  We present a solution to the time discontinuity paradox in rotating reference
frames by postulating that time is periodic. A kinematic restriction is
enforced that requires the discontinuity to be an integral number of the
periodicity of time. Quantized radii emerge for which the associated tangential
velocities are less than the speed of light. Using the de Broglie relationship,
we show that quantum theory may determine the periodicity of time. A rotating
Kerr black hole and a rigidly rotating disk of dust are also considered.
