Paper detail

Information travels in massless fields in 1+1 dimensions where energy cannot

It has been demonstrated that, in (1+1) spacetime dimensions, massless fields can be used for information transmission even between parties that are time-like rather than light-like separated - and even without the receiver obtaining any energy from the sender. Here, it is shown that this phenomenon is not limited to a particular model of signaling device, but is based on general properties of the quantum field: energy propagates strictly only on the lightcone, whereas perturbations to the field amplitude, which can carry information, permeate also the inside of the future lightcone of the sender. It is also shown that this timelike and energyless signaling in massless fields occurs in Dirichlet cavities, which shows that the phenomenon is not confined to setups with a zero mode. Moreover, it is shown that the phenomenon extends beyond perturbation theory, namely by deriving the phenomenon non-perturbatively for the case where the sender and receiver systems are modelled as harmonic oscillators. To illustrate the propagation of energy in massless fields, the energy density is calculated that results from temporarily coupling an Unruh-DeWitt detector at rest to the vacuum of the field.