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

[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"

 

[RandyD123]

Thanks for pointing that out "phinds", it was very intuitive of you, however, you can't stop time either. In my scenario you can do both. It's called suspending certain facts to carry out a thought experiment.

And thanks for your simple answer "the wire breaks because of expansion"...which makes very little sense, because in most explanations of expansion, the balloon analogy is used. I'm thinking my wire will just uncoil some more to make room for expansion.

 

[jerromyjon]

I'm thinking my wire will just uncoil some more to make room for expansion.

When you and your friend are separated by about 30 billion lightyears distance, how can you justify each of you and your friend's spools releasing wire at a velocity >c relative to the spool?

 

[RandyD123]

When you and your friend are separated by about 30 billion lightyears distance, how can you justify each of you and your friend's spools releasing wire at a velocity >c relative to the spool?

I guess I can't. So can only light move faster than light? Or is it "space/time" moving faster than light? Or is it both?

 

[jerromyjon]

So can only light move faster than light?

Not in mainstream accepted physics. Nothing moves faster than light from any point A to any point B. "Spooky action at a distance" Is not very spooky and no one can scientifically prove there is an action. Neutrinos are still questionable.

Or is it "space/time" moving faster than light?

To reach the case of >300000000m/s (8 zeroes) stretched out over 15 billion light years = 1.419 × 10²⁶ meters (300000000m/14190000000000000000000000m)=2.1141649 × 10^-17m/s. Show me when you see that meter grow that much or more if it is accelerating or prove it isn't locally, only galactically.

Or is it both?

You tell me, it's your universe.

 

[RandyD123]

Not in mainstream accepted physics. Nothing moves faster than light from any point A to any point B. "Spooky action at a distance" Is not very spooky and no one can scientifically prove there is an action. Neutrinos are still questionable.

To reach the case of >300000000m/s (8 zeroes) stretched out over 15 billion light years = 1.419 × 10²⁶ meters (300000000m/14190000000000000000000000m)=2.1141649 × 10^-17m/s. Show me when you see that meter grow that much or more if it is accelerating or prove it isn't locally, only galactically.

You tell me, it's your universe.

hahaha...my head just broke, my universe just broke and my wire just broke!

 

[jerromyjon]

Neutrinos are still questionable.

And all you had to do... was make it out of these.

 

[rede96]

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+Λg=8πT G+\Lambda g=8\pi T. 'Dark Energy' is just a colourful name chosen for the Λg \Lambda g part.

I probably need to read up a bit more on this, but in essence I did consider dark (EDIT energy not matter) and gravity to be the same phenomenon. They are both part of 'space' as I saw it. But I'm interested in how it all fits together but as I said need to do some more reading!

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 Fw

This is the bit I am having trouble understanding. Why one end wants to accelerate from the other. I know dark matter does not have zero effect, but from what I read it just changes the state of equilibrium but doesn't continue to 'expand' an object. And although space is expanding I didn't think it applied a tension to objects even on a cosmological scale. But from what you are saying the expanding space does apply a 'pressure' to objects that increases with mass. EDIT: OR size, I am not sure which!

 

[rootone]

Remember, this is the 'dark energy' which was being refferred to as intrinsically part of the 'gravity' phenomena.
Not dark matter, that's something else.

 

[rede96]

Remember, this is the 'dark energy' which was being refferred to as intrinsically part of the 'gravity' phenomena.
Not dark matter, that's something else.

Yes, sorry that was just a typo.

 

[andrewkirk]

This is the bit I am having trouble understanding. Why one end wants to accelerate from the other. I know dark matter does not have zero effect, but from what I read it just changes the state of equilibrium but doesn't continue to 'expand' an object. And although space is expanding I didn't think it applied a tension to objects even on a cosmological scale. But from what you are saying the expanding space does apply a 'pressure' to objects that increases with mass. EDIT: OR size, I am not sure which!

It certainly is difficult to conceptualise. And I think different metaphors or perspectives work better with different people, in making intuitive sense of it. It's hard, but not as hard as it is for quantum mechanics (in my opinion).

For me, it was focusing really hard on the notion of geodesic that first gave me an intuitive sense of GR. An object will follow a geodesic unless a non-gravitational force is applied to it, and the more radically you want to make an object diverge from its geodesic, the bigger the force you have to apply to it. The reason you have to apply a force to one end of the wire to stop it from rushing away (from the other end of the wire) with the nearby stars is the same as why you have to apply force to an apple on Earth to prevent it accelerating towards the core (of the Earth, not the apple). It's because you are trying to radically accelerate the object away from its geodesic. In the apple's case, the geodesic heads directly towards the centre of the Earth, and only a continuous force upwards - by your hand, or a basket, or the ground - can accelerate it away from that geodesic. Yes, the apple sitting in the fruit bowl on your table is being accelerated!

Strict language in GR does not regard gravity as a force. Only electromagnetic, strong and weak nuclear forces are real 'forces'. This is often inconvenient. People often describe it as a force when strict language is not necessary, because it's easier, and I think I may have done so above. But the reason for being strict when it counts is that it makes it easier (at least for me) to understand things. Gravity doesn't 'push things around'. Rather it just in a sense defines their 'natural' state of motion, which is the geodesic. In a loose sense, an object that is following its geodesic is 'stationary'. And any motion relative to a geodesic must be explained by the application of some (strict) force. To me, that way of looking at it simplifies things. But as I said, it's different for everyone and I can understand if for some it confuses them instead.

I suppose the mark of a really good teacher is the ability to offer a wide selection of metaphors so that most likely everybody will be able to find at least one that is intuitive for them. Unfortunately, I only have one.

