Superluminal Rod
Suppose we have a small rod with extremely high tensile strength (e.g. it never breaks). Now, in our lab, we set it up so that its angular velocity is steadily increased by a motor at the center.
What will happen to the rod (in the lab frame) after a long time?
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1 solution
The end of the rod cannot move faster than the speed of light, according to the Special Theory of Relativity.
Every observer must agree that an event either happens or does not happen in all frames of reference (they may not agree on when or where ), therefore the rod cannot contract, because it would never hit an object put exactly at rod's resting distance from the center in the lab frame of reference, but it would certainly do it so in the rod's frame.
Therefore, by elimination, it must warp into a spiral.
You can also think of it in therms of the trajectory made by each and every point of the rod as if it were a separate point particle. The Lorentz Transformation would yield the same result.
I just came up with this explanation. If something is wrong, please correct me. :)