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

[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.

 

[rede96]

Electrons hold the atoms together, keeping it "a wire".

Ah ok I see. Yes of course. The electronic forces keep the atoms together, keeping it a wire. But it is expansion that is moving the stars away. And relativisticly speaking it is just as accurate from the star's point of view to say the end of the wire is moving away.

Expansion is stretching the space it exists in.

Yes sure, but expansion is not stretching the wire. So objects can move away from the wire in any direction, but the wire itself is not effected by expansion.

 

[jerromyjon]

The ends of the wire are at a proper length from each other, moving in opposite directions(towards the middle) through space. That velocity must be <c.

 

[rede96]

The ends of the wire are at a proper length from each other, moving in opposite directions through space. That velocity must be <c.

I'd have said that ends of the wire don't move with respect to each other. This has to be the case or the proper length would not be maintained. For me it just the same as imagining it as a solid steel rod.

So the whole wire can move through space but of course not as speeds >c

 

[jerromyjon]

So the whole wire can move through space but of course not as speeds >c

So your "rod" stays a constant length, at zero relative velocity to itself, and the stars at the ends move away from it faster than c, still doesn't work.

 

[A.T.]

So even though the end of the wire is moving away from the local stars,

It is moving relative to the local stars.

it is due to expansion,

Doesn't matter why. Local relative speeds cannot exceed c.

 

[rede96]

So your "rod" stays a constant length, at zero relative velocity to itself, and the stars at the ends move away from it faster than c, still doesn't work.

Doesn't matter why. Local relative speeds cannot exceed c.

As I understand it, relativity only prohibits relative speeds greater than c if the two relative objects are moving through space-time. Hence why galaxies can recede at speeds greater than c.

So the issue seems to be is there a case where expansion could cause two objects to be moving apart at speeds >c in a local frame. And I don't think this is possible, but I need to think about it more.

In any case I think there is some confusion between the physics limiting the length of a wire and objects moving at speeds >c relative to each other.

If we assume just for a moment that it is possible to make an infinitely long wire, then the question is: Would this violate relativity in any way? And I don't think it would.

To make this wire I have to start somewhere in space. And where ever that local frame is, there are no stars that will be locally moving away from me at speeds > c. Any stars that are moving away from me at speeds > c I would never be able to reach. So I could continue to make this wire for as long as I have the will power, but as I make the wire, I can never catch up to distant objects which are moving > c

So there is no local frame where relative speeds exceed c EDIT No matter how long I make the wire.

 

[jerromyjon]

I can never catch up to distant objects which are moving > c

Think a little harder, because space expanding as you travel through it doesn't prevent you from reaching your destination, space would have to expand faster than you can travel through it.

 

[jerromyjon]

https://en.wikipedia.org/wiki/Metric_expansion_of_space
I strongly disagree with some of the assertions made in this page on the ΛCDM. The way I understand it light from a distant galaxy receding faster than 300,000Km/s would still reach us to be seen, it would just take a lot longer to arrive.

This seems to be a different view: ". For example, galaxies that are more than approximately 4.5 gigaparsecs (14.7 billion light-years) away from us are expanding away from us faster than light. We can still see such objects because the Universe in the past was expanding more slowly than it is today"

I don't believe the past rate being slower is necessary, if the rate of expansion was constant the light would still reach us.

 

[rootone]

It seems to me that, yes photons emmited from the distant object can arrive at Earth eventually - BUT,
Those photons which arrive will have been emitted a very long time ago when the object would have been less distant and not receding as fast as it is now.
If the object still exists 'right now' (simultaneously with us), any photons it emits will never be seen at Earth, since it's recession speed 'right now' is faster than c, and is likely to increase still further.
It makes more sense to me that in the distant future, objects such as galaxies beyond our local group which we can now see, will be seen no more as the expansion continues.
This as opposed to distant objects becoming seen which had not been seen previously

 

[A.T.]

If the object still exists 'right now' (for us), any photons it emits will never been seen since it's recession speed 'right now' is faster than c,

Photons can reach the target, even if emitted when the recession speed between emitter and target (due to metric expansion) is > c. See:

https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope



Only a sufficient amount of acceleration of the expansion can prevent them from ever reaching the target.

 

[rootone]

I read the wiki article, and will look at the video later.

