I have heard that it is impossible to send a signal faster than light. However, what if I had a long (4.5 light years) pole and placed one end on Earth and the another end around Proxima Centauri. If I pushed on one end of the pole, then it seems obvious that the other end of the pole would move too, without any delay. But then I could send information faster than light, which apparently is not possible. Why wouldn't this work?
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5Possible duplicates: http://physics.stackexchange.com/q/2175/2451 and links therein. – Qmechanic Oct 07 '15 at 06:56
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Yes it would violate causality. Also pushing the pole does not work in that way. – Horus Oct 07 '15 at 06:58
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No pole is entirely incompressible. You push some particles at one end of the rod, they move, then push the next particles along, all at the speed of light or less, so causality is never violated.
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Please see the Usenet Physics FAQ which gives a lot of background about this and similar questions. In particular, let me quote part of the question "Is Faster-Than-Light Travel or Communication Possible?" which addresses your question.
4. Rigid Bodies
If you have a long rigid stick and you hit one end, wouldn't the other end have to move immediately? Would this not provide a means of FTL communication?
Well, it would if there were such things as perfectly rigid bodies. In practice the effect of hitting one end of the stick propagates along it at the speed of sound in the material; this speed depends on the stick's elasticity and density. Relativity places an absolute limit on material rigidity in such a way that the speed of sound in the material will not be greater than c.
The same principle applies if you hold a long string or rod vertically in a gravitational field and let go of the top end. The point at which you let go will start to move immediately, but the lower end cannot move until the effect has propagated down the length at the speed of sound in the material.
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