Scott, there isn’t any known way of “instantaneous transmission” of anything in any medium. All “solid” object are made of atoms that are bonded to one another with varying amounts of force. Steel may not look very springy if you use an engine block or train coupling but trust me, it’s very elastic. The only way a material could be completely non-elastic would be if every bond had an infinite amount of force available to it. Not gonna happen unless God hisself whips some infinte force on some molecules and that’s not too likley.
And if it did the thread would be moved to GF anyway
As rigid as you please? Might as well ask if the speed of sound can be faster than the speed of light. Umm, no sorry. You may not have an object as rigid as you please. Sound may not travel faster than light.
What we perceive as rigidity is actually just coincidence of reference frame. The more resistance there is to changing part of said object’s reference frame, the more rigid we say the object is.
Now, take an object that is rigid. It must be bound by some means (that means force). Newton’s third says that for every action there is an equal and opposite reaction (or force). That means that the binding force must be able to counteract any force applied to the material in order to maintain structural integrity.
Okay, so we have a rigid, rigid body, and we push it. Whatever force we have holding the thing together has to push back in order to maintain it’s shape. So if we push on one end, no big deal, one set of molecules push another set of molecules etc. What we’re dealing with is propagation of sound by means of elastic collisions in the molecules of a medium. Can the speed of sound be faster than the speed of light? No sirree! There’s your problem right there.
My answer is some time between B and C. The medium you’re dealing with is not what the rod is passing through, but the rod itself. The speed of light outside the rod is not relevent.
The speed of sound is also not relevent. Sound is a mechanical compression wave in the media of transmission. If you make the rod infinately rigid, the compression wave would not move as compression (since the rod could not be compressed), but as a pure energy pulse.
That said. I think B is the answer because you are essentially transmitting an energy pulse through the rod, acting on the rod. Since no energy can travel faster than light, it can’t make the rod move any faster than that. You’d not see the rod “compress” or “bend” because it would be conforming to the local plane of space-time for any observer. If you assume the rod to have no inerta, and to be infinately rigid, then it would take one year for the energy pulse to travel the distance. Both observers would notice nothing odd, as no signal they send or receive can move faster that light. They would see the pole move at their end at the appropriate time, and as far as they would be able to see, the entire pole would be moving. The guy on the far end would just be waiting a while.
If I were him, I’d order a pizza, but that applies most times for me…
