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Author Topic: Can a rubber tube turn itself inside out perpetually?  (Read 3040 times)

Offline KALSTER

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Hey guys, nice to be here ;)

This is one of a few scenario's I was contemplating yesterday while on a trip.

Suppose you have a square sheet of rubber. This rubber has zero internal friction and perfect elasticity. Now, take two sides and join them, forming a cylinder. Take one end and start rolling it up so that you are turning it inside-out. When you have done a bit, give it a final yank and let go. This is done in a perfect vacuum with no external interference.

What will happen?

As I see it, it should keep on rolling until it is completely inside-out. But then I think it should continue (as a result of momentum) and keep turning itself inside-out perpetually. The initial energy applied can't dissipate, so it has to keep on moving.

Now, imagine that in one oscillation, when the two open ends meet they fuse together, forming a torus.

What will happen to the motion then?  I think a reference dot made on the inside of the torus should then move around in a circular motion around the outside and back to its original position, no?



Now on to a second and slightly more complex thought I had.

Suppose you have a skin enclosing a near infinite number of zero dimensional points. It would then simply be a single zero dimensional point. But let's say that each point can stray into any one of three dimensions at any time, forming a one dimensional string and then reverting back through the origin and into another dimension. The dimension it strays into is completely random. The degree to which it fluctuates, though, is determined by a probability curve. The smaller the fluctuation, the more likely it is. This probability curve might look something like a hyperbola, but with the symmetry being along the Y axis. The X axis would then be the vector degree of fluctuation (vector, as in it can fluctuate in any of two directions from the origin for each dimension) and the Y axis would be the frequency. Now, how would the volume look and behave now? It's size would be determined by the shape of the probability curve. The more likely larger fluctuations become, the bigger the volume gets. When only three dimensions are possible, the volume should average out into a cube, and if combination vectors are possible, it should average out into a sphere. If combination vectors are possible, it could statistically form almost any shape for an instant, given enough time. It could even form all kinds of shapes, or geometries, on the inside with varying density.

So how would the point sources fit together when the fluctuations occur? Does there have to be spaces in between? Would it still be able to have volume with no empty spaces in between? Each formed string should push away any adjacent strings, creating volume, no?

Now, what if we had an infinite number of point sources. Would shapes still be possible internally as density varies? How would the possible variety and frequency of geometries change between: (1)Only one of three vectors are possible at any one time, or (2)Combination vectors are possible?

What do you guys think? [?]
« Last Edit: 25/07/2008 17:45:11 by chris »


 

Offline LeeE

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #1 on: 22/07/2008 19:18:00 »
Without internal friction it wouldn't be elastic and it wouldn't hold any shape.  After rolling it in to a torus (and assuming you maintain it's shape until you let go) when you let go the torus will expand as all points of it try to move away centripetally from the axis of rotation.  This will happen regardless of whether the edges are joined or not.

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Suppose you have a skin enclosing a near infinite number of zero dimensional points. It would then simply be a single zero dimensional point.

I can't see this - a zero-dimensional point would have no surface to wrap a skin around.  Also, any +ve number of points, without assigning different attributes to them, in the same place would be indistinquishable from a single point.  I can't see why simply moving a point object results in it becoming a one dimensional string.  Sure, if you threw in another time dimension to look from, you could see every point in it's entire lifetime simultaneously, which would give the appearance of of a static object with length, except that it would really no more have length than a beam of light has solidity.
 

blakestyger

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #2 on: 22/07/2008 19:36:20 »
... while on a trip.

Since Timothy Leary and the '60s I thought that stuff had gone out of fashion. ;D
 

Offline KALSTER

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #3 on: 23/07/2008 08:50:24 »
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I can't see this - a zero-dimensional point would have no surface to wrap a skin around.  Also, any +ve number of points, without assigning different attributes to them, in the same place would be indistinquishable from a single point.
That is what I said, no? The reason I presented the premise with a finite, non-zero number of point sources is that an infinite number of point sources would have an infinite volume as result when their string forming attributes were added(assuming that volume would occur).

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I can't see why simply moving a point object results in it becoming a one dimensional string.
I can see how you might have thought that that is what I was saying. What I meant was that starting from the origin that an actual one dimensional line/string extends (strings in physics are supposed to be one dimensional) at a finite speed before retracting and then extending in another direction.

