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

[russ_watters]

But the distance between the wire ends is constant...

Because it is under tension!

...so both ends move at some constant speed relative to their local stars.

No, for the "moving" end (assume one end is fixed relative to its local stars), the distance to its local stars is increasing so the speed must also be increasing: speed is a function of distance in the Hubble parameter. The "local stars" are accelerating past/away from it.

It looks to me like this is similar to unrolling a wire vertically into a black hole. After the distance gets large enough, gravity/the Hubble flow provides the force to do the unrolling and the tension gets larger and larger as you unroll it, as a function of distance. After a while, if you don't stop unrolling it, the tension gets high enough to break the wire. If you do stop unrolling it, the tension just becomes constant.

Note: Nugatory already explained this in post #15.

 

[Dale]

I think that either way you cannot overcome the speed limit relative to the local stars.

I agree. But I don't think that is the same as the speed limit between ends of the wire. I just am unsure of the answer from intuition and would need to see or do the math to be confident.

 

[A.T.]

It looks to me like this is similar to unrolling a wire...

I'm not talking about the unrolling process. The wire is already unrolled and has a constant proper length. That means the recession speed between stars that are currently local to either end is also constant over time.

These local stars at the ends are obviously not the same ones over time, which seems to be the error you make here. We are not tracking two specific galaxies, whose recession speed increases over time, because their distances increases. We are looking at galaxies currently passing by the ends of the wire of constant proper length, where the distance is always the same and thus is recession speed.

 

[russ_watters]

I'm not talking about the unrolling process. The wire is already unrolled and has a constant proper length.

Please read the rest of the post, because I cover that: Thats not a relevant difference. Either way, in both cases (for unrolling into gravity or Hubble flow), the tension remains after the unrolling stops. You can stop the unrolling before the wire breaks or keep unrolling it until it breaks, but in both cases the tension due to the length is the same (whatever the breaking tensile strength is).

Looking at it another way: after a certain distance, gravity/the Hubble flow will start accelerating the unrolling.

That means the recession speed between stars that are currently local to either end is also constant over time.

These local stars at the ends are obviously not the same ones over time...

You're picking different stars at different times in order to try to ignore the fact that all of those stars are accelerating? What you are suggesting isn't how speed/acceleration work.

We are not tracking two specific galaxies, whose recession speed increases over time, because their distances increases.

You aren't, I am: you should be.

AT, just yesterday you correctly pointed out a fallacious derivation of a speed equation by differentiating from distance to speed to acceleration. This issue is somewhat similar. The galaxy has both a non-zero instantaneous speed and non-zero instantaneous acceleration. Looking at it only for an instant doesn't make it go away/allow you to ignore it.

 

[A.T.]

But I don't think that is the same as the speed limit between ends of the wire.

The recession speed between the ends of the wire is zero.

 

[Dale]

The recession speed between the ends of the wire is zero.

Hmm, that isn't obvious to me for a cosmologically sized wire.

 

[A.T.]

You can stop the unrolling...

I don't have to unroll anything. See post #31.

You're picking different stars at different times in order to try to ignore the fact that all of those stars are accelerating?

The stars have zero proper acceleration.

 

[A.T.]

Hmm, that isn't obvious to me for a cosmologically sized wire.

Doesn't constant proper length imply the ends aren't receding from each other?

 

[Dale]

Doesn't constant proper length imply the ends aren't receding from each other?

In a local inertial frame, yes. But this is neither local nor inertial. You could very well be correct, but it just isn't obvious to me.

 

[rede96]

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.

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).

Sorry for the layman type question but assuming a wire with neither end attached, could you explain why the ends of the wire are accelerating away from each other? What force makes this happen? Expansion itself produces no force.

 

[jerromyjon]

Expansion itself produces no force.

But it does cause galaxies to recede from each other, and if this hypothetical wire had a gravitational force from the galaxy at each end pulling in opposite directions...

 

[rede96]

But it does cause galaxies to recede from each other, and if this hypothetical wire had a gravitational force from the galaxy at each end pulling in opposite directions...

True, but gravity is quite week compared to the nuclear forces that hold the wire together. And in any case as the galaxies recede the force of gravity on the wire would get less as the wire wouldn't be receding with them.

 

[jerromyjon]

gravity is quite week compared to the nuclear forces that hold the wire together.

