Ehrenfest Paradox - Resolution of The Paradox

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:

1. 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.
2. 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.