Unruh effect without Rindler horizon

Abstract

We investigate the Unruh effect for a massless scalar field in the two-dimensional Minkowski space in the presence of a uniformly accelerated perfect mirror, with the trajectory of the mirror chosen in such a way that the mirror completely masks the Rindler horizon from the space–time region of interest. We find that the characteristic thermodynamical properties of the effect remain unchanged, i.e. the response of a uniformly co-accelerated Unruh detector and the distribution of the Rindler particles retain their thermal form. However, since in this setup there are no unobserved degrees of freedom of the field, the thermal statistics of the Rindler particles are inconsistent with an initial pure vacuum, which leads us to reconsider the problem for the more physical case when the mirror is inertial in the past. In these conditions we find that the distribution of the Rindler particles is non-thermal even in the limit of infinite acceleration times, but effective thermal statistics can be recovered provided that one is restricted to the expectation values of smeared operators associated with finite norm Rindler states. We explain how the thermal statistics in our problem can be understood in analogy with those in the conventional version of the effect.