Ehrenfest paradox
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The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original formulation as presented by Paul Ehrenfest 1909 in the Physikalische Zeitschrift, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (2 R) should appear Lorentz-contracted to a smaller value than at rest, by the usual factor . This leads to the contradiction that R=R0 and RR0.

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The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original formulation as presented by Paul Ehrenfest 1909 in the Physikalische Zeitschrift, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (2 R) should appear Lorentz-contracted to a smaller value than at rest, by the usual factor . This leads to the contradiction that R=R0 and RR0.