So the photons can in principal arrive at a target which is receding from their origin faster than light, (due to expansion)
However the time taken to get there can be unimaginably immense, exactly how immense depending on the rate of acceleration (of expansion).
There will be some acceleration rate beyond which the photons can NOT in fact arrive, but this precise rate seems to be undeterminable.
So since we don't know the future rate of acceleration, we can't really say confidently that such photons will or will not be 'seen'.
(If they are detected though they will red shifted so much that they will probably look more like long wave radio than light).

 

[rede96]

Think a little harder, because space expanding as you travel through it doesn't prevent you from reaching your destination, space would have to expand faster than you can travel through it.

I know light from stars outside of our Hubble horizon would eventually reach us, but I don't think we could travel to a star outside of that horizon as it would require traveling faster than light.

The star or destination I am trying to reach is constantly moving away from me and the rate is getting faster with time. So if it is already moving away faster than the speed of light, by definition it means I can't get to it.

The only thing I am not sure about is how length contraction would effect this. If I am traveling at relatively high speeds then distances are reduced from my frame so I would assume the rate of expansion would be reduced too.

But I would still imagine there will be a type of 'travel' horizon that would mean any object that is outside of this event horizon would be unreachable for ever.

 

[A.T.]

I know light from stars outside of our Hubble horizon would eventually reach us, but I don't think we could travel to a star outside of that horizon as it would require traveling faster than light.

You can reach destinations outside of the horizon at velocities less than c, it just would take even longer than for light.

So if it is already moving away faster than the speed of light, by definition it means I can't get to it.

It's not moving away, it receding due to metric expansion. Depending on how the expansion develops over time, one can reach all or some of the stars which were behind the horizon on launch.

 

[rede96]

Depending on how the expansion develops over time, one can reach all or some of the stars which were behind the horizon on launch.

I would have thought there must be some point where it becomes impossible to travel to a distant star?

 

[jerromyjon]

I would have thought there must be some point where it becomes impossible to travel to a distant star?

Only if you move slower than space is expanding, which is not really that fast. It is kind of like paddling upstream with a slow current, as long as you paddle faster than the current you make progress.

 

[rede96]

It is kind of like paddling upstream with a slow current, as long as you paddle faster than the current you make progress.

Yes, if the current is constant. But expansion is accelerating, so it is like the current is getting stronger the further upstream I paddle. So there will come a point where I am not able to paddle fast enough and I get stuck in the same place.

Another way of looking at it for me is like there is a car that is accelerating at a slow speed some distance ahead of me. If I am moving at my maximum velocity, and the car ahead is constantly accelerating, there is a limit to the time I have to catch it up. If I don't catch up to it before it exceeds my maximum velocity then I will never catch it.

As there is a limit to the maximum speed I can travel, then there must be a limit to which far away stars I can catch up to as they are constantly accelerating in relation to me.

 

[jerromyjon]

Another way of looking at it for me is like there is a car that is accelerating at a slow speed some distance ahead of me. If I am moving at my maximum velocity, and the car ahead is constantly accelerating, there is a limit to the time I have to catch it up. If I don't catch up to it before it exceeds my maximum velocity then I will never catch it.

This is what is confusing you, I believe, The distant galaxy is NOT accelerating away from you, so your example does not relate. It is more like walking against the movement of a conveyor belt, trying to reach the beginning of it. For some sense of magnitude, the belt is moving 1km/h and you start walking at 5km/h. After an hour of walking you have traveled 4km.

 

[rede96]

This is what is confusing you, I believe, The distant galaxy is NOT accelerating away from you, so your example does not relate

No, that isn't correct. The further something is away from me, the faster it is receding from me. Just Google accelerating universe.

 

[jerromyjon]

Recession and acceleration are totally different.

 

[rede96]

Recession and acceleration are totally different.

Ok, but I don't understand what point you are making?

 

[rede96]

The distant galaxy is NOT accelerating away from you,

If there are some galaxies now that are moving away from me at speeds less than the speed of light, but in some time in the future EDIT: be moving faster than the speed of light relative to me, then their velocity relative to me is changing with time. Changing velocities over time is acceleration.

 

[jerromyjon]

You are in a car sitting still. 1km ahead of you is a traffic light. Imagine expansion of space is like the road is stretching. Suppose after 1 hour the traffic light is 1.1km away now, but neither you or the traffic light has moved! After another hour the light is 1.21km away, the stretching of the road has increased! That is the acceleration of the expansion. Begin driving towards the light at 1km/h for one hour and you only have about 0.32km to go... starting to make sense yet?

