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Author Topic: The TWINE Paradox  (Read 14021 times)

Offline Solvay_1927

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Re: The TWINE Paradox
« Reply #25 on: 31/08/2006 01:48:32 »
George - that was a useful explanation of the Ehrenfest paradox, thanks. (I did find that article a bit confusing until you rephrased it that way.)
And thanks lightarrow (Alberto) for the link re: angular momentum.

But I still don't think I've got a resolution to the twine paradox (especially not the 2nd version above, where Albert runs 50m with the twine).
Regardless of what happens during acceleration and deceleration, the fact is that a constant velocity can be achieved for long enough for the problem still to occur: For a given time interval, there will be a fixed contraction in length which will lead to more than 50 knots passing through my fingers during that time.

Ian - I'm not sure I agree that the problem is "not realistic".  It may be a bit impractical (to say the least!), but that's not the same as being unrealistic.  In theory you don't have to be moving at an incredibly high speed - so long as your metal rod is long enough and has markings very close together (every tiny fraction of a millimetre, say) - and you do the experiment in deep space, say (i.e. effectively zero gravity).

In any case, even just as a thought experiment, this paradox needs a resolution - it can't just be ignored.  If a resolution can't be found (within the framework of relativity), then relativity must be "incomplete" in some way, mustn't it?
 

Offline thebrain13

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Re: The TWINE Paradox
« Reply #26 on: 31/08/2006 03:43:40 »
dude, whats wrong with my answer?
 

Offline Soul Surfer

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Re: The TWINE Paradox
« Reply #27 on: 01/09/2006 10:49:18 »
The problem requires rigid bodies and non elastic strings to exist at all.  If bodies are not rigid and strings elastic the problem does not exist.  Under the conditions required for the experiment to perform no body can be considered to be rigid and no string inelastic.

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« Last Edit: 01/09/2006 10:51:02 by Soul Surfer »
 

Offline lightarrow

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Re: The TWINE Paradox
« Reply #28 on: 01/09/2006 18:58:39 »
Ok, about the paradox with you, Solvay_1927 and Albert, I have made some simple computations.
Let's suppose the twine is made of the most rigid body on earth; anyway, the force between the particles with which it's made, cannot be transmitted faster than light.

Let's imagine that:
1. The twine has a knot every millimeter.
2. Albert travels for 50 Km ( = 50,000 m).
3. His speed is 59.96 Km/s = 0.0002C.

In this way, exactly 50,000,001 knots have passed through your hand, because of Lorentz contraction, instead of 50,000,000.

At this point, Albert stops.

How much time does the "stop" information take to reach your hand?
t = S/c = 50,000/299,792,458 = 0.0001668 seconds.

During these 0.0001668 s, the twine kept moving! So, how much more twine have passed? S = v*t = 59.96*0.0001668 = 0.010 Km = 10.00 m --> 10,000 more knots!

So, it doesn't seem to be a paradox anylonger, if this reasoning is correct.
« Last Edit: 06/09/2006 13:39:00 by lightarrow »
 

Offline Solvay_1927

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Re: The TWINE Paradox
« Reply #29 on: 01/09/2006 22:16:53 »
Brain (dude) - sorry for not responding to your contribution before - but the truth is that I found it a little confusing. (Your description assumes I'm holding the back end of the girder.  How would your description work if it was the front end that I was holding at the start of the experiment?)

Ian (Soul) - I accept what you say - when you put it that way, this experiment probably IS unrealistic.
But I still think that as a "thought experiment" involving theoretical 100% rigidity/inelasticity, it needs a resolution.  (And if it can't be resolved without recourse to rigidity/elasticity, then that suggests to me that there's something incomplete about relativity theory:  The derivation of relativity theory requires no assumptions about rigidity of bodies, etc., so if the theory gives rise to a potential paradox, it should be able to resolve that paradox without recourse to assumptions about rigidity.)

Alberto (lightarrow) - very well spotted - I haven't taken into account the time it will take for the "stop" command to travel from the front to the back of the twine.

But this didn't resolve the paradox for me.  What if, instead of Albert hitting a brick wall, the twine was stopped in the following way:

The 50km track along which the twine has been pulled has 50 million miniature hammers along it, and these hammers are set to all snap shut at exactly the same time (at a time much greater than 50,000/59.96 seconds in the scenario you've just described, to ensure that Albert has definitely got well past the 50km mark)

(Note: the hammers slam shut simultaneously according to my frame of reference.)

And while the twine is trapped inside these hammers, you can trim off the excess twine from either end of the track.

