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Assume for this thought experiment that there exists a material which has negligible rest mass density and arbitrarily high stiffness.

We build a tower out of this material, on the equator. The tip of this tower will spin faster as the tower is made taller.

When this tower reaches a hight of about $4\times10^{12}m$, the tip will be moving at the speed of light (circumference of 1 light-day). The mass density is negligible, so the angular velocity of the earth-tower is hardly changed during construction.

Without considering relativity, if we build the tower a bit higher, the tip will exceed $c$.

So, considering relativity, what's stopping us using this hypothetical material to build such a tower?

spraff
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1 Answers1

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No matter how small the mass of the tower is, it is non zero. It would take an infinite energy to propell the tip of the tower to the speed of light. This would take all the energy of the Earth rotation and stop the rotation before the tip of the tower could approach the speed of light.

safesphere
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