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Imagine a thought experiment: You have a rod 10 ft or 10 light nanoseconds long. On each side you have perfectly synchronized super high-speed cameras looking at the surface of the rod.

You rotate the rod from the left. On the left side the camera records that the rod started to rotate at T-left= 0. On the right side (other side), when would the other camera see the start of rotation? What would T-right be at the start of rotation as recorded by the right hand camera?

If we were to communicate the information of the start of rotation via a beam of light, it would take 10 ns to get to the other camera. So, T-right would equal 10 ns. Would communicating the same information via a physical rod beat a beam of light? Wouldn't that violate the idea that C is the absolute speed limit on everything, including information (outside of quantum entanglement)? Are there relativistic time dilation effects at play here? Would the rotation propagate through the rod in a wave form?

This is just a thought experiment, so let's assume that the rod is made from an absolutely rigid material and there are no spring effects or other purely mechanical effects.

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Would communicating the same information via a physical rod beat a beam of light? Wouldn't that violate the idea that C is the absolute speed limit on everything, including information (outside of quantum entanglement)?

Communicating the information mechanically through the rod would definitely not beat a beam of light. As you say, if it were to propagate faster than c then it would violate causality.

Would the rotation propagate through the rod in a wave form?

Yes. It is a shear wave. Typically shear waves in a solid propagate at a speed far slower than the speed of longitudinal waves in the same material. And the speed of longitudinal waves is orders of magnitude slower than c.

This is just a thought experiment, so let's assume that the rod is made from an absolutely rigid material and there are no spring effects or other purely mechanical effects.

You cannot talk about mechanical waves without those details. They are essential to the question.

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    $\begingroup$ I missed that point, that does make sense. If the rod is made out of atoms, and each atom needs to communicate to the atom next to it that it's moving, that communication is done via elector magnetic force, which propagates at the speed of light, but not necessarily in a straight line inside the rod. So, it's impossible to make a rod that wouldn't twist, and the twist wave would propagate at a slower speed than light through vacuum. Is that basically correct? I am just trying to stuff this in my head in a way it maps :) This is fun to think of, but tough. $\endgroup$
    – Bogdan
    Feb 21 '20 at 22:05
  • $\begingroup$ Yes. I explained it almost exactly that way on a different site. Even the speed of sound in “unobtanium” would be limited for that reason. $\endgroup$
    – Dale
    Feb 21 '20 at 22:25

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