How Long Can a Wire Be? Laws of Physics and Wire Length Explained

[rede96]

Hope this is the right place to ask this question. But I was wondering if there are any laws of physics that dictate how long I could make a wire?
Also, as ridicules as this might be, if I tied that wire to a planet in a nearby galaxy and then waited for that galaxy to start to recede at speeds greater than c, is there any law of physics that means the wire would have to break apart if certain parts of it reached velocities greater than c in my local frame?

 

[phinds]

Hope this is the right place to ask this question. But I was wondering if there are any laws of physics that dictate how long I could make a wire?
Also, as ridicules as this might be, if I tied that wire to a planet in a nearby galaxy and then waited for that galaxy to start to recede at speeds greater than c, is there any law of physics that means the wire would have to break apart if certain parts of it reached velocities greater than c in my local frame?

If the wire were connected to something in the distant galaxy, I guess it would have to break even without expansion (because of galactic rotation on both end), but if it were just but if it were just hanging in space on both ends it would not break. Expansion would not affect it because it would be internally connected by forces that are MUCH stronger than dark energy.

 

[A.T.]

if it were just hanging in space on both ends it would not break. Expansion would not affect it because it would be internally connected by forces that are MUCH stronger than dark energy.

In order not to break the wire would have to keep a constant proper length, and not to expand with the space. If the wire is long enough, that would require the ends to move faster than light relative to local stars, which is not possible.

 

[rede96]

If the wire were connected to something in the distant galaxy, I guess it would have to break even without expansion (because of galactic rotation on both end), but if it were just but if it were just hanging in space on both ends it would not break. Expansion would not affect it because it would be internally connected by forces that are MUCH stronger than dark energy.

Thanks for the reply. If we ignore the rotaion element, and just assume that I can put this on a body that doesn't roate but is large enough to be 'pushed' by expansion, then theoretically I could have an infinately long wire. Which means that the end that isn't attached to the large body could be thousands of light years away. Which meant that as the large object start to recede due to expansion, then at some point the wire would start to travel faster than c. So I thought the wire must break.

 

[rede96]

In order not to break the wire would have to keep a constant proper length, and not to expand with the space. If the wire is long enough, that would require the ends to move faster than light relative to local stars, which is not possible.

I agree it shouldn't be possible for the wire to travel faster than light relative to local stars, but as I understand it, the wire does not expand with space?

 

[A.T.]

I agree it shouldn't be possible for the wire to travel faster than light relative to local stars, but as I understand it, the wire does not expand with space?

Right, that's why I think the wire length is limited, even if the ends are free.

 

[rede96]

Right, that's why I think the wire length is limited, even if the ends are free.

Cool, as I was hoping to find out just what laws of physics goevern the length of the wire.

 

[phinds]

In order not to break the wire would have to keep a constant proper length, and not to expand with the space. If the wire is long enough, that would require the ends to move faster than light relative to local stars, which is not possible.

Ah, right. The remote galaxy would recede from the end of the wire then? I mean, the wire is locally coherent so should not follow the expansion at all, but I see no reason for it to break, just to get farther and farther away from the receding galaxy.

EDIT: OOPS ... I didn't see your second reply, which does agree w/ this. Thanks.

 

[rede96]

Ah, right. The remote galaxy would recede from the end of the wire then? I mean, the wire is locally coherent so should not follow the expansion at all, but I see no reason for it to break, just to get farther and farther away from the receding galaxy.

Just to clarify, in my thought experiment, one end of the wire is attached to an object in the galaxy which is receding. The rest of the wire could be coiled up for example in my local frame in another galaxy. So as the other galaxy starts to recede I see the wire start to uncoil. If the wire is infinitely long, at some point the wire will start to uncoil at speeds greater than the speed of light. So I assumed it must break.

By the way the wire doesn't need to be coiled, it could have been laid out along it's length across the universe, but I think it is easier to imagine if it is coiled.

 

[phinds]

Just to clarify, in my thought experiment, one end of the wire is attached to an object in the galaxy which is receding. The rest of the wire could be coiled up for example in my local frame in another galaxy. So as the other galaxy starts to recede I see the wire start to uncoil. If the wire is infinitely long, at some point the wire will start to uncoil at speeds greater than the speed of light. So I assumed it must break.

By the way the wire doesn't need to be coiled, it could have been laid out along it's length across the universe, but I think it is easier to imagine if it is coiled.

The wire that is not coiled but is stretched out but unattached at the end not in the galaxy that is receding from you will not break because it is in essence a part of the receding galaxy and is not affected by the expansion. The end closest to you will simple get farther away, as will the receding galaxy.

The coiled version will not uncoil. Why should it? The whole thing is a part of the receding galaxy and is not affected by expansion so there is nothing to make it uncoil.

