Abstract
The solution to the wave equation as a Cauchy problem with prescribed fields at an initial timet=0is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at timet>0in terms of operators att=0automatically yields purely retarded source-fields. However, we show that two-time quantum correlations between the retarded source-fields of a stationary dipole and the quantum vacuum-field possess advanced wave-like contributions. Despite their advanced nature, these correlations are perfectly consistent with Einstein causality. It is shown that while they do not significantly contribute to photo-detection amplitudes in the vacuum state, they do effect the statistics of measurements involving the radiative force experienced by a point charge in the field of the dipole. Specifically, the dispersion in the charge's momentum is found to increase with time. This entails the possibility of obtaining direct experimental evidence for the existence of advanced waves in physical reality, and provides yet another signature of the quantum nature of the vacuum.
Highlights
Electrodynamics describes the production, propagation and absorption of electromagnetic waves
The problem most commonly encountered in classical electrodynamics is that in which the source is specified at some initial time, and the electromagnetic fields are sought at later times
We show that the presence of the Accepted in Quantum 2017-12-15, click title to verify quantum vacuum and the distinct nature of quantum correlations imply that certain physical predictions involve advanced waves
Summary
Electrodynamics describes the production, propagation and absorption of electromagnetic waves. On the other hand the subject of advanced waves in the presence of sources has received more limited attention in quantum theory The reason for this may be that the problem of finding the Heisenberg picture source-fields at time t > 0 in terms of Schrodinger picture operators at time t = 0 is an initial value problem whose solution entails purely retarded source-fields. We show that the combination of purely retarded source-fields and quantum vacuum fields result in advanced-wave contributions to two-time quantum correlations. By considering a charge with relatively slow dynamics, we are able to develop a quantum description of the free charge, which is analogous to the multipolar description of bound charge systems This description enables us to properly identify the relevant vacuum and source-fields.
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