Now, when you prise open these hammers, the twine should be 50km long.  But will there be 50,000,000 or 50,000,001 knots in it?

(I hope your brain now hurts as much as mine has been for the past few months.:D)
 

Offline lightarrow

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Re: The TWINE Paradox
« Reply #30 on: 02/09/2006 16:22:57 »
quote:
Originally posted by Solvay_1927


The 50km track along which the twine has been pulled has 50 million miniature hammers along it, and these hammers are set to all snap shut at exactly the same time (at a time much greater than 50,000/59.96 seconds in the scenario you've just described, to ensure that Albert has definitely got well past the 50km mark)

(Note: the hammers slam shut simultaneously according to my frame of reference.)

And while the twine is trapped inside these hammers, you can trim off the excess twine from either end of the track.

Now, when you prise open these hammers, the twine should be 50km long.  But will there be 50,000,000 or 50,000,001 knots in it?

Solvay_1927: I can't visualize that situation. What exactly is a "hammer", here? I haven't found an appropriate meaning for that word, in my dictionary. Maybe you can make a simple draw of it?
 

Offline lightarrow

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Re: The TWINE Paradox
« Reply #31 on: 03/09/2006 03:09:18 »
For what concern Ehrenfest paradox, I thought Solvay's solution was the correct one: the geometry change from euclidean to non-euclidean, and circumference is not 2*(pi)*R anylonger. What's wrong with it?
 

Offline Solvay_1927

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Re: The TWINE Paradox
« Reply #32 on: 03/09/2006 15:23:21 »
Alberto - re: "hammers" - sorry, bad choice of words. I should have called them "clamps" or something.
These clamps (or hammers) snap shut and grip the twine so that it stops instantaneously.
So along the whole 50km (in my frame of reference) length of twine, we have a mechanism (50 million clamps) that causes every part of the twine to stop simultaneously (in my frame of reference).


In case it's of interest, the original thinking behind this paradox (i.e. why it was thought up in the first place) is as follows:

In the good old Twin Paradox, my (accelerating) twin experiences time dilation - i.e. she measures the "displacement in time" between two events as being different from what I would measure.
When she stops again, we both measure the same "displacement in time" from then on (i.e. our clocks tick at the same rate from then on).
But we can tell from our clocks that, during her journey, we must have measured different "displacements in time".

In the Twine paradox, my twin (or Albert in the above description), experiences length contraction - i.e. he measures the "displacement in space" (length) between two events as being different from what I would measure.
When he stops again, we both measure the same "displacement in space" from then on.
But is there a way to tell that, during his journey, we must have measured different "displacements in space"?  Is there something that does the equivalent of a clock, but for indicating past dispacements in space rather than past displacements in time?

Hence the possibility that, after the twine has stopped, you'll see it as being 50,000,000 mm in length but it will contain 50,000,001 knots in it.

OK, maybe that's a really stupid idea and I'm just demonstrating my lack of understanding about relativity.  But I just can't convince myself why it's wrong.

Paul.
 

Offline Soul Surfer

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Re: The TWINE Paradox
« Reply #33 on: 03/09/2006 17:40:26 »
You cannot stop anything with mass instantaneously. It requires infinite energy.

Thought experiments can be interesting and valid but they must have an element of practicality in them or as you have found they lead to anomalies.

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Offline lightarrow

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Re: The TWINE Paradox
« Reply #34 on: 04/09/2006 19:55:05 »
quote:
Originally posted by Solvay_1927

But is there a way to tell that, during his journey, we must have measured different "displacements in space"?  Is there something that does the equivalent of a clock, but for indicating past dispacements in space rather than past displacements in time?
Paul.

I found this very interesting, I'll think about it better, as well as the twine paradox with Albert and the clamps.

In a way, this last problem reminds me "The Barn and The Pole" paradox (http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/barn_pole.html), I think you know it: in the Barn reference frame, we see a pole shorter than the barn, so it can easily enter in the barn, then the two barn's doors are closed simultaneously and the pole is trapped inside (of course, from the pole's ref. frame, it seems this couldn't happen because the barn is shorter than the pole).

As it say, in the pole's ref. frame, the two doors don't close similtaneously, so it can actually enter in it.

In the same way, in the twine reference frame, it doesn't see all the clamps snapping shut simultaneously, so, more knots can enter there.
But what happens then?

I think that, while the twine is slowing down, it tries to take its initial (at rest) lenght, so it makes a force against the clamps to do it. How much is this force? Could the clamps be so strong to capture more knots than when the twine is at rest? I don't know, but it's an interesting topic.
« Last Edit: 04/09/2006 19:56:26 by lightarrow »
 

Offline lightarrow

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Re: The TWINE Paradox
« Reply #35 on: 04/09/2006 20:19:21 »
About the original twine paradox, with two pulleys.

