# How long can a wire be?

1. Jun 17, 2015

### rede96

Hope this is the right place to ask this question. But I was wondering if there are any laws of physics that dictate how long I could make a wire?
Also, as ridicules as this might be, if I tied that wire to a planet in a nearby galaxy and then waited for that galaxy to start to recede at speeds greater than c, is there any law of physics that means the wire would have to break apart if certain parts of it reached velocities greater than c in my local frame?

2. Jun 17, 2015

### phinds

If the wire were connected to something in the distant galaxy, I guess it would have to break even without expansion (because of galactic rotation on both end), but 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.

3. Jun 17, 2015

### A.T.

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.

4. Jun 17, 2015

### rede96

Thanks for the reply. If we ignore the rotaion element, and just assume that I can put this on a body that doesn't roate but is large enough to be 'pushed' by expansion, then theoretically I could have an infinately long wire. Which means that the end that isn't attached to the large body could be thousands of light years away. Which meant that as the large object start to recede due to expansion, then at some point the wire would start to travel faster than c. So I thought the wire must break.

5. Jun 17, 2015

### rede96

I agree it shouldn't be possible for the wire to travel faster than light relative to local stars, but as I understand it, the wire does not expand with space?

6. Jun 17, 2015

### A.T.

Right, that's why I think the wire length is limited, even if the ends are free.

7. Jun 17, 2015

### rede96

Cool, as I was hoping to find out just what laws of physics goevern the length of the wire.

8. Jun 17, 2015

### phinds

Ah, right. The remote galaxy would recede from the end of the wire then? I mean, the wire is locally coherent so should not follow the expansion at all, but I see no reason for it to break, just to get farther and farther away from the receding galaxy.

EDIT: OOPS ... I didn't see your second reply, which does agree w/ this. Thanks.

9. Jun 17, 2015

### rede96

Just to clarify, in my thought experiment, one end of the wire is attached to an object in the galaxy which is receding. The rest of the wire could be coiled up for example in my local frame in another galaxy. So as the other galaxy starts to recede I see the wire start to uncoil. If the wire is infinitely long, at some point the wire will start to uncoil at speeds greater than the speed of light. So I assumed it must break.

By the way the wire doesn't need to be coiled, it could have been laid out along it's length across the universe, but I think it is easier to imagine if it is coiled.

10. Jun 17, 2015

### phinds

The wire that is not coiled but is stretched out but unattached at the end not in the galaxy that is receding from you will not break because it is in essence a part of the receding galaxy and is not affected by the expansion. The end closest to you will simple get farther away, as will the receding galaxy.

The coiled version will not uncoil. Why should it? The whole thing is a part of the receding galaxy and is not affected by expansion so there is nothing to make it uncoil.

11. Jun 17, 2015

### rede96

In simple terms, expansion means that the distance between say two galaxies is increasing with time. As is the rate the distance increases. So if I attached one end of a wire to some object in galaxy A and then fly off with the other end to another galaxy B, and gather up the excess wire into a coil, then as galaxy A moves away due to expansion it must uncoil the wire as the distance between galaxy A and galaxy B is increasing.

12. Jun 17, 2015

### phinds

Ah, I didn't realize you were planning on attaching both ends. In that case the wire will break whether it is coiled or not.

13. Jun 17, 2015

### rede96

Sorry, I can be crap at explaining things sometimes! But technically the other end isn't attached, I could have just flown off in the opposite direction and would have had one end attached to a galaxy and the other end just floating free in space.

But I agree it must snap, or sooner or later the free 'end' will be moving with a speed greater than c.

So I am interested in what law of physics dictates that the wire must snap and at what point would it snap?

14. Jun 17, 2015

### phinds

No, I think you misunderstand. If one end is in one galaxy and the other in is in the other galaxy, then they ARE attached, whether you have them tether to a planet or something or not. The point is that if they are IN a galaxy they are a part of the galaxy as far as expansion is concerned.

Actually, now that I think about it more, you could never get in placed to start with if the other galaxy is receding at > c. If you start in one galaxy and head out for the other galaxy, you'll never get there. If the other galaxy is (relatively) nearby, then you could get there but assuming that galaxy is not part of our Local Group, the wire would likely break as soon as you were captured by the gravitational attraction of the receding galaxy since pretty much any recession is going to break it.

EDIT: All of this seems kind of pointless anyway. If you are using it to understand recession, it seems to me that you are over complicating things.

15. Jun 17, 2015

### Staff: Mentor

If you fix one end and let the other dangle free at a very great distance away, the free end will be accelerating relative to an observer in free fall near the free end. This acceleration will be produced by tensile forces in the wire, and the wire will snap when these tensile forces exceed the strength of the wire. No matter how strong the wire is, it will snap if you make it long enough because the forces in the wire will become infinite as the far end is required to approach the speed of light relative to the inertial observer at that end.

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).

16. Jun 17, 2015

### rede96

Ah ok, I see what you mean. Not sure I quite understand that, but understand your point.

I wasn't trying to understand recession fully at this point to be honest, I just wanted to know what laws of physics limit the length of the wire in the scenario I mentioned. But I find the point you raised above interesting, so will read up a bit more as I'd like to understand that in more detail. Thanks for your input.

Thanks for the explanation. Again, I kind of understand this. But I think phinds mentioned something in a previous reply where if both ends of the wire were unattached then there was no reason for the wire to break. So that would imply there has to be some force acting on the wire to make it snap. Is that correct? So if the wire was just dangling from some random object in space, where or when would the forces start to act upon it?

17. Jun 17, 2015

### phinds

After seeing Nugatory's post, I think I have to reconsider that. I can't flaw Nugatory's logic that something very far away HAS to be subject to the expansion. It doesn't feel quite right to me, but I'm used to being wrong about things in cosmology and quantum mechanics.

18. Jun 17, 2015

### Staff: Mentor

If both ends of the wire are unattached, it will take less tension in the wire to hold it together, so the wire can be longer. But it will still break if the wire is long enough.

(This entire problem is most easily modeled as two point masses connected by an ideal massless wire. That way you can just consider the force required to produce the proper acceleration that keep the ends on a path that preserves the proper length of the wire. If you instead consider a non-ideal wire with non-zero mass density along its length, it's like doing classical physics exercises with non-massless ropes - you end up doing a whole bunch of messy integrals that provide no additional insight).

19. Jun 17, 2015

### rede96

Thanks, that really helped to conceptualise the problem for me. So if I understand that properly, using your model, as one end 'moves away' due to expansion then once the force required to accelerate the other end becomes to great to maintain its proper length, the wire will snap.

And for relatively short cosmological distances, as the ends of the wire would never require a force to accelerate greater than the speed of the light, the wire would remain intact.

Does that mean this is a way to define cosmological frames of reference? (for want of a better term!) What I mean by that is if two bodies of a given mass could only be considered to be at rest wrt each other as long as the forces required to maintain this imaginary proper length between them did not exceed the force required to accelerate at c?

20. Jun 17, 2015

### phinds

Define "short". For any distance which seriously involves expansion at the ends, "c" is not needed. You don't need a sledgehammer to kill a flea.