Consider a worldline $\bf{W}$ that accelerates at constant rate $\alpha$ only between $-t_0$ and $t_0$, and is otherwise inertial before $-t_0$ and after $t_0$. For all finite $t_0$ there is no Rindler horizon, hence no Unruh radiation should be expected for all finite $t_0$.
Is there something wrong with the above argument? If it is correct, it seems to me that Unruh radiation is topologically inaccessible from all finitely-accelerated worldlines, so inherently unphysical
Can $\bf{W}$ detect Unruh photons for finite values of $t_0$?