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Many believe that nothing can travel faster than speed of light, not even information. Personally, i think theoretically information can. Consider this following imaginary experiment:

Imagine we are living on a planet that is big enough for a, let's say, 10-light-seconds-tall tower to erect. We hang a pendulum near the planet's surface using a long thin wire at the top of the tower. If someone at top of the tower cut the wire then the pendulum will instantly falling to the ground. In this case we can say that the information "someone cuts the wire" travels 10-light-seconds distance in no time.

Since someone on the surface can only see the act of cutting the wire 10 seconds later, can we infer that the information travels faster than light?

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    $\begingroup$ possible duplicate of The speed of gravity? $\endgroup$
    – Kyle Kanos
    Commented Mar 5, 2014 at 14:33
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    $\begingroup$ The information about the cord being cut isn't communicated to the mass instantly. Google 'the scissors paradox' for a very similar conundrum considered early in the days of relativity. There are some good notes on it here $\endgroup$
    – Chris Mueller
    Commented Mar 5, 2014 at 14:33
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    $\begingroup$ The logical fallacy here is begging the question. You've assumed the conclusion in the premises, i.e., you've assumed that information travels instantly ("then the pendulum will instantly falling to the ground") to 'conclude' that information travels instantly. $\endgroup$
    – Alfred Centauri
    Commented Mar 5, 2014 at 14:49
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    $\begingroup$ It could also be considered a duplicate of physics.stackexchange.com/q/2175. The question is framed slightly differently, but the answers to that question explain very well why the pendulum will not instantly drop to the ground. $\endgroup$
    – N. Virgo
    Commented Mar 5, 2014 at 15:01

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The idea that the pendulum would drop instantly isn't even true of short, Earth-bound pendula: c.f. various Internet videos about dropping slinkies (toy springs).

The reason why slinkies drop in this way is essentially the same reason why an idealised pendulum (strong enough to hold itself together, albeit maybe not as stretchy as a slinky) would not immediately drop: there is still a speed at which the tension in the pendulum is communicated, relating to the speed of sound in the material. Until each part of the pendulum/slinky "finds out" that the part above it isn't holding it up any more, it stays essentially at rest.

This speed of sound is limited by intra-molecular information transfer, which is itself limited by the speed of light; ergo the bottom of the pendulum in your thought experiment will not fall any sooner than ten seconds before the top is released.

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  • $\begingroup$ Awesome video linked there $\endgroup$
    – Kyle Kanos
    Commented Mar 5, 2014 at 15:42

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