  We show that the Sokolov--Ternov effect -- the depolarization of particles in
storage rings coming from synchrotron radiation due to spin flip transitions --
is physically equivalent to the Unruh effect for circular acceleration if one
uses a spin 1/2 particle as the Unruh--DeWitt detector. It is shown that for
the electron, with gyromagnetic number $g \approx 2$, the exponential
contribution to the polarization, which usually characterizes the Unruh effect,
is "hidden" in the standard Sokolov-Ternov effect making it hard to observe.
Thus, our conclusions are different in detail from previous work.