 

[rede96]

The coiled version will not uncoil. Why should it? The whole thing is a part of the receding galaxy and is not affected by expansion so there is nothing to make it uncoil.

In simple terms, expansion means that the distance between say two galaxies is increasing with time. As is the rate the distance increases. So if I attached one end of a wire to some object in galaxy A and then fly off with the other end to another galaxy B, and gather up the excess wire into a coil, then as galaxy A moves away due to expansion it must uncoil the wire as the distance between galaxy A and galaxy B is increasing.

 

[phinds]

In simple terms, expansion means that the distance between say two galaxies is increasing with time. As is the rate the distance increases. So if I attached one end of a wire to some object in galaxy A and then fly off with the other end to another galaxy B, and gather up the excess wire into a coil, then as galaxy A moves away due to expansion it must uncoil the wire as the distance between galaxy A and galaxy B is increasing.

Ah, I didn't realize you were planning on attaching both ends. In that case the wire will break whether it is coiled or not.

 

[rede96]

Ah, I didn't realize you were planning on attaching both ends. In that case the wire will break whether it is coiled or not.

Sorry, I can be crap at explaining things sometimes! But technically the other end isn't attached, I could have just flown off in the opposite direction and would have had one end attached to a galaxy and the other end just floating free in space.

But I agree it must snap, or sooner or later the free 'end' will be moving with a speed greater than c.

So I am interested in what law of physics dictates that the wire must snap and at what point would it snap?

 

[phinds]

No, I think you misunderstand. If one end is in one galaxy and the other in is in the other galaxy, then they ARE attached, whether you have them tether to a planet or something or not. The point is that if they are IN a galaxy they are a part of the galaxy as far as expansion is concerned.

Actually, now that I think about it more, you could never get in placed to start with if the other galaxy is receding at > c. If you start in one galaxy and head out for the other galaxy, you'll never get there. If the other galaxy is (relatively) nearby, then you could get there but assuming that galaxy is not part of our Local Group, the wire would likely break as soon as you were captured by the gravitational attraction of the receding galaxy since pretty much any recession is going to break it.

EDIT: All of this seems kind of pointless anyway. If you are using it to understand recession, it seems to me that you are over complicating things.

 

[Nugatory]

So I am interested in what law of physics dictates that the wire must snap and at what point would it snap?

If you fix one end and let the other dangle free at a very great distance away, the free end will be accelerating relative to an observer in free fall near the free end. This acceleration will be produced by tensile forces in the wire, and the wire will snap when these tensile forces exceed the strength of the wire. No matter how strong the wire is, it will snap if you make it long enough because the forces in the wire will become infinite as the far end is required to approach the speed of light relative to the inertial observer at that end.

Thus, the relevant laws of physics are the ones that govern the strength of wires (the wire breaks if you apply to much force to it) and the ones that govern metric expansion of the cosmos (the more different the expansion at the ends, the greater the force that the wire is subject to).

 

[rede96]

No, I think you misunderstand. If one end is in one galaxy and the other in is in the other galaxy, then they ARE attached, whether you have them tether to a planet or something or not. The point is that if they are IN a galaxy they are a part of the galaxy as far as expansion is concerned.

Ah ok, I see what you mean. Not sure I quite understand that, but understand your point.

EDIT: All of this seems kind of pointless anyway. If you are using it to understand recession, it seems to me that you are over complicating things.

I wasn't trying to understand recession fully at this point to be honest, I just wanted to know what laws of physics limit the length of the wire in the scenario I mentioned. But I find the point you raised above interesting, so will read up a bit more as I'd like to understand that in more detail. Thanks for your input.

If you fix one end and let the other dangle free at a very great distance away, the free end will be accelerating relative to an observer in free fall near the free end. This acceleration will be produced by tensile forces in the wire, and the wire will snap when these tensile forces exceed the strength of the wire. No matter how strong the wire is, it will snap if you make it long enough because the forces in the wire will become infinite as the far end is required to approach the speed of light relative to the inertial observer at that end.

Thus, the relevant laws of physics are the ones that govern the strength of wires (the wire breaks if you apply to much force to it) and the ones that govern metric expansion of the cosmos (the more different the expansion at the ends, the greater the force that the wire is subject to).

Thanks for the explanation. Again, I kind of understand this. But I think phinds mentioned something in a previous reply where if both ends of the wire were unattached then there was no reason for the wire to break. So that would imply there has to be some force acting on the wire to make it snap. Is that correct? So if the wire was just dangling from some random object in space, where or when would the forces start to act upon it?

 

[phinds]

But I think phinds mentioned something in a previous reply where if both ends of the wire were unattached then there was no reason for the wire to break.

After seeing Nugatory's post, I think I have to reconsider that. I can't flaw Nugatory's logic that something very far away HAS to be subject to the expansion. It doesn't feel quite right to me, but I'm used to being wrong about things in cosmology and quantum mechanics.