Actually the electrons hold the atoms together, the nuclear forces hold the nucleus of the atoms together, but gravity is certainly weaker. That's what got us to the megaparsec range in the first place. At some point this thought experiment strays off into fantasy.

 

[rede96]

Actually the electrons hold the atoms together, the nuclear forces hold the nucleus of the atoms together, but gravity is certainly weaker. That's what got us to the megaparsec range in the first place.

Ok, thanks.

At some point this thought experiment strays off into fantasy.

If you read all the relevant posts then you'll see that I agree, my objective isn't to prove a 'fantasy', but to understand the laws of physics that prevent it. Which is still on going.

 

[jerromyjon]

but to understand the laws of physics that prevent it.

Of course.

And in any case as the galaxies recede the force of gravity on the wire would get less as the wire wouldn't be receding with them.

This is true but we are trying to reach a conclusion about what limits the integrity of a length of wire, not what happens if it does remain intact.

 

[jerromyjon]

At some point this thought experiment strays off into fantasy.

I can't think of anything in physics alone that would prevent it from being infinite, which only leaves environmental factors of how far can it span.

 

[rede96]

This is true but we are trying to reach a conclusion about what limits the integrity of a length of wire, not what happens if it does remain intact.

Yes, exactly. In fact going through the other posts again, it seems that it might not even be possible to deploy a wire over a certain length.

I can't think of anything in physics alone that would prevent it from being infinite, which only leaves environmental factors of how far can it span.

I didn't realize at the time but I did a very similar post about 5 years ago. So I am just going through that again as the total thread ended up being over 7 pages.

But for now I think I have gone as far as I am able to understand with my limited knowledge of physics.

 

[rootone]

The wire has a finite number of atoms in it.
So the longest it could get, however you might stretch it, would be as long as a line of that number of atoms can be while still being bound to each other in some way.
Once it is stretched beyond that point the wire becomes a bunch of disassociated atoms subject to whatever forces are locally prevailing upon them.

 

[A.T.]

if this hypothetical wire had a gravitational force from the galaxy at each end pulling in opposite directions..

That would create stress in the wire even without expansion. And if the wire is dense enough it might collapse under it's own gravity. But I think the OP is interested in the effect of the expansion itself.

 

[rede96]

But I think the OP is interested in the effect of the expansion itself.

Understanding the effects of expansion is certainly something I'd like to know more about for sure. But my goal was to understand just what laws of physics would limit the length of such a wire. As far as expansion is concerned I read that it produces no forces, so in that respect expansion itself couldn't be a factor in limiting the length of the wire.

That would create stress in the wire even without expansion.

This is one of the main things I am struggling with. How are stresses created in a wire just due to it's length? Ignoring all other influences for the moment, I don't understand which basic principles of physics would create such a stress just due to the length of something that eventually limit it's length.

And if the wire is dense enough it might collapse under it's own gravity.

I understand that if again we ignore all other influences on the wire, gravity would eventually draw the wire towards it's centre of mass. But as gravity is so week compared to the forces the bind the wire together, and as its mass is spread over such vast distances I didn't see how this would limit the length of the wire.

 

[A.T.]

As far as expansion is concerned I read that it produces no forces, so in that respect expansion itself couldn't be a factor in limiting the length of the wire.

The expansion does limit the proper length that can remain constant because of the speed limit c. The rest of the discussion is about whether the wire could be made stress free below that length.

How are stresses created in a wire just due to it's length?

Tidal forces can introduce stresses on extended objects.

I understand that if again we ignore all other influences on the wire, gravity would eventually draw the wire towards it's centre of mass. But as gravity is so week compared to the forces the bind the wire together, and as its mass is spread over such vast distances I didn't see how this would limit the length of the wire.

If Nugatory and Russ are right that there would be wire tension because of the expansion alone, then self gravity could potentially help to counter that, and thus allow to make the wire longer.

 

[rede96]

The expansion does limit the proper length that can remain constant because of the speed limit c. The rest of the discussion is about whether the wire could be made stress free below that length.

Could you expand on that please. (No pun intended!) Here is a link to an article on expansion posted by bccrowell in another thread: https://www.physicsforums.com/threads/proper-time-0-is-nonsense.819329/#post-5143259

Towards the end of the article there is part on the effects of expansion on objects. (Its called "Is Brooklyn Expanding?") It states that constant expansion produces no forces on any object. It goes on to say that if expansion is not constant but accelerating, it does not make things expand, they will just settle into a new state of equilibrium. It is only if the rate of acceleration is changing that there could be a problem as eventually it could rip things apart. But this is just speculation and wouldn't directly limit the length of a wire initially.

