Can a Universe-Sized Rubber Pipe Exist in Two States at Once?

[_StrongArm_]

I was thinking of this problem recently and thought it'd be best if I got an answer from a physicist (or anyone else who'd know how to solve this).

Imagine a thin rubber pipe about a meter long. Holding each end of the pipe with both hands (respectively), you bend the ends inwards to form a torus (circle) with a gap where your hands are. Firmly gripping the ends of the pipe, by twisting your left hand, your right hand instantly feels the right end of the pipe twist as well, and vice versa.

Now hypothetically speaking, imagine if this pipe were the size of the universe (or at least large enough where the speed of light would take considerable time to travel it's length). With the same setup as above, if I were to simultaneously twist the right side clockwise and the left size ANTI-clockwise;

- What direction is the pipe twisting?
- What happens when these twists (moving at the speed of light) meet?
- Is this a physical paradox whereby a single object can exist in two states at once?

Even more puzzling;

- What happens if I shift both my hands outwards in opposite directions? (in comparison to doing this with the 1m pipe, where moving my left hand outwards in reference to the circle would see the other end of the pipe replace the area where my left hand was)

Answers appreciated.

 

[_StrongArm_]

http://s18.postimg.org/u2ek6cycp/Circular_Pipe_Experiment.jpg

To help visualize my 4th question. Grey ovals are where your hands are. Interesting to consider that because the effects of doing this on a hypothetical galactic pipe are delayed, the mind (from experience and through intuition) visualizes the pipe as decreased/decreasing in length.

 

[Gordianus]

Unfortunately your experiment is flawed. When you twist one end the other one doesn't twist instantly. It takes some time for the disturbance to travel.

 

[Crazymechanic]

And the time it takes to travel is considerably longer than the one light takes to go through vacuum at the speed of c , so in real life light would have completed it's journey to the other end while the material would still be twisting to get to the newly given shape.

 

[Nugatory]

There's an FAQ in the relativity forum that may be a helpful starting point: https://www.physicsforums.com/showthread.php?t=536289

It focuses on rigid objects, but it's applicable to your non-rigid rubber tube as well because the basic point is that when dealing with relativistic speeds... Nothing is rigid.

 

[_StrongArm_]

Unfortunately your experiment is flawed. When you twist one end the other one doesn't twist instantly. It takes some time for the disturbance to travel.

'Instantly' as in if I were to punch you, you'd feel the pain "instantly". I was talking in a general sense. Technically, the twist is moving much slower than c, but that doesn't change anything. Irrelevant to how slow or fast the twist is going, it's going. And what happens when they meet?

And the time it takes to travel is considerably longer than the one light takes to go through vacuum at the speed of c , so in real life light would have completed it's journey to the other end while the material would still be twisting to get to the newly given shape.

I understand this, but as stated above, nothing changes.

There's an FAQ in the relativity forum that may be a helpful starting point: https://www.physicsforums.com/showthread.php?t=536289

It focuses on rigid objects, but it's applicable to your non-rigid rubber tube as well because the basic point is that when dealing with relativistic speeds... Nothing is rigid.

Interesting link, but my question is not an attempt to have something travel faster than light. It's one questioning the object itself and how we define it and it's state in an abstract situation. For example, here's another question:

When the two twists meet;

- Does the pipe break?

I'd say no, because there's not enough force being applied for that to happen. So if it doesn't break;

- What happens?

 

[Nugatory]

When the two twists meet;
- Does the pipe break? I'd say no, because there's not enough force being applied for that to happen. So if it doesn't break;
- What happens?

OK, I think I see what you're asking. We can simplify the problem some by not making the length of the tube anywhere close to the size of the universe; all that's necessary is that it be long enough so that the twist/wave takes a noticeable amount of time to get from one end to the other. That's going to be at most a few tens of meters for any reasonable rubber tube-like object - no relativity, no weird universe-wide effects.

You're right that the tube won't break. There's no reason why it should, as we're only twisting it by a quarter-turn or so, and it's elastic enough to handle that easily.

So what does happen? First, imagine that you twist the tube only with your left hand, so there's only one wave traveling through the tube; it will eventually arrive at your right hand. Behind the wavefront, the tube is twisted one-quarter turn and ahead of the wavefront the tube is untwisted. The interesting stuff is happening at the wavefront, where the rubber between the twisted and untwisted regions is stretched; the force of the stretching rubber is tending to twist the untwisted region, moving the wavefront towards your right hand.