 

[eltodesukane]

--Wikipedia: Bell's spaceship paradox (A delicate string or thread hangs between two spaceships)
https://en.wikipedia.org/wiki/Bell's_spaceship_paradox

Some references about the tethered galaxy problem:
--Solutions to the tethered galaxy problem in an expanding universe
http://arxiv.org/abs/astro-ph/0104349
http://www.mso.anu.edu.au/~charley/papers/DavisLineweaverWebb03.pdf
--Tethered galaxies and the expanding space paradigm
http://www.chronon.org/papers/current/untethered.pdf
--A look at tethered and untethered galaxies
http://www.chronon.org/papers/tethered_galaxy.html
--How Does Hubble's Expansion Affect Two Rope-Tied Galaxies?
http://physics.stackexchange.com/qu...bbles-expansion-affect-two-rope-tied-galaxies
--Wikipedia: Redshift, reference 43
https://en.wikipedia.org/wiki/Redshift#cite_ref-43

 

[rede96]

You are in a car sitting still. 1km ahead of you is a traffic light. Imagine expansion of space is like the road is stretching. Suppose after 1 hour the traffic light is 1.1km away now, but neither you or the traffic light has moved! After another hour the light is 1.21km away, the stretching of the road has increased! That is the acceleration of the expansion. Begin driving towards the light at 1km/h for one hour and you only have about 0.32km to go... starting to make sense yet?

Yes, thanks. But I still see it that the traffic light is accelerating away from me. After one hour it has moved 0.1km, and after 2 hours it has moved another 0.11km and so on.

So if I can only travel at a maximum of 0.1 km an hour, then I will never catch up to it. If in your example 0.1 was equivalent to the speed of light, then the traffic light has gone for ever. I could still see the traffic light of course, as light from it will still reach me. But I could never catch up to it.

 

[rede96]

Some references about the tethered galaxy problem:
--Solutions to the tethered galaxy problem in an expanding universe
http://arxiv.org/abs/astro-ph/0104349
http://www.mso.anu.edu.au/~charley/papers/DavisLineweaverWebb03.pdf
--Tethered galaxies and the expanding space paradigm
http://www.chronon.org/papers/current/untethered.pdf
--A look at tethered and untethered galaxies
http://www.chronon.org/papers/tethered_galaxy.html
--How Does Hubble's Expansion Affect Two Rope-Tied Galaxies?
http://physics.stackexchange.com/qu...bbles-expansion-affect-two-rope-tied-galaxies
--Wikipedia: Redshift, reference 43
https://en.wikipedia.org/wiki/Redshift#cite_ref-43

Thanks for links, will check them out later.

 

[rede96]

That is the acceleration of the expansion. Begin driving towards the light at 1km/h for one hour and you only have about 0.32km to go... starting to make sense yet?

Just an after thought, I think what you were trying to explain to me is that the traffic light is not moving relative to the road. But as I can move relative to the road, then I can catch up to the traffic light. Is that correct?

 

[jerromyjon]

Is that correct?

Exactly.

 

[jerromyjon]

So if I can only travel at a maximum of 0.1 km an hour, then I will never catch up to it. If in your example 0.1 was equivalent to the speed of light, then the traffic light has gone for ever. I could still see the traffic light of course, as light from it will still reach me. But I could never catch up to it.

That is not right. If space were expanding faster than light, nothing, not even 2 photons, could ever reach each other.

The recession of galaxies separated by roughly 14 billion light years only increases by roughly 300,000 km/s. That's about .000002 meters per kilometer?

 

[rede96]

Exactly.

Cool :D

 

[andrewkirk]

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.

When we deduce an absurdity, reduction ad absurdam requires that something we have assumed must be incorrect.

One assumption is that the wire would not break, so falsifying that is one option.

But another assumption - not yet explicitly noted as far as I can see (although I've only read the first few posts) - is that the wire could have been put there in the first place, such that it is (a) connected and (b) the ends are initially motionless relative to nearby stars. Falsifying this seems easier to me. We just conclude that it would be impossible to create that initial state, and hence it may be possible to deduce absurdities if we assume the initial state, including deducing that the ends are moving superluminally relative to nearby stars, .