Unruh effect without trans-horizon entanglement

We estimate the transition rates of a uniformly accelerated Unruh-DeWitt detector coupled to a quantum field with reflecting conditions on a boundary plane (a “mirror”). We find that these are essentially indistinguishable from the usual Unruh rates, viz. that the Unruh effect persists in the presence of the mirror. This shows that the Unruh effect (thermality of detector rates) is not merely a consequence of the entanglement between left and right Rindler quanta in the Minkowski vacuum. Since in this setup the state of the field in the Rindler wedge is pure, we argue furthermore that the relevant entropy in the Unruh effect cannot be the von Neumann entanglement entropy. We suggest, an alternative, that it is the Shannon entropy associated with Heisenberg uncertainty.

Figure 1

Wightman functions in the $(z,t)$ plane, for a massless scalar field in empty space. (a) with a mirror at $z=0$; (b) the dashed hyperbolae represent uniformly accelerated trajectories $x(\tau )$ with $a=1$, the dots indicate the switching time ${\tau }_0$, and the solid line $\{z=t\}$ is the boundary of the causal past of $x(\tau )$ as $\tau \to \infty$.

Figure 2

Wightman functions in the $(z,t)$ plane for a massless scalar field in empty space. (a) with a mirror at $z=0$, which is now moving towards the detector when $\tau ={\tau }_0$; (b) the black dots (bottom) indicate the switching time ${\tau }_0$, and the red dots (up) represent the end of the transient regime $2{\tau }_1$.