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

[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, .

 

[andrewkirk]

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.

I think it can be shown that there is a length beyond which it would break, without having to resort to reductio ad absurdam, with its accompanying problems, per my previous post.

Let F be the breaking strain of the wire, and the wire's mass be w kg/m. The impact of the cosmological constant is that there is some distance D such that $l>D\Rightarrow \frac{d^2{l}}{dt^2}>\frac{F}{w}$ where $l$ is the distance between two free-falling bodies.
Say the wire is longer than 2(D+1) metres and consider the one-metre length at either end. Each is being accelerated by $\Lambda$ away from the centre of the wire with acceleration greater than $\frac{F}{w}$ and since it has mass $w$ that imparts a force of F outwards along the wire. These two opposite forces of F are sufficient to break the wire.

(I think I made the wire twice as long as it needs to be to break, but never mind.)

The length D is enormously more than it would need to be to break the wire if it were attached to a planet at either end, because the force from 'dark energy' is proportional to the mass at either end of the wire. However, there is some length at which an unattached straight wire would break.

Ah: I see that Nugatory has already made this point a few posts earlier. I had only read the first page of this thread.

 

[rede96]

The length D is enormously more than it would need to be to break the wire if it were attached to a planet at either end, because the force from 'dark energy' is proportional to the mass at either end of the wire. However, there is some length at which an unattached straight wire would break.

You'll have to excuse my ignorance, but what I am really struggling to understand is just what forces are interacting with the wire that would make the ends accelerate to a point where it creates enough stress for it to break.

As I understand dark energy, it doesn't directly interact with matter. I assume as the effects of dark energy are in all directions they tend to cancel out. So it is just a part of space that is persistent everywhere and it is that persistence which leads to the expansion.

So how I am understanding the relationship between gravity, which is also present everywhere,(EDIT and also part of space) and expansion is that as space expands, it requires work for objects to 'move' back to the distance they were at before the space between them started to expand. Gravity can provide that work. But there comes a point where gravity has tailed off to the point where it can no longer provide the work needed to maintain the original distance. So I don't see gravity as a force that keeps things together, more the it provides the work to bring things back together to compensate for expansion.

However for systems that are bound in some way as solid objects, expansion or dark energy has no effect on them, it produces no stress or forces on these systems. And as such they need to do no work to keep together.

So I am struggling to understand just where the stress / forces are being produced that would cause an untethered wire of any length to break. As I understand it, there is nothing to suggest that expansion would accelerate the ends of the wire.

So where does that logic breakdown?

 

[andrewkirk]

(1)As I understand dark energy, it doesn't directly interact with matter.
...
(2) So how I am understanding the relationship between gravity, which is also present everywhere,(EDIT and also part of space) and expansion is that as space expands
...
(3) However for systems that are bound in some way as solid objects, expansion or dark energy has no effect on them, it produces no stress or forces on these systems. And as such they need to do no work to keep together.

The logic breaks down where you are trying to think of 'dark energy' as a phenomenon distinct from 'gravity', rather than just being part of the same phenomenon, which is Einstein's field equation $G+\Lambda g=8\pi T$. 'Dark Energy' is just a colourful name chosen for the $\Lambda g$ part.

That equation determines a geodesic for the one metre section S at the end of the wire, which is the path it would follow if it were not attached to the rest of the wire and subject to no non-gravitational forces. The geodesic of S is accelerating away from the opposite end of the wire at rate $\frac{F}{w}$. Let P be the tip of S that is the very end of the wire. To make P deviate from its geodesic requires applying a non-gravitational force to S. The point in space that is coincident with P at a fixed time t0 and thereafter maintains a constant distance from the other end of the wire is accelerating away from P with acceleration $\frac{F}{w}$. Hence, to make P follow that point - ie to accelerate rapidly away from its geodesic - requires the rest of the wire to pull S towards it with a force of F, which will break the wire.

Relating this to your questions, we get the following answers:
(1) It does interact with matter, as specified in the Einstein equation.
(2) The relationship is that it is gravity - construed as the phenomenon described by Einstein's equation - that causes the universe to expand. You can think of the dark energy as a sort of 'negative gravity' if you like, although it's not a strict negative because it's not related to mass-energy in the same way that the rest of the gravitational equation is.
(3) Dark energy doesn't have no effect on bound systems. It just has an effect that is proportional to their size, and the constant of proportionality is so tiny that its effect is generally immeasurably small. It's not zero though. The particles in your body sit an infinitesimally small distance further away from each other than they would if there were no dark energy, as an equilibrium is reached between the very strong electrostatic forces holding them together and the incredibly weak dark energy (pseudo-)forces pushing them apart. It is only when we start to consider things on an inter-galactic scale that dark energy becomes significant enough to take into account, and that's what is happening in this thought experiment of the wire.

 

[RandyD123]

I'm looking at it this way. Let's suppose you can stop time just for a moment. You in one galaxy and a friend in another. You have both found a way to meet in the middle and tie your wires together in an unbreakable knot. And you both have an infinite amount of wire on a coil.

Now start time again. Since both of you are now moving away from each other FTL from your own reference, what happens and why?

 

[phinds]

I'm looking at it this way. Let's suppose you can stop time just for a moment. You in one galaxy and a friend in another. You have both found a way to meet in the middle and tie your wires together in an unbreakable knot. And you both have an infinite amount of wire on a coil.

Now start time again. Since both of you are now moving away from each other FTL from your own reference, what happens and why?

The wire breaks because of expansion. By the way, you can't HAVE "an infinite amount of wire"