  In a flat spacetime with one spatial dimension compactified, inertial
reference frames are not all equivalent, but there are the preferred ones. This
paper investigates the nonequivalence of inertial frames and also that of
uniformly accelerated frames in connection with the response of the
Unruh-DeWitt detector coupled to a massless scalar field. The detector's
transition rates of both excitation and de-excitation are studied in depth for
three different cases: (i) the detector moving at an arbitrary constant
velocity, (ii) moving with a constant acceleration in the compact direction,
and (iii) moving with a constant acceleration in noncompact directions. The
instantaneous transition rate in relation to the switching function is also
taken into account.