Now if you start a second wave by twisting the other end of the tube in the opposite direction with your right hand, we have two wave fronts moving towards each other, and dividing the tube into three regions: one behind the right-moving wavefront, where the tube is corkscrewed by a quarter-turn clockwise; another behind the left-moving wavefront, where tube is corkscrewed by a quarter-turn counter-clockwise; and a third between the two, where the tube is still untwisted. This third region gets smaller as the two waves approach one another and disappears when they meet.

Calculating exactly what happens at the exact moment that the two wavefronts meet is seriously hairy and requires detailed knowledge of the physical characteristics of the material the tube is made from. But for most reasonably elastic rubber-like substances, the two wavefronts will pass through each other, again leaving the tube divided into three regions. The region between the left-moving wave and your left hand is still corkscrewed by a quarter turn clockwise; the region between the right-moving wave and your right hand is corkscrewed by a quarter turn counterclockwise; and the region in the middle is twisted by a full half-turn. As the waves move towards your hands, this middle region grows while the other two shrink and then disappear completely when the waves reach your hands.

And when they do, the entire tube is corkscrewed by one-half, just as you'd expect from twisting the ends one-quarter turn each in opposite directions.

(Note that depending on just how elastic your tube is, the waves may travel back and forth and the tube may bounce around quite a bit before everything settles down. And calculating the exact speeds and magnitudes of the wave is going to be complex and messy - but the above will do for a qualitative description of how it all plays out).

 

[_StrongArm_]

OK, I think I see what you're asking. We can simplify the problem some by not making the length of the tube anywhere close to the size of the universe; all that's necessary is that it be long enough so that the twist/wave takes a noticeable amount of time to get from one end to the other. That's going to be at most a few tens of meters for any reasonable rubber tube-like object - no relativity, no weird universe-wide effects.

You're right that the tube won't break. There's no reason why it should, as we're only twisting it by a quarter-turn or so, and it's elastic enough to handle that easily.

So what does happen? First, imagine that you twist the tube only with your left hand, so there's only one wave traveling through the tube; it will eventually arrive at your right hand. Behind the wavefront, the tube is twisted one-quarter turn and ahead of the wavefront the tube is untwisted. The interesting stuff is happening at the wavefront, where the rubber between the twisted and untwisted regions is stretched; the force of the stretching rubber is tending to twist the untwisted region, moving the wavefront towards your right hand.

Now if you start a second wave by twisting the other end of the tube in the opposite direction with your right hand, we have two wave fronts moving towards each other, and dividing the tube into three regions: one behind the right-moving wavefront, where the tube is corkscrewed by a quarter-turn clockwise; another behind the left-moving wavefront, where tube is corkscrewed by a quarter-turn counter-clockwise; and a third between the two, where the tube is still untwisted. This third region gets smaller as the two waves approach one another and disappears when they meet.

Calculating exactly what happens at the exact moment that the two wavefronts meet is seriously hairy and requires detailed knowledge of the physical characteristics of the material the tube is made from. But for most reasonably elastic rubber-like substances, the two wavefronts will pass through each other, again leaving the tube divided into three regions. The region between the left-moving wave and your left hand is still corkscrewed by a quarter turn clockwise; the region between the right-moving wave and your right hand is corkscrewed by a quarter turn counterclockwise; and the region in the middle is twisted by a full half-turn. As the waves move towards your hands, this middle region grows while the other two shrink and then disappear completely when the waves reach your hands.

And when they do, the entire tube is corkscrewed by one-half, just as you'd expect from twisting the ends one-quarter turn each in opposite directions.

(Note that depending on just how elastic your tube is, the waves may travel back and forth and the tube may bounce around quite a bit before everything settles down. And calculating the exact speeds and magnitudes of the wave is going to be complex and messy - but the above will do for a qualitative description of how it all plays out).

Apologies for the late reply.

Thanks for the well thought out answer, bro. I suppose I need to read up on wave dynamics. definitely sparks my interest.

 

[CWatters]

what happens when they meet

What happens when waves meet on a string?