lewblue83
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I find this an interesting question.
the conditions set down are good, completely solid, non elastic, so we're ignoring bending and flexing.
in theory the answer is yes, you communicate faster than the speed of light.
in practice, it seems as though it should be impossible,
I'm guessing that the real problem is that it's impossible because if you push on one end or the rod all the molecules in the rod also have to move, you've not pushing the rod, you're pushing the atoms at the end of the rod, which in turn are pushing other atoms, so you actually send a wave of compression up the rod rather than moving it as a solid object.
in practise, with the materials that we have today this is impossible.
but in theory, the completely solid, non elastic rod that doesn't bend or flex.
it seems like it should be possible...
I guess the question here is, can a force be transmitted faster than the speed of light? we're asking if electromagnetic radiation can travel faster that a molecule can transmit a compressive force...
the principal being that you're sending a really simple 1 bit of information with a push, and that 1 bit gets there very quickly because the rod is solid, faster than the few minutes it would take radiation to get there.
but the wave of compression still has to travel up the rod, we don't know how long that takes, (because we don't have this infinitely stiff material).
we're not talking about the rod moving faster than light though, it's just got to be able to move backwards and forwards at a rate of a couple of shoves a second and it beats radio communication to the moon.
I guess the answer is, in principal, if you add some conditions that are impossible to meet, yes. you can communicate faster with a solid medium than using radio transmissions,
in practice, it's probably going to be impossible.
it still doesnt "beat" anything. its already there! its in both spots at once so it is not traveling. it needs to travel a few inches back and forth, while radio transmissions need to travel a full 238,000 miles.
so in theory, YES there was no delay in getting the astronaut the message. and you got it done FASTER than a radio transmission. BUT you did not travel the same "distance" the radio waves had to. so no you did not move faster than the speed of light.