 

[Nugatory]

if both ends of the wire were unattached then there was no reason for the wire to break.

If both ends of the wire are unattached, it will take less tension in the wire to hold it together, so the wire can be longer. But it will still break if the wire is long enough.

(This entire problem is most easily modeled as two point masses connected by an ideal massless wire. That way you can just consider the force required to produce the proper acceleration that keep the ends on a path that preserves the proper length of the wire. If you instead consider a non-ideal wire with non-zero mass density along its length, it's like doing classical physics exercises with non-massless ropes - you end up doing a whole bunch of messy integrals that provide no additional insight).

 

[rede96]

(This entire problem is most easily modeled as two point masses connected by an ideal massless wire. That way you can just consider the force required to produce the proper acceleration that keep the ends on a path that preserves the proper length of the wire.

Thanks, that really helped to conceptualise the problem for me. So if I understand that properly, using your model, as one end 'moves away' due to expansion then once the force required to accelerate the other end becomes to great to maintain its proper length, the wire will snap.

And for relatively short cosmological distances, as the ends of the wire would never require a force to accelerate greater than the speed of the light, the wire would remain intact.

Does that mean this is a way to define cosmological frames of reference? (for want of a better term!) What I mean by that is if two bodies of a given mass could only be considered to be at rest wrt each other as long as the forces required to maintain this imaginary proper length between them did not exceed the force required to accelerate at c?

 

[phinds]

And for relatively short cosmological distances, as the ends of the wire would never require a force to accelerate greater than the speed of the light, the wire would remain intact.

Define "short". For any distance which seriously involves expansion at the ends, "c" is not needed. You don't need a sledgehammer to kill a flea.

 

[rede96]

Define "short". For any distance which seriously involves expansion at the ends, "c" is not needed.

Any distance less then where the rate of expansion would require a force too great for the two end to maintain proper length. So I guess that is going to be different for different cases.

You don't need a sledgehammer to kill a flea.

I know but I always feel better when I am certain it is dead :D

 

[phinds]

Any distance less then where the rate of expansion would require a force too great for the two end to maintain proper length. So I guess that is going to be different for different cases.

OK. As long as you realize that that's WAY less than the distance at which recession equals c.

I know but I always feel better when I am certain it is dead :D

 

[A.T.]

his entire problem is most easily modeled as two point masses connected by an ideal massless wire. That way you can just consider the force required to produce the proper acceleration that keep the ends on a path that preserves the proper length of the wire.

Why would there by any proper acceleration of the ends? Keeping the proper length constant requires movement of the ends relative to local stars, not acceleration.

 

[Dale]

But technically the other end isn't attached

If only one end is attached then I see no reason for it to snap. Wires snap because of stress. If you only fix one end then there should be a divergence free congruence.

The coordinate velocity is just an artifact of the coordinate system. I would see no reason for it to limit the length of an object.

Of course, this is all just guesswork without the math. And it seems my intuition does not match others.

 

[Nugatory]

Why would there by any proper acceleration of the ends? Keeping the proper length constant requires movement of the ends relative to local stars, not acceleration.

And it seems my intuition does not match others.

Hmm... With both A.T. and DaleSpam asking, I'm beginning to worry about whether I should be trusting my own intuition...

Intuitively, I started with the thought that two wires extended in opposite directions from a common center (one end of each wire free, the other end of each wire fixed at the common center) is equivalent to a single wire with both ends free. We agree that in the first case the stress in the wire can be made to increase without limit if the wire is long enough, so if the two cases are equivalent we will get stress without limit in the second case as well.

Or, we can model the problem as two masses connected by a wire of negligible mass: If the mass at each end were to follow the same geodesic path that a nearby unconstrained mass would follow, the proper distance between the worldlines of the two ends would increase. The wire prevents the two end masses from following these geodesic paths, meaning that the the end masses are experiencing proper acceleration and there must be tension in the wire.

I do agree that the coordinate acceleration of each endpoint relative to the stuff around it is a red herring.

 

[A.T.]

...one end of each wire free, the other end of each wire fixed at the common center... the stress in the wire can be made to increase without limit if the wire is long enough...

Is this assuming that the Hubble parameter increases over time? Because if we assume it to be constant I don't see the reason for stress in the wire. The free end moves at constant speed relative to the local stars, so it is inertial.

Or, we can model the problem as two masses connected by a wire of negligible mass: If the mass at each end were to follow the same geodesic path that a nearby unconstrained mass would follow, the proper distance between the worldlines of the two ends would increase. The wire prevents the two end masses from following these geodesic paths...

But it doesn't prevent them from following some other geodesic paths, which keep the wire length constant.