So I am struggling to understand how expansion is an issue if we assume constant acceleration.

Tidal forces can introduce stresses on extended objects.

Are these tidal forces from within the wire? Like the atoms or molecules trying to move towards one end? (or something like) Or do you mean external forces?

If Nugatory and Russ are right that there would be wire tension because of the expansion alone, then self gravity could potentially help to counter that, and thus allow to make the wire longer.

ignoring expansion for the moment, I wouldn't have thought gravity alone could limit the length of the wire. Would you agree?

 

[A.T.]

Could you expand on that please.

See post #3.

Are these tidal forces from within the wire?

https://en.wikipedia.org/?title=Tidal_force
But eventually we can ignore those, if we assume uniform matter distribution.

ignoring expansion for the moment, I wouldn't have thought gravity alone could limit the length of the wire. Would you agree?

Yes.

 

[rede96]

See post #3.

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.

If we are assuming constant acceleration for expansion and ignoring other influences, then there is nothing acting on the wire to stop it from keeping proper length. No?

EDIT: Or in other words proper length is its natural state.

 

[A.T.]

... there is nothing acting on the wire ...

See post #29.

 

[rede96]

See post #29.

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.

I don't think this is correct. If we assume that expansion is not going to have an effect on wire, then we can also assume that the wire is not moving 'through' space. So the wire, or at least an end of the wire, can be seen as is if It was in an inertial FOR.

So I could start with just a short length of wire, which would be at rest WRT to me, then move along to the end of the wire and attach another piece. I could do this indefinitely as the end of the wire is always in my local frame. So I could move along the wire at what ever speed I like as relative to me it is at rest.

 

[jerromyjon]

I think A.T. has a good point. The wire can only be at "rest" in space in the middle. The ends are at a velocity in local space due to expansion. If each end of the wire is in space being expanded by more than 2c the ends of the wire would have to move through space faster than c to remain intact.

 

[rede96]

The ends are at a velocity in local space due to expansion.

No, I don't think this is the case. If you read the article I mention, then it quite clearly states that expansion does not produce any force on an object. The ends are bound to wire, so they will not 'move away' with expansion.

 

[jerromyjon]

Velocity doesn't require a force AKA "tends to stay in motion", acceleration requires a force. The wire has a force holding it together against the expansion, and that stress will increase as you make the wire longer.

 

[A.T.]

The ends are bound to wire, so they will not 'move away' with expansion.

That's exactly why the ends would have to move relative to the local stars, which are 'moving away' with expansion. And that relative velocity is bound by c.

 

[rede96]

Velocity doesn't require a force AKA "tends to stay in motion", acceleration requires a force. The wire has a force holding it together against the expansion, and that force will increase as you make the wire longer.

I'm probably out my depth here, but if I apply the logic from the article I read then I am not sure that is correct. It states that an object is not 'expanded' in any way due to expansion. Constant acceleration (Edit: of expansion not the wire) would cause the wire to expand slightly but only until it found its new state of equilibrium. Once this was done, then this 'force' would cease.

So if there is no 'action' on the wire from expansion, there is no opposite reaction from the wire. So the wire doesn't have to work against expansion. Unless, the rate of acceleration is increasing. Which I think was stated as just speculation, so I was going to ignore that.

 

[rede96]

That's exactly why the end would have to move relative to the local stars, which are 'moving away' with expansion.

Ah ok, I see what you mean. But that recession is not a movement 'through' space. It is caused by expansion. So even though the end of the wire is moving away from the local stars, or vice versa, it is due to expansion, not movement though space-time so relativistic effects don't come into play and it doesn't cause any stresses or force on the wire. (ignoring local gravity from the stars)

 

[jerromyjon]

So even though the end of the wire is moving away from the local stars, or vice versa, it is due to expansion

No, it is due to the electronic forces holding the wire together, in the expansion.

 

[rede96]

No, it is due to the electronic forces holding the wire together.

Sorry, you'll need to explain that. How do electronic forces in the wire cause it to move away from local stars?

 

[jerromyjon]

Electrons hold the atoms together, keeping it "a wire". Expansion is stretching the space it exists in.