A rotating vacuum and a quantum version of Newton's bucket experiment

In this work we consider a quantum analogue of Newton's bucket experiment i n a flat spacetime: we take a Unruh-DeWitt detector in interaction with a r eal massless scalar field. We calculate the detector's excitation rate When it is uniformly rotating around some fixed point and the field is prepared in the Minkowski vacuum and also when the detector is inertial and the fie ld is in the Trocheries-Takeno vacuum state. These results are compared and we show that they raise questions analogous to those discussed by Mach in Newton's bucket experiment.