Volume 20: Pages 281-295, 2007

Rotating Frames and Locality; Lorentz Contraction and Ehrenfest's Paradox

D. T. Cornwell ¹

¹Honnekinberg 13, B‐1950 Kraainem, Belgium

This paper examines the origins of (Lorentz) spatial contraction, concluding that the principle according to which one always measures segments of a body as contracted in the direction of motion, while true for steady translation and assumed in generating Ehrenfest's paradox, is false for a steadily rotating body. Using both physical arguments and explicit calculation, we show that an inertial observer comoving with a segment of the rim of a rotating disk measures the segment's tangential length as dilated by a factor γ(ν), where ν is the rim speed measured in the unique frame in which the disk is not being translated. The hypothesis of locality (HoL) is thereby seen to be false. A simple theoretical argument for its invalidity is also given for the case of a general noninertial frame.

Keywords: Lorentz contraction, rotating frames, locality, Ehrenfest's paradox

Received: September 8, 2006; Published Online: March 26, 2009