If the solution to Ehrenfest paradox, really is the fact that the geometry changes from euclidean to non euclidean, so that the circumference is not 2*(pi)*R anylonger, then I can visualize a possible solution for your paradox: when the twine enters the pulley's accelerated frame, the geometry changes and the twine actually has to cover a longer path than simply Cir/2 where Cir is the circumference lenght in the rest frame of ref. (shorter than 2*(pi)*R).

Why I say this? Because, as in the warped space-time representation (with a massive object = an accelerated fr. of ref., warping down an elastic net), the twine has to go down, then go around the pulley's center and then go up; so in these going down and going up, it actually covers a longer path then what we think, looking at the situation on a plane (that is, on an euclidean space).

I had this idea after having read an explanation on a "Feynman's Physics" book, about what happens to a circle drawn on a saddle surface: its line has to go up and down on the saddle, so the total path is more than 2*(pi)*R.

I really don't know if this reasoning is correct.
 

Offline lightarrow

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Re: The TWINE Paradox
« Reply #36 on: 06/09/2006 13:49:01 »
I have correct numbers in my previous post: it's not 0.01 m and 10 knots, but 0.01 Km and 10,000 knots!

About the TWINE paradox, I think there is also an effect during the time of twine's acceleration (apart from accelerating motion in the pulleys): probably, it's necessary to add more twine, that is, more twine's particles (and hence more knots) in order to have, when the twine's speed becomes constant, the same spacing between any two knots.
 

Offline yor_on

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The TWINE Paradox
« Reply #37 on: 23/02/2009 14:24:57 »
I know this is a old thread, but it's good, and made me wonder again.

I've always had trouble understanding if Lorentz contraction was a 'real' effect or if it was more of an optical 'illusion' having to do with referenceframes moving against each other at high speeds. And this thought experiment was really interesting.

One of the things making me wonder is that if the contraction was real would be the question if we then can say that the 'matter' in that 'elongated planet' we crash in before we should be able to, if it was seen as we observe it without that motion, acceleration,  really have 'changed' in our 3D + time. If that is true then it makes our universe a very 'plastic' relation to me.

On the other hand, if it is so then spacetime is not defined by 'distances' in itself if you see what I mean. And the idea of seeing object as being at a 'defined distance' is just a description from your 'frame of reference'. If that is so the whole idea of lightyears, time, and a 3D universe will be a very special expression relating to us, of whatever frame we may be, inside it.

The problem also seems to go back to what we think of as 'time'. Whatever observation we make is done in 'time', we can't take 'time' away from any observation we make. As long as you see some sort of causality chain there must be a 'time' aspect to it. No matter if you are looking at a Feynman diagram or doing an actual experiment. We should be able to device an experiment in where we create an 'opening' smaller than a particle(s) accelerated and then see if that particle(s) can go through that 'opening', or something similar.

---
Although that seems hard to do due to the wave/particle duality.
But maybe it would be possible?
------


If 'distances' is a relation of 'time' and also related to 'deformation' of matter, as seen when traveling at high accelerations, then what is 'speed'. We can't define any speed of anything in this universe. We can only define speed and velocity when comparing it to something 'outside' our locality. So there is no way to say that any object in this universe has a velocity of zero, except when comparing it to yours or some others frame(s). And if frames is defined as being something 'moving' against each other then that is a circular argument to me, as we have no 'gold standard' for defining movement other than by comparing. So to me 'frames of reference' is very difficult to define as we always will go out from an arbitrary defined frame, say Earth, having this or that 'speed' 'velocity' but only when compared to some other 'frame of reference'.

If we then to that take in the ideas of expansion and (later) inflation it gets even more difficult to define. So to explain our universe, if Lorentz contraction is a true description, it seems to me that we also need to ask ourself what that states about our three descriptions of length, width and height. That plus time is our universe, isn't it? So do our universe really need, as seen from another 'frame of reference' (aka another ??? observing our 'bauble') really need to be of any 'size' at all? If you agree with me in that 'distances' 'sizes' and all those other 'measurements' we use only can be described as something related to relative 'measurements' amongst moving 'frames of reference' made in time, with acceleration and speed as well as velocity, being arbitrarily defined by us observing. I'm not saying that we don't refine our observations and definitions of relative motion distances, etc, constantly, just that as we have no 'gold standard', or 'guarantee' if you like, for what a 'zero motion' in our universe really would consist of, and therefore we can't say that we know any motion, except when defining 'something' as being in a 'relation' motion wise to whatever other frame you choose.

