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Well... kind of hard to translate in English so bare with me :).

Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$.

That means that for any $ω$, there is an $r$ sufficiently big that $c = ω r_c$. That would mean that for an $r > r_c$, the speed of the point would be higher than $c$.

But we also know that c is limit. So... where is the mistake?

I'm presuming that it has something to do with the "limit" between classic mechanic approach and relativistic approach.

AccidentalFourierTransform
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zozo
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1 Answers1

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The link given by LLlAMnYP for the Ehrenfest paradox gives the classical physics rational :

Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of material

So one cannot construct such a rigid body, even before one can reach velocities close to c. I want also to stress, contrary to a comment, that quantum mechanics is important, because all the macroscopic properties of materials, as is the velocity of sound, emerge from the underlying quantum mechanical organization of atoms and molecules.

The forces holding solids together are electromagnetic quantum mechanical exchanges, and any impulse for the turning wheel cannot travel faster than the velocity of light. The velocity of sound is dependent on the quantum mechanical exchanges on the lattice of the solid.

anna v
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