  Two particularly simple ideal clocks exhibiting intrinsic circular motion
with the speed of light and opposite spin alignment are described. The clocks
are singled out by singularities of an inverse Legendre transformation for
relativistic rotators of which mass and spin are fixed parameters. Such clocks
work always the same way, no matter how they move. When subject to high
accelerations or falling in strong gravitational fields of black holes, the
clocks could be used to test the clock hypothesis.
