Quantum observables in accelerated frames: observing particles beyond the Rindler horizon

We compute the Wigner characteristic function for particle states prepared by an inertial observer and detected by an accelerated observer. This provides an explicit Wigner formulation of Minkowski particle states for the non-inertial observer and a way to derive mean values of quantum observables in the accelerated frame.

This method is adopted for the case of a single-particle state. We derive the difference between the Rindler particle distribution due to the presence of an inertial single-particle and the Minkowski vacuum background induced by the Unruh effect. The surprising result is that the variation of the particle distribution is not vanishing, even when the single-particle is localized beyond the Rindler horizon. The accelerated observer is, hence, able to detect the presence of an inertial particle emitted beyond the horizon.

Furthermore, we consider a two-particle state and derive a correlation function between Rindler particles with different momenta through the Wigner characteristic function in the accelerated frame. We show that an observer is able to detect acceleration by measuring such correlation.