# Rope Going Off Hook Paradox

1. Jun 19, 2011

### hprog

Hi all.
Suppose we have two objects A and B, and suppose we tie a rope R to the objects with the rope R's two edges hooked to a pole or hook on each of the objects.
The rope is loosely connected to the hooks on such a way that as objects will move away from each other, then as the rope will get stretched to the maximum the rope will go off hook as a result of the farther motion.

Now as par classical physics when one of the objects A will move away and the rope will get stretched to its maximum, than the rope will go off A's hook but not off B's hook.
This is due to the fact that since A is the one in motion, and as such the tension to rope is applied at A, and as such the rope is immediately caused to get off hook.
But while the tension is traveling towards B, the rope is no longer tied to A which result in the rope tension being released and as such the rope is not going off hook at B.

This should be true no difference whether A is in accelerated motion or in linear motion, and in either case the rope will go off hook the object in motion and not at the object in rest.

But according to relativity A might claim to be at rest and B in motion, and according to A then the rope should go off at B.
But clearly only one of them can be right (note that if the rope goes off hook at both then both must be wrong!), so clearly one of them will get disproved.
So how does this fit with relativity?

2. Jun 19, 2011

### bcrowell

Staff Emeritus
You seem to be assuming that tension in a rope is always constant throughout the rope. Releasing the tension at A can't cause the wave that has begun propagating down the rope to be retroactively stopped. Constant tension throughout the rope is only an approximation that is valid when the rope has a low mass. If you try to get around this by making the mass of the rope extremely low, the rope will break when you put tension on it. This is not just a practical fact about real ropes but a fundamental limitation arising from special relativity, because the speed at which disturbances propagate along the rope will always be less than c.

-Ben

3. Jun 19, 2011

### hprog

Let it be breaking the rope, still this will happen closer to one side according to the laws of physics which we can use to determine the one in motion.
So the problem is still there.

4. Jun 19, 2011

### hprog

Here is an easy experiment that every one can conduct.
Take two objects and tie them with a plastic rope that will be riped off when stretching to much, and start to move one of the objects, you will see that the rope will rip off at the side of the moving object even if the motion is uniform.
(The fact that this experiment is at low speeds should not affect anything, since relativity should hold true at low speeds as well.)

5. Jun 19, 2011

### DaveC426913

The rope is statronary in the frame of reference of A or B. Which is it?

Your experiment does not tell you anything about which is "in motion"; it simply tells you which frame of reference the rope is stationary in.

6. Jun 19, 2011

### DaveC426913

OK. A couple of things here.
1] Starting to move one of the objects means that that object is accelerating. It is easy to tell which object is the accelerating one and which is the stationary one. Relativity has no problem with this.

2] If you change the scenario so that they are moving away from each other inertially then there's no acceleration. In this scenario, it is meaningless to try to determine which one is moving and which one is not, since there is no absolute frame of reference. The question of which end of the rope lets go is determined entirely by whether the rope is statonary wrt A or wrt B.