The Brass Tacks of the Ehrenfest Paradox
Coordinate Transforms for Rotating Reference Frames Back Story Wikipedia explains the conundrum in the Ehrenfest paradox thusly. Imagine a disk of radius R rotating with constant angular velocity . The reference frame is fixed to the stationary centre of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disk is . So the circumference will undergo Lorentz contraction by a factor of . However, since the radius is perpendicular to the direction of motion, it will not undergo any contraction. So {\displaystyle {\frac {\mathrm {circumference} }{\mathrm {diameter} }}={\frac {2\pi R{\sqrt {1-(\omega R)^{2}/c^{2}}}}{2R}}=\pi {\sqrt {1-(\omega R)^{2}/c^{2}}}.} This is paradoxical, since in accordance with Euclidean geometry , it should be exactly equal to π . (Image credit: By Geek3 - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=24038062 ) Conventional Wisdom I won't bore you with the details, but Wikipedia goe