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Information & the Speed of Light

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Hi there! So, my question is a bit of a lengthy one: First off, suppose that you have two astronauts, one hovering above the earth and the other hovering above Mars. On average, earth and Mars are about 12 light minutes away from each other, meaning that it would take 12 minutes for one astronaut to communicate with the other via radio, and 24 minutes to hear a reply. This because, of course, nothing can travel faster than the speed of light. But my question is, if you were to take for example, a long, LONG metal rod, completely rigid, and stretch it that distance of 12 light minutes in between the two astronauts, and they were to push and pull that rod between them, would you not then have a system where you can communicate faster than light speed? If the astronaut above the earth pushes and pulls on the rod, he/she could communicate with the other one using morse code or binary.
But would it work? Would the astronaut on the other end feel those pushes and pulls immediately, thus sending and receiving information instantaneously, or would it take 12 minutes for the impulse to reach the other side of the rod, despite the rod being totally rigid?

I hope this makes sense- it’s just a hypothetical obviously, but I cant figure out if this would work or not. It seems to me that it would, but at the same time information is supposed to obey the light-speed barrier. So I’m hoping you can get back to me, I’d love to hear what someone much more knowlegable in physics says about this! 😀

Thanks,
Aiden Cook

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