What’s wrong with my yo-yo thought experiment?

[Gweedz]

Let’s say you have a yo-yo firmly attached to an almost weightless, yet unbreakable string.

 

The string is 1 light year long.

 

You attach the free end of the string to your super strong finger

 

Now you flick the yo-yo into outer space. Speed doesn’t matter, and assume gravity has no net effect on it, so it keeps traveling in a straight line away from you.

 

For one light year the yo-yo cruises along taking up the slack of the string behind it.

 

What happens to the yo-yo when all the slack is taken up?

 

Does it rebound back like a regular yo-yo? If so, then how did it know that the other end of the string is fixed? Information can only travel along the string and if it does at the speed of light then it would take 2 years for the yo-yo to know what to do. Does it just sit there for 2 years? That doesn’t make sense to a local observer of the yo-yo.

 

What if 1 millimeter before the yo-yo reached the end of the string you let go of the string? How does the yo-yo know that it’s now supposed to keep traveling in a straight line (since the string is not fixed)?

 

What am I missing here? Help me sleep at night, haha.

 

 

[DrRocket]

Let's say you have a yo-yo firmly attached to an almost weightless, yet unbreakable string.

 

The string is 1 light year long.

 

You attach the free end of the string to your super strong finger

 

Now you flick the yo-yo into outer space. Speed doesn't matter, and assume gravity has no net effect on it, so it keeps traveling in a straight line away from you.

 

For one light year the yo-yo cruises along taking up the slack of the string behind it.

 

What happens to the yo-yo when all the slack is taken up?

 

Does it rebound back like a regular yo-yo? If so, then how did it know that the other end of the string is fixed? Information can only travel along the string and if it does at the speed of light then it would take 2 years for the yo-yo to know what to do. Does it just sit there for 2 years? That doesn't make sense to a local observer of the yo-yo.

 

What if 1 millimeter before the yo-yo reached the end of the string you let go of the string? How does the yo-yo know that it's now supposed to keep traveling in a straight line (since the string is not fixed)?

 

What am I missing here? Help me sleep at night, haha.

 

 

 

You are missing the elasticity of the string. Special relativity precludes the existence of rigid bodies or infinitely stiff strings. The elastic stress wave propagates at about the speed of sound (the speed of sound strictly speaking applies to a vanishingly small stress), much less than c.

[Gweedz]

I was going to say "lets assume the string has no elasticity", until you mentioned it's a requirement for special relativity.

 

So in that case does it mean that once all the slack is taken up, the string begins to stretch? And will continue to do so for a long time (that approx. time for sound to travel more than 2 light years (2 lengths of stretched string))?

 

And when the "information" is received at the yo-yo that the other end is tied, will the yo-yo basically be at zero velocity at this time, and begin traveling back up the string?

[DrRocket]

I was going to say "lets assume the string has no elasticity", until you mentioned it's a requirement for special relativity.

 

So in that case does it mean that once all the slack is taken up, the string begins to stretch? And will continue to do so for a long time (that approx. time for sound to travel more than 2 light years (2 lengths of stretched string))?

 

And when the "information" is received at the yo-yo that the other end is tied, will the yo-yo basically be at zero velocity at this time, and begin traveling back up the string?

 

Think about a regular yo-yo with a piece of weak elastic in place of the usual string. Several things happen at once -- the yo-yo starts to wrap up the string, but it also continues to stretch at the end of the initial "down" movement.

 

.01% strain is still a lot of movement in a string that is a light-year in length.

 

To make it easy think about the yo-yo moving slowly. If t is going fast then thev speed of the elastic wave (about sound speed) gets into the act and it gets more complicated.

Edited May 18, 2011 by DrRocket

[Gweedz]

With your explanations and by rewording the problem in simpler terms I think I understand the issue as follows:

 

 

Think of a ball traveling through space with string attached behind it. They are both traveling at constant speed, in unison, the string is straight yet relaxed.

 

The ball and string travel by me, and before it passes I grab the end of the string (opposite of the ball) and hold it tight.

I imagine from that instant the string will begin to feel tension and an elastic wave will travel towards the ball. However, until the wave reaches the ball, the ball has no idea the other end of the string is not moving, so it keeps traveling with the same vector. Once the wave reaches the ball it will begin to slow down, and eventually stop and reverse direction.

 

Let's assume the string is 750 miles long, and the ball is traveling at 100 mph. The wave (traveling at approx. 750mph) will take 1 hour to reach the ball. During this time the string would have stretched 100 miles (13%) before the ball begins to slow down and reverse direction.

 

If all this makes sense then I think I can use it to explain the yo-yo problem:

 

Using the same criteria (750 miles, 100mph), as soon as the yo-yo reaches the end of the string it will send a wave back along the string. It will take 2 hours for the wave to make a round trip (ignoring the extra length of the stretched string). During these 2 hours no observer of the yo-yo can determine if the other end of the string is fixed or free. The yo-yo keeps slowing down (due to weight of string I guess). But shortly after the 2 hrs the yo-yo will either continue slowing down (fixed), or it will maintain a constant speed (free). This is the earliest an observer can determine the state of the other end of the string.

 

The above scenario is valid regardless of string length and yo-yo speed.

 

Did I get it?

[Gweedz]

Does what I said in my previous post make sense? Because if it does then I have some follow up questions.

 

Thanks.

[DrRocket]

Does what I said in my previous post make sense? Because if it does then I have some follow up questions.

 

Thanks.

 

It is considerably more complicated than that. To put numbers to it would require getting into propagation of stress waves in solids. I am not ready o break out the books and delve into that detail.