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Without internal friction it wouldn't be elastic and it wouldn't hold any shape.
Are you sure about this? From the Wiki page on rubber:
“Elasticity

In most elastic materials, such as metals used in springs, the elastic behavior is caused by bond distortions. When force is applied, bond lengths deviate from the (minimum energy) equilibrium and strain energy is stored electrostatically. Rubber is often assumed to behave in the same way, but it turns out this is a poor description. Rubber is a curious material because, unlike metals, strain energy is stored thermally.

In its relaxed state rubber consists of long, coiled-up polymer chains that are interlinked at a few points. Between a pair of links each monomer can rotate freely about its neighbour. This gives each section of chain leeway to assume a large number of geometries, like a very loose rope attached to a pair of fixed points. At room temperature rubber stores enough kinetic energy so that each section of chain oscillates chaotically, like the above piece of rope being shaken violently.

When rubber is stretched the "loose pieces of rope" are taut and thus no longer able to oscillate. Their kinetic energy is given off as excess heat. Therefore, the entropy decreases when going from the relaxed to the stretched state, and it increases during relaxation. This change in entropy can also be explained by the fact that a tight section of chain can fold in fewer ways (W) than a loose section of chain, at a given temperature (nb. entropy is defined as S=k*ln(W)). Relaxation of a stretched rubber band is thus driven by an increase in entropy, and the force experienced is not electrostatic, rather it is a result of the thermal energy of the material being converted to kinetic energy. Rubber relaxation is endothermic, and for this reason the force exerted by a stretched piece of rubber increases with temperature (metals, for example, become softer as temperature increases). The material undergoes adiabatic cooling during contraction. This property of rubber can easily be verified by holding a stretched rubber band to your lips and relaxing it.”
 

Offline KALSTER

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #4 on: 23/07/2008 15:31:51 »
... while on a trip.

Since Timothy Leary and the '60s I thought that stuff had gone out of fashion. ;D
 

Offline KALSTER

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #5 on: 25/07/2008 13:27:49 »
Let me provide a hopefully clearer discription of the second one. I said a finite number of point sources, meaning point sources that have the added attributes as I discribed. If the construct were to be able to exhibit volume, then starting with an infinite number of point sources would negate the role the sphere/bag/skin plays in the setup, which is that one could form an intuative picture of volume created by the construct.

I wanted to set up the experiment in my mind with some added particulars and then see what happens. Points are, as has been said, zero dimensional. Lines are one dimensional. In physics a string is defined as a vibrating one dimensional line. I wanted to add the vibrating property of the strings into the construct later on, only after I have formed a complete mental picture of what is happening.

Anyway, the points I am talking about do not physically exist, only as the point of origin through which the physical one dimensional lines fluctuate.

These fluctuations occur roughly according to this graph:



As you can see from the graph, the chance of the strings being smaller increases substantially the smaller they get. In fact, one could describe the limit where the deviation from zero tends towards zero. So large deviation become unlikely to the extreme quite quickly.

That is, they can go in any direction and can elongate to any length, but with the constraint that they are more likely to be small than large. Let me make the speed at which they elongate, arbitrarily, the speed of light. So then my question was if this setup could exhibit volume. A point source will, over a sufficient period of time, form the rough appearance of a sphere. I am just wondering if, since the lines are only one dimensional, if a confined finite number or an infinite number would be able to affect each other, or “push” against each other. If the answer to this were to be no, that is when I would have to introduce the extra condition of the lines/strings vibrating (as proposed in current string theories). That would provide a measure of volume to each string, but it would also then force the necessity for gaps to form, that is, areas in the volume that is not occupied by anything at all. I was trying to avoid these gaps, for reasons to be discussed later.

You see, I am trying to consider candidate constructs for the space-time fabric, of which this one seems the most promising to date. At the moment I am thinking about whether the formed strings need to vibrate in order for the construct to be able to exhibit volume. The variation of two variables I can identify can then be responsible for inflation, namely the amount of vibration of the strings and the frequency distribution of longer deviations from zero of the strings.
 

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Re: Can a rubber tube turn itself inside out perpetually?
« Reply #5 on: 25/07/2008 13:27:49 »

 

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