If distance and size is a 'relative measurement' to speed, velocity, (and yes, most important 'gravity well' defined, and that would then be, ah, acceleration:). Then only acceleration seems to give us some 'real' objective proof of something changing 'inside' our frame of reference, that as it creates that 'gravity well' :)

So, what do you think?
« Last Edit: 23/02/2009 14:39:22 by yor_on »
 

Offline Vern

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The TWINE Paradox
« Reply #38 on: 23/02/2009 15:02:13 »
Hi yor_on; you are reasoning along the same lines that I followed before I gave up on Einstein and decided that the Lorentz version of relativity phenomena made more sense. With the Lorentz version, all relativistic distortion is the result of distortions of the massive objects. With Einstein, all the distortions are the result of space-time variations.

The paradox of this thread comes from trying to mix the Einstein space-time distortion and the Lorentz matter distortion. The two don't mix. It's either all space-time, or all matter distortion :)

Here is a physicist who also likes the Lorentz version of relativity phenomena :) You haven't contributed to that thread. Are you a little bit chicken? :) Translation: Arkansas talk for being afraid.
« Last Edit: 23/02/2009 15:17:34 by Vern »
 

Offline yor_on

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The TWINE Paradox
« Reply #39 on: 23/02/2009 21:27:06 »
Chicken?
Nah.

Scared witless is a better description.
No, I'm reading you Vern, but this is where I'm 'stuck' for the moment.
Don't worry man, your time will come too :)

Ps: are you saying that Einstein didn't accept Lorenz contraction  as being 'real'?
"It's either all space-time, or all matter distortion"
 

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The TWINE Paradox
« Reply #40 on: 23/02/2009 22:22:03 »
I have not seen this thread before but it is a fascinating one. I think lightarrow may be on the right track when he considers the distance traveled by the twine as it goes around the end pulleys. This is where all the acceleration will take place and, if there is acceleration, there will be a discrepancy in distances. The two straight portions of the twine will follow  SR and the spaces between the knots will appear to be less, and the total number of knots on those sections would be more ,requiring fewer knots to exist on the accelerated portions.
I was thinking of what you would see with a stroboscope. This could be adjusted to render the knots all 'stationary'. So would the pulleys appear to be circular, still?
The pulley circumference is constantly accelerating towards the centre and the twine experiences this acceleration too as it goes round the ends. The geometry gets difficult because the separation of the straight bits cannot change but the pulley diameter would seem to be changing. Unfortunately, there would be a step change in acceleration where the twine meets the pulley and leaves it. Does this mean that there is some apparent distortion of the geometry at the lead in and lead out sections?
 

Offline Vern

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The TWINE Paradox
« Reply #41 on: 23/02/2009 22:46:18 »
Chicken?
Nah.

Scared witless is a better description.
No, I'm reading you Vern, but this is where I'm 'stuck' for the moment.
Don't worry man, your time will come too :)

Ps: are you saying that Einstein didn't accept Lorenz contraction  as being 'real'?
"It's either all space-time, or all matter distortion"
I'm saying that Einstein explained the Lorentz contraction as a contraction of space itself, not as a physical contraction of the object in space. If we distort space-time due to motion, then want to allot  some of that distortion to a physical object in space, how do we decide how much distortion belongs each mode of distortion? :)

So I'm saying you can do it according to Lorentz, and attribute all the distortion to the physical objects, or you can do it according to Einstein and attribute all the distortion to space-time. Either way gives the same answer.
« Last Edit: 23/02/2009 23:00:56 by Vern »
 

Offline yor_on

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The TWINE Paradox
« Reply #42 on: 23/02/2009 23:30:59 »
I've looked for that before but haven't seen it?
Would you, by any chance, have a good link describing Einsteins thoughts on what he saw as the Lorentz contraction?

Just as a comment Vern, to me (for now:) time is what seems to rule over all other aspects. Gravity is to me defined by matter 'bound' in space, and those two states are in their turn on a 'sliding scale' depending on what frame of time you have compared to other 'frames of reference' in spacetime. Uniform motion is also 'something' changing the balance between 'frames of reference', even though there are no 'gravity well' seen, as when compared to acceleration. So Gravity seems somewhat like inertia, a 'unwillingness' to 'change', when observed when thinking like this.

I really would like to see what Einstein meant, if he saw "Lorentz contraction as a contraction of space itself, not as a physical contraction of the object in space.
 

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The TWINE Paradox
« Reply #42 on: 23/02/2009 23:30:59 »

 

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