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

[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.

 

[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.