulls the rope towards himself, in a straight "tugging" motion.

What does the person at the other end of the pole feel/see at the instant that the first person pulls the rope? Keep in mind that the object is one piece and it spans the entire universe.

If the person pulls the rope, the light from this event occuring would not reach him/her instantaneously, as we all know, since light takes time to travel over long distances. But if the object was truly solid, then the man on the opposite side of the universe should feel the rope move instantly (since the rope is one object.) So he paradoxically sees the rope move but doesn't see it move at the same time.

I am aware that this kind of paradox has been pointed out before, and that Einstein's theories imply that no two events can happen truly instantaneously. However, I beleive this case is different because of the solid object between them. Can someone please explain this to me?

On a side note, what does the person who pulled the rope experience after he has made the initial "tug"? If he were to look with a telescope to the other end of the universe, he would see that the rope at the other end has not yet been tugged. But this implies that the rope is longer than it really is, since it is further away from where it started before being "tugged" yet also appears not to have moved on the opposite side of the universe.

I hope I explained this paradox understandably. I brought this up with my dad a few nights ago and he was also unable to provide me with answers. I would really appreciate if someone could shed some light on what occurs in this hpothetical situation.

2. Jul 26, 2012

Staff: Mentor

Please take a look at our FAQ entry: Can I send a signal faster than light by pushing a rigid rod?

Bottom line: The signal would travel at the speed of sound in the material. No matter how rigid or taut you make the rope, that speed will never exceed the speed of light. There are no perfectly 'rigid' bodies in relativity.

3. Jul 26, 2012

Math Buddy

Fascinating, thanks for clearing that up!