Summary

Portrait of Paul Ehrenfest Paul Ehrenfest Translation:On v. Ignatowsky's Treatment of Born's Definition of Rigidity (1910)

The electrons actually satisfy the rigidity requirement, yet they don't rotate. The theory of electrons nowhere unconditionally requires the assumption of rotating electrons. 2. The macroscopic "rigid" bodies are molecular aggregates, thus they are elastically deformable, so they don't satisfy the rigidity requirement and are able to rotate.
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Portrait of Paul Ehrenfest Paul Ehrenfest Translation:On v. Ignatowsky's Treatment of Born's Definition of Rigidity (1910)

Indeed: that Born's rigidity definition allows stationary rotation, is proven for a long time. It's known that the difficulty exclusively lies in the question after the passage from rest to uniform rotation [10] . I have formulated this difficulty in the following way:
"Let a relative-rigid cylinder of radius and height be given. A rotation about its axis which is finally constant, will gradually be given to it.
Source: Wikisource

Portrait of Paul Ehrenfest Paul Ehrenfest Translation:On v. Ignatowsky's Treatment of Born's Definition of Rigidity (1910)

There he accepts, that any rigid body must be imagined as having – with respect to the rigidity definition – a preferred point once and for all. [7] Yet also in this way, by far not all difficulties of the rotation problem can be totally resolved: As demonstrated by Born, a stationary (!) rotation about a fixed axis takes place here, so that the resting observer sees the multi-axial layers rotating with larger angular velocity as the peripheral layers, thus the "rigid" body (starting from the axis) increasingly stirs itself.
Source: Wikisource

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