Entanglement between the Future and the Past in the Quantum Vacuum

We note that massless fields within the future and past light cone may be quantized as independent systems. The vacuum is shown to be a nonseparable state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. This leads to a notion of timelike entanglement. We describe an inertial detector which exhibits a thermal response to the vacuum when switched on at $t=0$, due to this property. The feasibility of detecting this effect is discussed, with natural experimental parameters appearing at the scale of 100 GHz.

Figure 1

Space-time divided into quadrants consisting of regions contained by the future and past light cones ($F$ and $P$), and the right and left Rindler wedges ($R$ and $L$).