 

[rede96]

I am probably out of my depth here, but the way I originally thought about this was that the ‘stress' (for want of a better word) on the wire from expansion would be equally distributed over the length of the wire, as space is expanding everywhere. So it wouldn’t be like a tug-of-war situation where we had 1000’s of people at either end pulling the wire apart. It would be more like we had pairs of people pulling against each other equally spaced over the length of the wire. So the effects would cancel.

If I now attach one end of the wire to some very massive object then the situation doesn’t change too much unless I start to accelerate that large object, which would put stress on the wire. As I understand it, expansion doesn’t ‘accelerate’ objects; it simply grows the distance between them and other objects. So any other objects that lie further down the length of the wire which may be moving wrt the wire, isn’t a movement caused by the application of any forces.

So I was struggling to understand how the wire could snap. But this lead me to the conclusion that if the wire didn’t snap, and if could be infinitely long, then at some point further down the length of the wire, objects will see the wire moving past them at speeds greater than the speed of light. So I assumed it must snap.

I sort of thought about this now and maybe my error (or one of many!) wasn’t that the wire would snap but to assume that a massive object attached to an arbitrary long wire would actually move with expansion. As I understand it, even very large galaxies are not torn apart by expansion, as the gravitational forces are easily greater than the work required to keep the objects in the galaxy together.

So my conclusions would be that as long as there were no forces other than expansion working on the wire, it could be infinitely long. However a wire attached to a massive object would become 'one system' and the effeects of exansion equally distributes, hence the object would not recede with expansion. So that solves my paradox.

EDIT: Probably should have said doesn't recede relative to any objects that lay along the length of the wire.

Does that make any sense?

 

[rede96]

So my conclusions would be that as long as there were no forces other than expansion working on the wire, it could be infinitely long. However a wire attached to a massive object would become 'one system' and the effeects of exansion equally distributes, hence the object would not recede with expansion. So that solves my paradox.

I just thought about this a bit more and not so sure that is correct as if I had an infinatley long wire, although the wire wouldn't recede, any galaxies that lay along the path of the wire would still move apart due to expansion. So at some point (assuming infinate length) a galaxy would be moving along the length of the wire at a relative speed greater than c. Ok I am confused again! lol

 

[A.T.]

So I was struggling to understand how the wire could snap. But this lead me to the conclusion that if the wire didn’t snap, and if could be infinitely long, then at some point further down the length of the wire, objects will see the wire moving past them at speeds greater than the speed of light. So I assumed it must snap.

The speed limit rules out that such a wire can be build. How exactly the construction will fail in practice depends on the method by which you try to build it.

 

[Dale]

Are we assuming that any force needed to move the wire comes only from tension in the wire, or could the wire be accelerated along its length by external forces applied along its length?

 

[A.T.]

Are we assuming that any force needed to move the wire comes only from tension in the wire, or could the wire be accelerated along its length by external forces applied along its length?

I think that either way you cannot overcome the speed limit relative to the local stars. To avoid any tension you could build the wire from many small pieces, which are connected while floating inertially at relative rest to each other. But this would require accelerating the pieces to increasing speeds relative to the local stars before the connection, which is bound by c.

 

[russ_watters]

Thus, the relevant laws of physics are the ones that govern the strength of wires (the wire breaks if you apply to much force to it) and the ones that govern metric expansion of the cosmos (the more different the expansion at the ends, the greater the force that the wire is subject to).

Is this assuming that the Hubble parameter increases over time? Because if we assume it to be constant I don't see the reason for stress in the wire. The free end moves at constant speed relative to the local stars, so it is inertial.

All that means is that it is impossible to even deliver the wire to set up the scenario. It breaks before being unrolled completely. As you fly your spaceship across the universe, pulling the wire with it (with the other end being unrolled near earth), one end or the other would be accelerating as it crosses a wider and wider swath of expanding space, if not for the wire, so the tension is increasing.

Indeed, if we assume the wire is so strong that relativity/expansion provides the limit for the spaceship unrolling it, the unrolling gets slower and slower until the distance reaches far enough that the recession velocity would have to be c.

 

[A.T.]

All that means is that it is impossible to even deliver the wire to set up the scenario.

Right, up from a certain wire length it becomes impossible to place the wire. But below that length, where it is still possible, the placed wire could keep it's proper length, while being completely inertial and tension free.

 

[russ_watters]

Right, up from a certain wire length it becomes impossible to place the wire. But below that length, where it is still possible, the placed wire could keep it's proper length, while being completely inertial and tension free.

I don't think so. I think you may be missing that even with constant expansion, two points in space are accelerating away from each other because the expansion speed is not constant, it is a function of distance (the rate is constant d/t/d0, not d/t). I think that makes the effect similar to holding a rope vertically under its own weight.

 

[A.T.]

the expansion speed is not constant, it is a function of distance

But the distance between the wire ends is constant, so the recession speed between their local stars is constant, so both ends move at some constant speed relative to their local stars, meaning they are both inertial.