  The thermal radiance felt by a uniformly accelerated
detector/oscillator/atom--the Unruh effect-- is often mistaken to be some
emitted radiation detectable by an observer/probe/sensor. Here we show by an
explicit calculation of the energy momentum tensor of a quantum scalar field
that, at least in 1+1 dimension, while a polarization cloud is found to exist
around the particle trajectory, there is no emitted radiation from a uniformly
accelerated oscillator in equilibrium conditions. Under nonequilibrium
conditions which can prevail for non-uniformly accelerated trajectories or
before the atom or oscillator reaches equilibrium, there is conceivably
radiation emitted, but that is not what Unruh effect entails.