 

[rede96]

For me, it was focusing really hard on the notion of geodesic that first gave me an intuitive sense of GR. An object will follow a geodesic unless a non-gravitational force is applied to it, and the more radically you want to make an object diverge from its geodesic, the bigger the force you have to apply to it. The reason you have to apply a force to one end of the wire to stop it from rushing away (from the other end of the wire) with the nearby stars is the same as why you have to apply force to an apple on Earth to prevent it accelerating towards the core (of the Earth, not the apple). It's because you are trying to radically accelerate the object away from its geodesic. In the apple's case, the geodesic heads directly towards the centre of the Earth, and only a continuous force upwards - by your hand, or a basket, or the ground - can accelerate it away from that geodesic. Yes, the apple sitting in the fruit bowl on your table is being accelerated!

Thanks, that does really help to conceptualise it. Where I am still struggling is understanding why the gravity from the local stars near the end of the wire is strong enough to overcome the forces in the wire that hold it together, so the wire snaps. We have the local mass of the milky way, but it doesn't rip anything apart. So I just was finding it difficult to see how gravity from local stars could be that strong.

Strict language in GR does not regard gravity as a force. Only electromagnetic, strong and weak nuclear forces are real 'forces'. This is often inconvenient. People often describe it as a force when strict language is not necessary, because it's easier, and I think I may have done so above. But the reason for being strict when it counts is that it makes it easier (at least for me) to understand things. Gravity doesn't 'push things around'. Rather it just in a sense defines their 'natural' state of motion, which is the geodesic. In a loose sense, an object that is following its geodesic is 'stationary'. And any motion relative to a geodesic must be explained by the application of some (strict) force. To me, that way of looking at it simplifies things. But as I said, it's different for everyone and I can understand if for some it confuses them instead.

Again, as above I would have thought the forces that hold the wire together would have been sufficient to accelerate the end away from the geodesic. The only thing I have read that would be strong enough to tear things apart is a black hole. And you'd need to be quite close as I understand it. And as there will be various local stars along the path of such a long length of wire, I thought the wire would just find its state of equilibrium and would follow various geodesics along its length to the point where the forces in the wire become too great and would hold it back.

I suppose the mark of a really good teacher is the ability to offer a wide selection of metaphors so that most likely everybody will be able to find at least one that is intuitive for them. Unfortunately, I only have one.

Well that one was good enough! I really appreciate it thanks.

 

[DrGreg]

Where I am still struggling is understanding why the gravity from the local stars near the end of the wire is strong enough to overcome the forces in the wire that hold it together, so the wire snaps.

First it's not gravity from local stars that is responsible, it's dark energy everywhere. Second, the influence isn't just at the ends of the wire, it's cumulative along all its billion light years of length. A really tiny effect multiplied by a billion light years becomes enormous.

 

[rede96]

First it's not gravity from local stars that is responsible, it's dark energy everywhere. Second, the influence isn't just at the ends of the wire, it's cumulative along all its billion light years of length. A really tiny effect multiplied by a billion light years becomes enormous.

Yes sure. But as dark energy is everywhere then I read somewhere that the effects would cancel out. So I had ruled that out previously. Was I wrong to do so?

 

[andrewkirk]

Where I am still struggling is understanding why the gravity from the local stars near the end of the wire is strong enough to overcome the forces in the wire that hold it together, so the wire snaps. We have the local mass of the milky way, but it doesn't rip anything apart. So I just was finding it difficult to see how gravity from local stars could be that strong.

It's not gravity from the local stars that does the ripping. I only mentioned them as a reference point against which to measure motion. Their gravitational influence is insignificant.

The gravitational influence that does the ripping is the 'dark energy' of the enormous distance between the two ends of the wire. The Einstein equation says that empty space has a gravitational influence, which is given by the term \Lambda g in Einstein's field equation G+\Lambda g=8\pi T - the bit that is called 'dark energy'. The scalar quantity \Lambda determines the strength of that gravitational influence per unit distance and the item g which is the metric tensor (something that measures distance, amongst other things), is what makes the gravitational influence proportional to the distance.

The reason we often read about black holes ripping things apart but not usually dark energy is that black holes do constantly rip things apart in practice, whereas the sort of ripping described in this experiment could never happen because the universe does not contain electromagnetically connected objects like wires that are long enough for this to happen. Having said that, there is something called 'The Big Rip' which I think is something to do with Dark Energy. I think it's a name for one of the possible ultimate fates of the universe. But I've never looked into it.

EDIT: Oh I see Dr Greg already answered this. For some reason it didn't show up on my screen at first. Never mind.

 

[rede96]

It's not gravity from the local stars that does the ripping. I only mentioned them as a reference point against which to measure motion. Their gravitational influence is insignificant.

The gravitational influence that does the ripping is the 'dark energy' of the enormous distance between the two ends of the wire. The Einstein equation says that empty space has a gravitational influence, which is given by the term Λg \Lambda g in Einstein's field equation G+Λg=8πT G+\Lambda g=8\pi T - the bit that is called 'dark energy'. The scalar quantity Λ \Lambda determines the strength of that gravitational influence per unit distance and the item g g which is the metric tensor (something that measures distance, amongst other things), is what makes the gravitational influence proportional to the distance.

As I mentioned above I think the mistake I was making was that I had read that dark energy was responsible for expansion, and that expansion itself had no effect (or little) on matter. (With the exception of the change in equilibrium mentioned earlier.) I had also read that as dark energy is everywhere and in all directions that it would cancel out.

So if that isn't the case, that is were I was confusing myself.