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If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen?

  1. Is the structural integrity of the rope enough to "overcome" the expansion of the universe all along the rope, causing the rope to break, or the rocks to "slide off" the planets? Or will the rope expand?
  2. If the rocks slide off the planets, and the planets were far enough apart, why would the rope not be able to move away from either planet faster than the speed of light?
Qmechanic
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LazyJones
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    Just so I think I understand what you're asking -- you want to know if matter (the rope) expands along with the metric expansion of space if it were to stretch across the universe? It just needs to be clear because your rope is already completely impossible, so asking if it would "break" doesn't have an answer -- it's a magical rope, we can make it do whatever we want. – tpg2114 Sep 05 '14 at 17:59
  • Correct, in point 1 I am asking whether the matter expands along with the metric expansion of space, or whether the forces maintaining its rigidity will apply on such an absurd scale...

    In point 2, I am asking for the explanation of why objects that appear to be moving away from us faster than the speed of light (outside the Hubble Volume) would not move away from the end of the rope at the same speed, as they "slide out from under the rope".

     – LazyJones Sep 05 '14 at 18:02
  • We have to look at two different cases: a non-accelerating universe, and an accelerating one. In an accelerating universe, the theoretical rope would experience actual forces that would tear it apart (there is no material that has a speed of sound that exceeds the speed of light). Even in a non-accelerating universe, the far, far end of the rope would still experience a red-shift, so the atomic bonds at that end would look weaker, and weaker, so it would look as if it would stretch with the local expansion. – CuriousOne Sep 05 '14 at 18:53
  • So, from Earth's viewpoint, in our apparent accelerating universe, it would look as if the rope was stretching at both ends due to the redshift. And from the viewpoint of either of the two planets at the end of the rope? – LazyJones Sep 05 '14 at 19:05
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    This is known as the "tethered galaxy" problem, and there are some papers on it: http://arxiv.org/abs/astro-ph/0104349 http://arxiv.org/abs/astro-ph/0511709 –  Sep 05 '14 at 22:22
  • This is actually similar to the question of how gravitational wave detectors detect gravitational waves. Suppose we assume the lattice of a crystal moves with the gravitational waves thus rendering the latter undetectable: this would imply that the proper distance corresponding to a lattice period would change, thus the crystal would find itself in a strained state, thus in reality will oppose the strain to some extent. Like reasoning applies here, where the proper distance between the tethered objects changes. – Selene Routley Sep 01 '15 at 10:32

1 Answers1

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Let's allow your rope to have fantastical properties but not violate conservation of energy or causality. Then if the ends of the rope are within the event horizon, your rope could conceivably not stretch. But if the ends are outside the event horizon:

  1. The rope must expand. There is no such thing as a rigid object in special relativity, because the concept of rigidity is dependent on simultaneity. If I yank on one side of a rope, the other side can't move instantly because information/influence can only propagate at the speed of light. See the pole in the barn paradox.
  2. Of course no part of the rope will be moving faster than the speed of light. However if the rope is strong enough the rocks will indeed lift off the planets, accelerating closer and closer to the speed of light. The rope is still expanding, just not as quickly as the space around it.

Different magic rope properties would have different final fates. A spring-like rope (F=kx) with a high but finite maximum tension would eventually snap explosively all along its length. With a sufficiently high maximum tension it should eventually have the energy density to become a very long black hole.

adipy
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    I wonder if anything special happens when a black hole takes the form of slightly elongated slinky. Is such a thing possible, or must it collapse into a spherical hole at some location? – zibadawa timmy Sep 05 '14 at 21:45
  • The rope must expand initially, but couldn't it reach an equilibrium where the proper distance between the galaxies stayed constant? The easiest case to analyze here would be a "Milne universe", which is what you get when you let the mass density go to zero in an FRLW universe...then it turns out that the negatively-curved space expanding with time is really just a non-inertial coordinate system on flat spacetime, there's a diagram after "if we plot exactly the same space-time in the special relativistic x and t coordinates we get" on this page – Hypnosifl Jan 15 '15 at 17:55
  • (cont.) You can see on the diagram that test particles that would be understood as being at rest in comoving coordinates, pulled apart by the expansion of space, are in the SR inertial frame just moving apart inertially at different velocities within a single future light cone, so what would happen if two were linked by a rope should be no different than what would happen if two inertial objects were attached by a rope in SR with some initial large velocity difference between them. Given a very flexible springlike rope they might be brought to rest relative to one another with no breakage. – Hypnosifl Jan 15 '15 at 17:59