Resolution of The Paradox
Grøn states that the resolution of the paradox stems from the impossibility of synchronizing clocks in a rotating reference frame.
The modern resolution can be briefly summarized as follows:
- Small distances measured by disk-riding observers are described by the Langevin-Landau-Lifschitz metric, which is indeed well approximated (for small angular velocity) by the geometry of the hyperbolic plane, just as Kaluza had claimed.
- For physically reasonable materials, during the spin-up phase a real disk expands radially due to centrifugal forces; relativistic corrections partially counteract (but do not cancel) this Newtonian effect. After a steady-state rotation is achieved and the disk has been allowed to relax, the geometry "in the small" is approximately given by the Langevin-Landau-Lifschitz metric.
Read more about this topic: Ehrenfest Paradox
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