Information Transfer and the speed of light

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Hi, I have a question about the transfer of information at speeds faster than c. I have devised a thought experiment in order to express the logical problem I am having.

Suppose you have a string of beads in a tube from here to alpha centauri where each bead in the tube touches the next sequential bead in the tube and so on. Now suppose you place a bead into the Earth side of the tube forcing the bead on the end of the alpha centauri side out of the tube. Would one have effectively transferred information faster than light?
 
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The push from one side of a bead to the other travels at the speed of sound through the bead.
It's the same as the old push a lightyear long rod proposal.
 
What your thought experiment proves is that, in relativity, there cannot be "perfectly rigid" objects. As each bead presses against the other, it compresses slightly. That is the "push" mqb phys is talking about.
 
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