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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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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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